Handling Data 1
5 marks · HardA television station surveyed 120 viewers about their favourite type of programme: Sports, News, Drama, or Comedy. Their results are summarised as follows:
| Programme type | Frequency |
|---|---|
| Sports | 37 |
| News | 19 |
| Drama | 46 |
| Comedy | 18 |
Calculate the mean number of viewers per programme type.
The head of the station claims the survey shows most viewers like Drama. Is this justified? Support your answer with calculations.
If the station wants to advertise to the largest possible audience, which average should they use and why?
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
(a) Mean = 120/4 = 30 · must show Sum of 37, 19, 46, 18 = 120; 120 ÷ 4 = 30
(b) Drama has the highest frequency (46/120 = 38.3%), but this is not more than half, so most viewers do not prefer Drama. Claim is not justified. · must show Percent for Drama ≈ 38% < 50%; so 'most' is incorrect
(c) They should use the mode (Drama, 46), because it represents the most popular single category, not the mean or median, which do not reflect popularity in categories. · must show States mode, Justifies as reflecting most popular category
Also accept: For part (a): Accept rounding to 1 decimal place
Common mistakes: Dividing by 120, not by 4 for mean; Not connecting mode to most popular item
Show mark scheme and worked solution
Marking points
M1 (a) · 1 mark · Adds frequencies and divides by number of categories (4)
B1 (b) · 1 mark · Calculates Drama percentage: 46/120 = 38.3% (follow-through)
E1 (b) · 1 mark · Rejects 'most' claim; explains it's not more than half (follow-through)
B2 (c) · 1 mark · Correctly identifies mode as best average for category popularity
E2 (c) · 1 mark · Explains the choice based on what mode represents in this context
Worked solution
a. Mean per programme type: (37 + 19 + 46 + 18) ÷ 4 = 120 ÷ 4 = 30 viewers.
b. Drama: 46/120 ≈ 0.383 = 38.3%. 'Most' requires more than 50%. Claim is not justified.
c. The mode (Drama, 46 viewers) shows the most popular single category; mean/median would not pinpoint popularity.