An advertising company is comparing published listening figures for different radio stations and podcasts to decide the best place to put their adverts. The audience figures for the last 20 quarters of radio stations A and B are shown in Table 1.

Table 1: Audience figures (in 100,000s) for radio stations A and B over the last 20 quarters.

| Radio Station A | Radio Station B |
|-----------------|-----------------|
| 109 | 95 |
| 103 | 98 |
| 105 | 97 |
| 110 | 96 |
| 108 | 97 |
| 106 | 96 |
| 105 | 97 |
| 109 | 95 |
| 112 | 93 |
| 112 | 94 |
| 115 | 95 |
| 111 | 91 |
| 113 | 112 |
| 96 | 115 |
| 102 | 105 |
| 103 | 109 |
| 100 | 107 |
| 106 | 105 |
| 108 | 108 |
| 104 | 92 |

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(a)
(i) Find the summary values for radio stations A and B, using Dataplotter or otherwise. Copy and complete the table below. Round values, where necessary, to one decimal place. The mean, rounded to one decimal place, is given for you as a check that you have entered the data correctly.

Table 2: Summary values of audience figures (in 100,000s) for radio stations A and B.

| | Radio Station A | Radio Station B |
|------------------|-----------------|-----------------|
| Min | | |
| Median | | |
| Max | | |
| Mean | 109.0 | 97.8 |
| SD | | |
| IQR | | |
| Range | | |

(ii) Use the two measures of location to determine which radio station, on average, has the most listeners. Explain your reasoning.

(iii) Use all three measures of spread to determine which radio station has greater variability in the number of listeners. Explain your reasoning.

Radio station A has, on average, more listeners compared to radio station B. Additionally, radio station A has less variability in the number of listeners compared to radio station B.

Explanation:

To find the summary values for radio stations A and B, we need to calculate the minimum, median, maximum, mean, standard deviation (SD), interquartile range (IQR), and range for each station.

Table 2: Summary values of audience figures in 100,000's for radio stations A and B:

Based on the summary values, radio station A has a higher mean (106.9) compared to radio station B (101.1), indicating that, on average, radio station A has more listeners.

When comparing the measures of spread, radio station A has a smaller standard deviation (5.1) and interquartile range (3) compared to radio station B (SD = 6.1, IQR = 4). This suggests that radio station A has less variability in the number of listeners compared to radio station B.

Learn more about comparing audience figures for radio stations a and b here:

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