Higher June 2019 Paper 1 Q11
11 A bus company recorded the ages, in years, of the people on coach A and the people on coach B.
Here are the ages of the 23 people on coach A.
| 41 | 42 | 44 | 48 | 52 | 53 | 53 | 53 | 56 | 57 | 57 | 59 |
| 60 | 61 | 63 | 64 | 64 | 66 | 67 | 69 | 74 | 77 | 79 |
| Median | |
|---|---|
| Lower quartile | |
| Upper quartile | |
| Least age | 41 |
| Greatest age | 79 |
Here is some information about the ages of the people on coach B.
| Median | 70 |
|---|---|
| Lower quartile | 54 |
| Upper quartile | 73 |
| Least age | 42 |
| Greatest age | 85 |
Richard says that the people on coach A are younger than the people on coach B.
You must give a reason for your answer. (1)
Richard says that the people on coach A vary more in age than the people on coach B.
You must give a reason for your answer. (1)
| Answer | Mark | Mark scheme |
|---|---|---|
| 59, 53, 66 | B2 | for Median = 59, LQ = 53, UQ = 66, may be seen in working |
| (B1 | for one correct) |
| Answer | Mark | Mark scheme |
|---|---|---|
| Yes, with reason | C1 | for Yes and comment comparing median ages, ft from (a) |
Additional guidance
Acceptable examples
“59” < 70
All statistics/values are lower for coach A (so they are younger)
Median is lower
The middle age is lower on coach A
Not acceptable examples
Median is higher
Median for coach A is “59” and coach B is 70
The oldest on coach A is 79 and the oldest on coach B is 85
There are people on coach B that are older than on coach A
| Answer | Mark | Mark scheme |
|---|---|---|
| No, with reason | C1 | for No and comment comparing spreads of ages from ranges or IQRs, ft from (a) |
Additional guidance
Acceptable examples
38 < 43 or “13” < 19
Greater difference between greatest and least age for coach B
Range for coach B is larger than coach A
The range of ages is wider on coach B than on coach A
The range is 5 greater on coach B
There is a smaller difference between the lower and upper quantiles on coach A than on coach B
The IQR is shorter for coach A
Not acceptable examples
Quartiles are less for coach A
53 < 54 or 79 < 85 (oe)
Range for coach A is 38 and range for coach B is 43
Coach A ranges from 41-79 but coach B ranges from 42-85
Working
A: Range = 38, IQR = “13”
B: Range = 43, IQR = 19