BMS 1110 · Common Core (Tronc commun)Section 5.1 · Centre, spread and rates

Section 22 of 30

Quartiles, percentiles and position

Find Q1, Q2 and Q3 in a small ordered set, state the percentage of observations below each one, translate a quartile into a percentile, and read a growth-chart percentile or a laboratory reference range as a position rather than a diagnosis.

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Learn gives you one short idea at a time. Each idea starts with a single sentence, then explains it, gives an example, and asks you a small question you can answer straight away.
Explore shows a diagram of the same ideas. Click the numbered parts to read what each one is.
Check asks a few questions. Answer them all correctly to finish the section and unlock the next one.
“Go deeper” is optional. It adds mechanism and extra detail for when you are ready — nothing you need for the checks is hidden there.

Why this matters

A child’s weight on the 10th percentile, a laboratory value with an arrow beside it, a blood pressure described as “high for her age” — these are all statements about position, and they arrive at the bedside every day. Read them as verdicts and you will frighten parents over values that are merely uncommon; ignore them and you will miss the ones that matter. This section gives you the small set of ideas that turns a percentile into something you can explain, check and act on: what ordered data looks like, where the three quartiles fall, what a percentile compares, and why “unusual” is not the same word as “abnormal”.

What you need to know first

You need two skills you have already used with the median: putting a list of numbers into ascending order, and finding the middle value of a list — averaging the two middle values when the list has an even length. Nothing else is assumed. Percentages appear often in this section, and every one of them is worked out in full, step by step.

Words to know (5)

Measure of position: A summary that says where one value sits inside an ordered set — near the bottom, in the middle, in the top quarter — instead of saying how large the value is. “This patient is in the oldest tenth of the ward” is a statement of position; it says nothing about the patient’s actual age.
Quartile: One of the three values that cut ordered data into four approximately equal parts: the first quartile Q1, the second quartile Q2 and the third quartile Q3. In 60, 64, 68, 72, 76, 80, 84, 88, the quartiles are Q1 = 66, Q2 = 74 and Q3 = 82 beats per minute.
Percentile: One of the ninety-nine values that cut ordered data into one hundred approximately equal parts; the pth percentile has about p per cent of the observations below it. The 90th percentile of a set of weights is the weight below which about 90% of the observations fall.
Reference population: The large, defined group of people whose measurements are used to build a growth chart or a laboratory range. A percentile always compares the patient with this group. A growth chart for girls aged 0–5 years is built from thousands of girls measured at many ages, which is why the chart states the age and the sex it applies to.
Reference range: The interval of laboratory values that contains the central 95% of a healthy reference population, so its ends sit near the 2.5th and the 97.5th percentiles. A potassium range of 3.5–5.0 mmol/L flags a result of 5.4 mmol/L as above the range, which is above about the 97.5th percentile of that population.

One idea at a timeIdea 1 / 6

In one sentence A measure of position does not tell you how big a value is; it tells you where that value sits among all the others.

A measure of position answers a different question from an average

Until now, every summary you have met — the mean, the middle value, the most common value — described the data as a whole. A measure of position does something narrower and more personal: it takes one value and asks where it stands. The answer is given as a place in an ordered list: first, middle, near the top, in the lowest quarter, above ninety in a hundred. Nothing about the size of the value enters that answer. A ward that records the ages of everyone on it can say that one patient is in the oldest tenth of that ward without ever saying how old the patient is. That is exactly what a position measure gives you, and it is why positions are the language of growth charts and laboratory reports, where the real question is never “how big is it?” but “compared with whom?”.

For example

A newborn weighing 3.2 kg can be described as being on the 40th percentile for gestational age, which tells the team how this baby compares with babies of the same age without repeating the weight.

Pause and check yourself

A ward of 40 patients includes one whose age is described as being in the oldest tenth of the ward. Does this tell you how old that patient is?

Show the answer

No. It gives a position: the patient is older than about 90% of the patients on that ward. A position measure ranks a value among comparable values; it does not report size. To know the age you still need the age itself.

