Exam-Style Problem
⬅ Back to SubchapterJune 2022 p51 q3
2416
The times taken to travel to college by 2500 students are summarised in the table.
| Time taken \( t \) (minutes) | \( 0 \le t < 20 \) | \( 20 \le t < 30 \) | \( 30 \le t < 40 \) | \( 40 \le t < 60 \) | \( 60 \le t < 90 \) |
|---|---|---|---|---|---|
| Frequency | 440 | 720 | 920 | 300 | 120 |
(a) Draw a histogram to represent this information.
From the data, the estimate of the mean value of \( t \) is \( 31.44 \).
(b) Calculate an estimate of the standard deviation of the times taken to travel to college.
(c) In which class interval does the upper quartile lie?
It was later discovered that the times taken to travel to college by two students were incorrectly recorded. One student’s time was recorded as \( 15 \) instead of \( 5 \) and the other’s time was recorded as \( 65 \) instead of \( 75 \).
(d) Without doing any further calculations, state with a reason whether the estimate of the standard deviation in part (b) would be increased, decreased or stay the same.
