GB-31-04-001 · Estimated mean of grouped data
The table shows journey times t in minutes.
| Time | Frequency |
|---|---|
| 0 < t ≤ 10 | 9 |
| 10 < t ≤ 20 | 25 |
| 20 < t ≤ 40 | 7 |
(a) Calculate an estimate of the mean journey time. Give your answer to 2 decimal places.
(b) Explain why this is only an estimate.
Part (a)
Averages: Estimating the Mean from a Grouped Table
Booklet p. 67
Method
1) Use the actual value x for ungrouped data; use a midpoint only for a class interval
2) Multiply each value by its frequency
3) Divide the total fx (or fm) by the total frequency
Worked Example (GB-31-04-001 · Part (a))
Calculate an estimate of the mean journey time. Give your answer to 2 decimal places.
1)
| Time interval | f | Midpoint m | fm |
|---|---|---|---|
| 0 < t ≤ 10 | 9 | 5 | 45 |
| 10 < t ≤ 20 | 25 | 15 | 375 |
| 20 < t ≤ 40 | 7 | 30 | 210 |
| Total | 41 | 630 |
2)
Ans =
15.37 minutes
Part (b)
Averages: Estimating the Mean from a Grouped Table
Booklet p. 67
Method
Explain the effect of using class midpoints
Worked Example (GB-31-04-001 · Part (b))
Explain why this is only an estimate.
1)
We used each class midpoint to represent every journey in that class. The exact individual times are unknown, so the calculated mean is an estimate.
Ans =
The exact journey times within each interval are unknown.