Read detailed explanations

Locating a quartile in a small ordered set: two conventions and an interpolation: The three quartiles are found by splitting, not by one arithmetic formula, and the splitting convention has to be stated because more than one convention genuinely exists. Proceed in four moves. First, order the observations from smallest to largest and count them; call the count n. Second, find Q2 by the median rule you already know: with an odd n take the middle observation, and with an even n take the mean of the two central observations. Third, split the ordered list at that midpoint. With an odd n the median observation itself belongs to neither half; with an even n the split falls between the two central observations, so the lower half is everything below that gap. Fourth, take the median of the lower half as Q1 and the median of the upper half as Q3. The eight systolic pressures 100, 108, 112, 120, 128, 132, 140 and 148 mmHg give Q2 = 124, Q1 = 110 and Q3 = 136 under this convention. A second convention expresses the same work as a fractional position. Compute (n + 1) × p ÷ 100, where p is 25, 50 or 75. The result is a rank that may fall between two observations, and when it does you interpolate: move partway along the gap in proportion to the decimal part. For the same eight pressures, Q1 has rank (8 + 1) × 25 ÷ 100 = 2.25, one quarter of the way from the second value to the third, which gives 108 + 0.25 × (112 − 108) = 108 + 1 = 109 mmHg. Q3 has rank 6.75, giving 132 + 0.75 × (140 − 132) = 132 + 6 = 138 mmHg, while Q2 keeps rank 4.5 and the value 124 mmHg, exactly as before. Notice that Q1 comes out at 109 mmHg here and at 110 mmHg under the median-of-halves convention. Both answers are defensible; they differ only because a sample of eight cannot support more precision than that. Textbooks and software packages really do disagree, and the disagreement shrinks as n grows. For teaching, audit and handover alike, the safe habit is to report the smallest value, Q1, the median, Q3 and the largest value together, and to name the convention you used: a reader who cannot reconstruct your half-split cannot reproduce your numbers. Two practical consequences follow for your own work: state the method whenever you publish a quartile, and never treat the last decimal of a quartile from a small set as if it were exact. The 25 / 50 / 75 count remains the safeguard, because whichever convention you choose, the number of observations below Q1 should still be roughly a quarter of the group.
Where a percentile comes from: reference populations and percentile rank: A percentile is never computed from one person, because it is a statement about a group. That group is the reference population: a large sample of people measured under defined conditions, chosen to represent the healthy or typical population the patient belongs to. Growth standards are built this way. A national or international standard draws on thousands of children measured at many ages, and the measurements are smoothed by a statistical model — the LMS method is the usual one — that describes, for each age, the median, the spread and the slight asymmetry of the distribution. Without that smoothing, every month of age would produce a ragged curve, and two clinics using different samples would give two different percentiles for the same child. Two terms are easy to confuse. The percentile is a value on the measurement scale: the 10th percentile of weight at 9 months might be 7.6 kg. The percentile rank is the percentage of the reference group at or below a given value, so a girl weighing 7.6 kg has a percentile rank of 10. Clinicians often say “she is on the 10th centile” and mean both at once, but the two quantities are not interchangeable and they carry different units — kilograms against a percentage. Percentiles are also not evenly spaced along the measurement axis. Where a distribution is crowded, near its middle, a difference of a few hundred grams can move a child from the 50th to the 30th percentile; out in the tail, the same few hundred grams may barely move the rank at all. Biological measurements are slightly skewed rather than perfectly symmetric, so the gap between the 10th and the 50th percentile is not the same size as the gap between the 50th and the 90th. This is why a percentile carries information that a raw difference in kilograms does not — and equally why one percentile must never be subtracted from another as though the difference were an ordinary quantity.
Why a flagged result is unusual rather than abnormal: A reference interval is manufactured, and knowing how it is manufactured removes most of its mystery. A laboratory measures a reference sample — blood donors, volunteers, or patients screened to exclude the disease in question — and then takes the central band that contains 95% of those values. The lower end therefore sits near the 2.5th percentile and the upper end near the 97.5th. By construction, one healthy person in twenty falls outside the band, half of them below it and half above. A flag is a statement about that arithmetic, not an observation about the person in front of you. Screening sharpens the point. Any test that separates two groups by a numerical cut-off trades sensitivity against specificity: lower the cut-off and you catch more true cases while flagging more healthy people. Because the cut-off is chosen rather than discovered, a flag can only be interpreted alongside the patient. The positive predictive value of a result — the chance that a flagged patient really has the condition — also depends on how common that condition is among the people tested. The same haemoglobin value, flagged in a general clinic, carries much more weight in a renal unit where anaemia is frequent. Three further sources of variation keep a single number from being a verdict in itself. Biological variation means an individual has their own habitual level, which may sit in the tail of the population band while being entirely normal for them; serial measurements compared with the patient’s own baseline therefore often beat a population range. Pre-analytical factors change the specimen before it is measured — a tourniquet left on too long, a sample haemolysed in transit, a patient who was not fasting. Analytical variation adds a little scatter from the machine and the reagent batch. Laboratories defend against both with delta checks, which compare each new result with the previous stored value for that patient, and with calibration and internal quality control that verify the analyser before any result is released. Nursing judgement sits on top of all of this: check the specimen and the identification, ask what the patient’s previous values were, consider the symptoms in front of you, and treat “outside the range” as a question to be answered rather than a conclusion already reached.

