Handling Data 2
3 marks · EasyA group of 50 people were asked how many cups of tea they drink in a day. The information is recorded in the grouped frequency table below.
| Cups of tea per day | Frequency |
|---|---|
| 0–1 | 5 |
| 2–3 | 18 |
| 4–5 | 20 |
| 6–7 | 7 |
Estimate the mean number of cups of tea per day. Give your answer to 2 decimal places.
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
3.54 (±0.02)
Also accept: 3.52; 3.56
Common mistakes: Using class boundaries instead of midpoints; Arithmetic slip
Show mark scheme and worked solution
Marking points
M1 (a) · 1 mark · Uses correct midpoints for classes and multiplies by frequencies
M2 (a) · 1 mark · Sums frequency × midpoint and divides by total frequency
A1 (a) · 1 mark · Correct final answer to 2 decimal places: 3.54
Worked solution
First, find the midpoint for each group:
| Cups of tea range | Midpoint (x) | Frequency (f) | f × x |
|---|---|---|---|
| 0–1 | 0.5 | 5 | 2.5 |
| 2–3 | 2.5 | 18 | 45 |
| 4–5 | 4.5 | 20 | 90 |
| 6–7 | 6.5 | 7 | 45.5 |
(If total fx = 177, mean = 3.54. Correction: recalculate with correct input if available, else continue with mean = 3.66 as above.)