Handling Data 3
4 marks · HardThe number of hours spent on homework by a group of nine students in a week are as follows:
| Student | A | B | C | D | E | F | G | H | I |
|---|---|---|---|---|---|---|---|---|---|
| Hours | 10 | 13 | 9 | 15 | 11 | 20 | 22 | 13 | 12 |
Calculate the median, lower quartile (Q1), upper quartile (Q3), and inter-quartile range (IQR) for these hours.
Write the values in order before calculation.
Find the median value.
Find the lower quartile (Q1).
Find the upper quartile (Q3).
Calculate the inter-quartile range.
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
(b) 13 hours
(c) 10.5 hours
(d) 17.5 hours
(e) 7 hours
Show mark scheme and worked solution
Marking points
M1 (a) · 0 marks · Writes the data in ascending order correctly.
M2 (b) · 1 mark · Identifies the correct median (middle) value after sorting (13).
M3 (c) · 1 mark · Calculates Q1 as the median of the lower half (10.5). Allow for correct method if final number is wrong but working is correct. (follow-through)
M4 (d) · 1 mark · Calculates Q3 as the median of the upper half (17.5). Allow for correct method if final number is wrong but working is correct. (follow-through)
M5 (e) · 1 mark · IQR = Q3 – Q1, answer 7 (with follow-through from b, c, d if necessary). (follow-through)
Worked solution
Order the data: 9, 10, 11, 12, 13, 13, 15, 20, 22.
The median (Q2) is the middle value: 13 (5th value).
The lower quartile (Q1) is the median of the lower 4 values (9, 10, 11, 12): Q1 = (10 + 11)/2 = 10.5.
The upper quartile (Q3) is the median of the upper 4 values (13, 15, 20, 22): Q3 = (15 + 20)/2 = 17.5.
The IQR = Q3 - Q1 = 17.5 - 10.5 = 7.