Explore the diagram

Look at the whole drawing first. Then select one numbered part and connect it to the idea you just read.

Quartiles, percentiles and position

Three views of the same idea, position in ordered data. The first orders eight pulse rates and marks the three quartiles, with the 25 / 50 / 75 count written underneath as the check. The second shows quartiles and percentiles as one ladder, so Q1, Q2 and Q3 are read off as the 25th, 50th and 75th percentiles. The third shows a percentile on a growth chart and a laboratory reference range, and states why a value outside the common range is unusual before it is abnormal.

New to diagrams? Read this first

Look at the whole drawing once without clicking anything. Ask yourself only: what kind of picture is this (a comparison, a route, a sequence, a table)?
Press Play, or use the arrows, to move through the numbered parts in order. The drawing stays still; only the highlight moves.
Click a number, or its name in the list below, to read what that part is and why it matters. Use “Hide labels” when you want to test your memory.

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01 / 4Ordered data and the three quartiles

If the drawing is wider than this panel, scroll it sideways. Labels stay readable; the numbered explanations below show the same ideas.

Ordered data and the three quartiles

Eight pulse rates ordered from the smallest to the largest: 60, 64, 68, 72, 76, 80, 84 and 88 beats per minute. Q2, the median, is the mean of the fourth and fifth values, 74. Q1 is the median of the lower half, 66, and Q3 is the median of the upper half, 82. Counting below each one gives exactly 25%, 50% and 75% of the group, which is the check that the three positions are right.

Schematic teaching figure: the axis of the first panel is drawn to a regular scale in beats per minute, and the dots mark whole-number rates only. Quartile lines are placed at their calculated positions; the percentile ladder and the reference bar are evenly divided for teaching and are not drawn to a measuring scale.

Key points to remember

A measure of position says where a value sits in an ordered set, not how large the value is.
Quartiles divide ordered data into four approximately equal parts: Q1, Q2 and Q3, and Q2 is the median.
About 25% of the observations lie below Q1, 50% below Q2 and 75% below Q3; count them to check any quartile you calculate.
Percentiles divide the same data into one hundred parts, and the quartiles are the 25th, 50th and 75th percentiles.
A growth percentile compares a child with a reference population of the same age and sex; it is not a diagnosis, and the trend over time matters more than one point.
A value outside a laboratory reference range is unusual, since about 5% of healthy people fall outside it; whether it is abnormal for the patient needs symptoms, history and previous results.

