Let’s solve each part step by step. We need to find:
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Lower Quartile (Q1) – the median of the lower half of the data
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Upper Quartile (Q3) – the median of the upper half of the data
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Interquartile Range (IQR) – Q3 minus Q1
We’ll do this for each set, making sure the data is sorted first (it already is in most cases — we’ll check).
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a) 3, 4, 4, 4, 6, 7, 7, 8, 10, 11
There are 10 numbers → even number → split into two halves of 5 each.
Lower half: 3, 4, 4, 4, 6 → median = middle value =
4 → Q1 = 4
Upper half: 7, 7, 8, 10, 11 → median = middle value =
8 → Q3 = 8
IQR = 8 - 4 =
4
✔ Check: Data is sorted. Halves are correct. Medians taken from 5-number sets → middle is 3rd number. Correct.
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b) 25, 25, 27, 28, 31, 31, 32, 35
8 numbers → even → split into two halves of 4 each.
Lower half: 25, 25, 27, 28 → median = average of 2nd and 3rd = (25 + 27)/2 =
26 → Q1 = 26
Upper half: 31, 31, 32, 35 → median = average of 2nd and 3rd = (31 + 32)/2 =
31.5 → Q3 = 31.5
IQR = 31.5 - 26 =
5.5
✔ Check: Sorted? Yes. Split correctly. For even-sized halves, average the two middle numbers. Correct.
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c) 2.3, 2.4, 2.7, 2.8, 2.9, 3.0, 3.0
7 numbers → odd → median is the 4th number: 2.8 → but we don’t need overall median for quartiles here.
For Q1: take lower half *excluding* the median → first 3 numbers: 2.3, 2.4, 2.7 → median =
2.4 → Q1 = 2.4
For Q3: take upper half *excluding* the median → last 3 numbers: 2.9, 3.0, 3.0 → median =
3.0 → Q3 = 3.0
IQR = 3.0 - 2.4 =
0.6
✔ Check: Odd count → exclude median when splitting. Lower half = positions 1–3, upper = 5–7. Correct.
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d) 2, 6, 8, 6, 5, 4, 2, 2, 3
First, sort it: 2, 2, 2, 3, 4, 5, 6, 6, 8 → 9 numbers → odd.
Median is 5th number: 4 → exclude it for quartiles.
Lower half: first 4 numbers: 2, 2, 2, 3 → median = average of 2nd and 3rd = (2 + 2)/2 =
2 → Q1 = 2
Upper half: last 4 numbers: 5, 6, 6, 8 → median = average of 2nd and 3rd = (6 + 6)/2 =
6 → Q3 = 6
IQR = 6 - 2 =
4
✔ Check: Sorted correctly. Excluded median. Took averages for even-sized halves. Correct.
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Final Answer:
a) Q1 = 4, Q3 = 8, IQR = 4
b) Q1 = 26, Q3 = 31.5, IQR = 5.5
c) Q1 = 2.4, Q3 = 3.0, IQR = 0.6
d) Q1 = 2, Q3 = 6, IQR = 4
Parent Tip: Review the logic above to help your child master the concept of iqr worksheet.
