Handling Data 3
3 marks · NormalThe table shows the number of seeds in each of 8 apples:
| Apple | Seeds |
|---|---|
| A | 4 |
| B | 6 |
| C | 6 |
| D | 7 |
| E | 7 |
| F | 8 |
| G | 12 |
| H | 16 |
Calculate the range and the inter-quartile range of the number of seeds per apple.
Work this out on paper, then compare with the answer and worked solution below. With a free account you can submit written answers for marking.
Show answer
Must show: Range: 16 - 4 = 12, Interquartile range: 9.5 - 6 = 3.5
Also accept: If quartiles use n+1 method: accept valid alternative method shown
Common mistakes: Using wrong position formula for quartiles
Show mark scheme and worked solution
Marking points
M1 · 1 mark · Data arranged in order and method for quartiles/range shown or implied.
A1 · 1 mark · Correct answer for range.
A2 · 1 mark · Correct lower and upper quartile or interquartile range value.
Worked solution
Seeds in order: 4, 6, 6, 7, 7, 8, 12, 16
Range = 16 - 4 = 12
Lower quartile (Q1) at position 1/4 × (8+1) = 2.25th value → between 2nd and 3rd: Q1 = 6
Upper quartile (Q3) at 3/4 × (8+1) = 6.75th value, between 6th (8) and 7th (12): Q3 = 8 + 0.75×(12-8) = 11
Interquartile range = 11 - 6 = 5
Or, using nearest integer position, Q1 = 6 (2nd value); Q3 = 12 (7th value); IQR = 12 - 6 = 6