Go deeper

Worked example

Finding the three quartiles of eight blood pressures. A clinic records the systolic blood pressures of the eight patients seen on a Tuesday morning, in the order they arrived: 120, 100, 148, 112, 128, 108, 140 and 132 mmHg. Before any of these patients is described as typical or unusual, the nurse reduces the list to its three quartiles and checks them.

Put the list in ascending order and count the observations: 100, 108, 112, 120, 128, 132, 140, 148. There are eight values, so n = 8. Units stay in mmHg on every line.
Find Q2. With eight values the middle falls between the fourth and the fifth, 120 and 128, so Q2 = (120 + 128) ÷ 2 = 248 ÷ 2 = 124 mmHg. Q2 is the median and the 50th percentile.
Split the ordered list at that midpoint. The lower half is 100, 108, 112, 120; the upper half is 128, 132, 140, 148. The midpoint is a gap between two values, so no observation is lost.
Q1 is the median of the lower half: (108 + 112) ÷ 2 = 110 mmHg. Q3 is the median of the upper half: (132 + 140) ÷ 2 = 136 mmHg.
Check with the 25 / 50 / 75 rule. Below 110 there are two values, and 2 ÷ 8 = 25%. Below 124 there are four, 4 ÷ 8 = 50%. Below 136 there are six, 6 ÷ 8 = 75%. The three positions are consistent.

Q1 = 110 mmHg, Q2 = 124 mmHg and Q3 = 136 mmHg cut these eight pressures into four approximately equal groups. The quartiles are positions in an ordered list, and the count below each one is what proves the answer is right.

Tutorial 1 — finding Q1, Q2 and Q3 by hand

Eight patients on a ward have their resting pulse rates recorded as 76, 60, 88, 68, 80, 64, 84 and 72 beats per minute. Find Q1, Q2 and Q3 for this group and check them against the 25 / 50 / 75 rule.

Rule used: Rule, stated before it is used: with the observations in ascending order, Q2 is the median; Q1 is the median of the lower half and Q3 is the median of the upper half. When the number of observations is even, the median is the mean of the two middle values and the split falls between them. Q2 has 50% of the observations below it, Q1 has 25% below it and Q3 has 75% below it. The unit of every quartile is the unit of the data, here beats per minute.

Put the eight rates in ascending order and write down how many values there are.
Reveal this step
60, 64, 68, 72, 76, 80, 84, 88 beats per minute. Counting them gives n = 8, an even number, so the middle will fall between two values.
There is no single middle value in a list of eight. How do you find Q2, and what is it?
Reveal the answer
The middle falls between the fourth and the fifth values, 72 and 76. Q2 is the mean of those two: (72 + 76) ÷ 2 = 148 ÷ 2 = 74 beats per minute. Half the group lies below 74.
Split the ordered list into a lower half and an upper half, and name the values in each.
Reveal this step
The lower half holds the four values below the midpoint: 60, 64, 68, 72. The upper half holds the four values above it: 76, 80, 84, 88.
Find the median of the lower half for Q1, then the median of the upper half for Q3.
Reveal this step
Q1 = (64 + 68) ÷ 2 = 132 ÷ 2 = 66 beats per minute. Q3 = (80 + 84) ÷ 2 = 164 ÷ 2 = 82 beats per minute.
Now run the 25 / 50 / 75 check. How many of the eight observations lie below each quartile, and what percentage is that?
Reveal the answer
Below Q1 = 66 lie 60 and 64, so two values: 2 ÷ 8 = 25%. Below Q2 = 74 lie four values, 4 ÷ 8 = 50%. Below Q3 = 82 lie six values, 6 ÷ 8 = 75%. The rule holds exactly, which confirms the three quartiles.
A ninth patient joins the group with a rate of 68 beats per minute. Without recalculating, is 68 above or below Q2, and roughly what share of the group does it exceed?
Reveal the answer
68 is above Q1 = 66 and below Q2 = 74, so it sits in the second quarter of the ordered data. It exceeds only about the lowest quarter of the group, which is why a rate of 68 is best described as near the lower quartile rather than near the middle.

Answer: Q1 = 66, Q2 = 74 and Q3 = 82 beats per minute, with exactly 25%, 50% and 75% of the eight observations below them.

Keep this habit: Order the data first, split it at the median, then take the median of each half — and finish by counting how many observations lie below each quartile. That count is the check that catches an ordering slip or a half-split in the wrong place, and it costs nothing.

Tutorial 2 — reading a child’s weight on the 10th percentile

A health centre weighs a 9-month-old girl. Her weight is 7.6 kg. On the growth chart for girls of her age, the point lies on the curve labelled 10. Her mother asks whether her daughter is too small. Read the chart properly before you answer her.

Rule used: Rule, stated before it is used: a percentile for age is the value below which that percentage of a healthy reference population of the same age and sex falls. At 9 months, the 10th percentile is the weight below which about 10% of the reference girls of that age weigh and above which about 90% weigh. The percentile is a position in the reference group; its unit is a percentage, not a kilogram, while the weight it refers to is in kilograms.

Before reading anything off the chart, name the three things it compares.
Reveal this step
The measurement (here weight in kilograms), the age in months along the horizontal axis, and the sex, because boys and girls have separate reference curves. Reading a girl’s weight off a boys’ curve would give a meaningless position.
Plot the point: 9 months across, 7.6 kg up. Say which curve it lies nearest.
Reveal this step
The point falls on the curve labelled 10, so her weight is on the 10th percentile for age.
In plain words, what does that position mean for this child?
Reveal the answer
It means that about 10% of the girls of her age in the reference population weigh less than 7.6 kg and about 90% weigh more. It is a comparison of position, not a statement about her health.
The mother says: “So she is too small.” Is a weight on the 10th percentile abnormal?
Reveal the answer
No. The 10th percentile lies inside the usual range of a healthy reference population — by definition about one child in ten sits at or below it. Being low on the chart is not the same as being ill, and a percentile is not a diagnosis. The honest answer is that the chart shows where she stands, not that she has a health problem.
Say what else you look at before deciding whether any action is needed.
Reveal this step
Whether her weight has followed a similar curve at earlier visits or has dropped across centile lines; whether her length and head circumference are proportionate to her weight; and her feeding, development and general condition on examination.
Which is more informative: today’s single point, or the series of points from earlier visits?
Reveal the answer
The series. A single measurement can be moved by a growth spurt, a recent illness, a feeding change or simply a different scale. A child who has tracked steadily near the 10th percentile for months is following her own curve, whereas a sustained fall across two or more centile lines is the signal that prompts assessment.

Answer: Her weight of 7.6 kg at 9 months is on the 10th percentile: about 10% of reference girls of her age weigh less and about 90% weigh more. This is a comparison, not a diagnosis, and her trend over time is what the team must watch.

Keep this habit: Name what the chart compares — measurement, age and sex — before reading a percentile, then translate the number into a sentence about the reference group. Never let a percentile become a diagnosis, and always ask how the child has moved along the chart rather than where she stands today.

Tutorial 3 — reading a laboratory reference range

A 68-year-old man has a haemoglobin result of 11.2 g/dL. The laboratory prints the reference range 13.0–17.0 g/dL and marks the result with a downward arrow. A student asks whether this patient has anaemia. Work out exactly what the arrow does and does not tell you.

Rule used: Rule, stated before it is used: a laboratory reference range is an interval built from the central 95% of values measured in a healthy reference population, so its lower end sits near the 2.5th percentile and its upper end near the 97.5th percentile. The unit here is g/dL. A value outside the interval is flagged as unusual for that population; the flag is a position, not a diagnosis, and about 5% of healthy people fall outside such a range by construction.

Say where the boundaries 13.0 and 17.0 g/dL sit in percentile terms, and how much of a healthy reference group they exclude.
Reveal this step
If the range is the central 95%, then 13.0 g/dL is about the 2.5th percentile and 17.0 g/dL about the 97.5th percentile. About 5% of the healthy reference group lies outside the two ends: 2.5% below and 2.5% above.
Place the patient’s 11.2 g/dL on that picture.
Reveal this step
It lies below the lower boundary of 13.0 g/dL, in the lowest 2.5% of the reference group, which is why the laboratory prints the downward arrow beside it.
Does the arrow prove that this patient is ill?
Reveal the answer
No. It says his value is unusual compared with the reference group. It does not name a cause and it is not a diagnosis; by construction, about 5% of healthy people fall outside a central 95% range, so some healthy results are always flagged.
What other information decides whether 11.2 g/dL matters for this man?
Reveal the answer
His history and symptoms, whether he has bled, and above all his own previous results. A man who usually runs at 15.0 g/dL has fallen a long way, while a man whose usual level is 12.0 g/dL has changed little. The red-cell indices, the ferritin and the blood film then help to identify the mechanism.
State the action the flag should trigger, in one sentence.
Reveal this step
Check that the sample is correctly identified and not diluted or haemolysed, relate the value to the patient’s history, symptoms and previous results, and escalate for clinical assessment rather than treating the number on its own.

Answer: 11.2 g/dL lies below the 2.5th percentile of the reference group and is therefore flagged as unusual. Whether it is abnormal for this man is a clinical judgement that needs his history, his symptoms and his previous results.

Keep this habit: A reference range is the central 95% of a healthy group, so 5% of healthy people are outside it. Read every flag as a position first, then ask how far outside it lies, how it compares with the patient’s own usual values, and what the patient’s condition and symptoms say. The number begins the assessment; it does not end it.

Now you try

Attempt each one on paper first. Write the formula, substitute the numbers, then check the unit of your answer.

Eight children in a clinic have their weights recorded, in ascending order, as 12.4, 13.1, 13.8, 14.6, 15.2, 16.0, 16.9 and 17.5 kg. Find Q1, Q2 and Q3 and check them with the 25 / 50 / 75 rule.
Hint
With eight values the median falls between the fourth and the fifth. Do not include the median in either half when you split, then take the median of each half.
Show the worked answer
Q2 = (14.6 + 15.2) ÷ 2 = 29.8 ÷ 2 = 14.9 kg. The lower half is 12.4, 13.1, 13.8, 14.6, so Q1 = (13.1 + 13.8) ÷ 2 = 26.9 ÷ 2 = 13.45 kg. The upper half is 15.2, 16.0, 16.9, 17.5, so Q3 = (16.0 + 16.9) ÷ 2 = 32.9 ÷ 2 = 16.45 kg. Check: below 13.45 kg there are two children, 2 ÷ 8 = 25%; below 14.9 kg there are four, 50%; below 16.45 kg there are six, 75%.
A 2-year-old boy’s length is plotted on the 90th percentile of the growth chart. His mother asks whether he is too tall. What does the 90th percentile mean, and what is the correct answer?
Hint
Translate the percentile into two sentences about the reference group, one for the share below and one for the share above. Then say what a percentile is not.
Show the worked answer
It means that about 90% of boys of his age in the reference population are shorter than he is and about 10% are taller. A length on the 90th percentile is inside the usual range of the reference group, so it is a normal position on the chart, not a diagnosis of excessive growth. The mother can be told that he is tall compared with the reference group; what matters for follow-up is whether his length has followed a similar curve over time and whether his growth is proportionate overall.
An adult woman’s haemoglobin is 11.0 g/dL and the laboratory reports the reference range as 12.0–15.5 g/dL. Where does her value sit in percentile terms, and does that flag diagnose her?
Hint
Assume the range is the central 95% of a healthy reference group, so its two ends are the 2.5th and the 97.5th percentiles.
Show the worked answer
If the range is the central 95% of a healthy reference group, then 12.0 g/dL is about the 2.5th percentile and 15.5 g/dL about the 97.5th percentile. Her 11.0 g/dL lies below the lower end, in the lowest 2.5%, which is why the result is flagged. The flag says her value is unusual compared with the reference group; it does not diagnose anaemia. Whether it is abnormal for her depends on her symptoms, her history and whether her own usual level is higher, so the next step is clinical assessment rather than a verdict from the number.
A student writes: “the 10th percentile means that 10% of the children are abnormal.” Explain what is wrong with that sentence and rewrite it correctly.
Hint
Separate two ideas the sentence has merged: a rank in a group, and a judgement about an individual’s health.
Show the worked answer
The sentence merges a position with a diagnosis. The 10th percentile is a rank inside the reference group: about 10% of comparable children weigh less and about 90% weigh more. It says nothing about whether any of those children is ill, and low on a chart is not the same as diseased — a central 95% reference band leaves about 5% of healthy children outside it by construction. The corrected sentence is: “this child’s weight is below about 90% of the reference children of the same age and sex, so we should look at the trend over time and at the whole clinical picture.”

Common misconception

The most persistent wrong model is that a percentile is a mark out of a hundred — that being on the 10th percentile means scoring 10%. A percentile is a position, not a score: it says what share of a comparison group lies below the value, and no group ever marked the child. The second wrong model, which follows from the first, is that outside the reference range means disease. Because a range is usually built from the central 95% of a healthy population, about 5% of healthy people fall outside it by construction, so a flagged result is unusual before it is abnormal. Keeping the two words apart is the whole skill of this section.

Check your reasoning

A parent says: “The doctor told me my daughter is on the 10th percentile. Does that mean she is malnourished?” Write the answer you would give, using the words position, reference population and trend.

Reveal an answer

I would say that the percentile describes her position: her weight is below about 90% of the girls of her age in the reference population and above about 10% of them. That group is a large set of girls measured in a defined way, so it is a comparison, not a test she passed or failed. The 10th percentile is inside the usual range of that group, so it does not mean malnourished and it does not make a diagnosis. What I would then look at with the parent is the trend: whether her weight has followed a similar curve over the last months or has dropped across centile lines, together with her length, head circumference, feeding and general condition. A steady curve is reassuring; a fall across centiles is what prompts a closer assessment.

Where this comes from

BMS 1110 Applied Mathematics and Medical Biostatistics lecture notes (supplied) · Unit Four, “Quartiles” and “Percentiles”, notes lines 823–841: quartiles divide ordered data into four approximately equal parts; Q1, Q2 (which corresponds to the median) and Q3; approximately 25% of observations lie below Q1, 50% below Q2 and 75% below Q3; percentiles divide data into 100 parts; the 90th percentile as the value below which approximately 90% of observations fall; percentiles used in medicine for child growth, weight, height, blood pressure and laboratory measurements.
Note on the course code · The supplied cover page reads “Course Number: BMS 110”. The curriculum catalogue in this project records “BMS 1110”; the catalogue is treated as authoritative and the notes’ cover value is retained here for provenance.
Beyond the supplied notes: locating quartiles, growth standards and reference intervals · The notes give no rule for finding a quartile in a small set, no account of how a percentile is built from a reference population, and no basis for the reference ranges they mention. The median-of-halves and fractional-rank conventions with interpolation, the role of the reference population and the LMS smoothing model, percentile rank, the central-95% construction of laboratory ranges, sensitivity and specificity, and the distinction between a value being unusual and being abnormal are standard clinical statistics supplied here to complete the curriculum.

Lesson progress is saved on this device for the current learner. Practice answers stay separate and are not stored.

About this course and its sources

Bilingual lessons organised from the supplied BMS 1110 Applied Mathematics and Medical Biostatistics lecture notes (Mr. Ebangan Prosper Achuanoh). Diagrams are original educational schematics; sections that go beyond the supplied notes say so in their sources. Mathematics, clinical and French-language review are pending.