Question 2 - 17 marks An advertising company is comparing published listening figures for different radio stations and podcasts in order to decide where is the best place to put their adverts. The audience figures for the last 20 quarters of radio stations A and B are in Table 1. Table 1 Audience figures in 100 000s of radio stations A and B for the last 20 quarters. Radio Station A Radio Station B 112 98 106 101 108 100 113 99 111 100 109 99 108 100 112 98 115 96 115 97 118 98 114 87 116 88 115 92 113 98 103 99 107 96 105 102 103 104 106 100(iii) 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 gures in 100 000s for radio stations A and B. Radio Station A Radio Station B 110.5 97.6 Use the two measures of location to say which radio station, on average, has most listeners. Explain your reasoning. Use all three measures of spread to say which radio station has the greater variability in the amount of listeners. Explain your reasoning. Create boxplots for these two data sets (either drawn by hand or as a printout from Dataplotter or another suitable computer package). Include all the relevant information required for drawing boxplots as set out in Subsection 1.2 of Unit 11. The summary values can be displayed an the hamlets themselues or in a table to the side of the chart, as they appear in Dataplotter. Use the boxplot for radio station B to say whether the data are symmetric or skewed. If the data are skewed, then state whether they are skewed to the left or skewed to the right. What does this tell you about the spread of the data for radio station B? The advertising company tries to summarise what the boxplot for radio station A is saying. Are the following statements true or false? In each case justify your answer. (1) About one-quarter of the reporting periods for radio station A had less than 10 650 000 listeners. (2) About three-quarters of the reporting periods for radio station A had more than 11 150 000 listeners. [2] [2] [2] [2] (c) The advertising company also looked at the two top podcasts available for download from the two radio stations. The summary values are in the table below. Table 3 Summary values for the audience figures for the top podcast from radio stations A and B (1000s). Station A Station B Min 140 281 Median 222 297 Max 300 331 Mean 220.6 301.1 SD 65.7 13.4 IQ range 134.5 18.5 Range 160 50 (i) State what kind of data these are, discrete or continuous. Justify your answer. [1] (ii) The advertising company creates histograms, shown in Figure 1, for the podcasts data, but forgets to label them. Which histogram represents the data for the podcast from radio station A? Explain your answer. [2] 8- frequency A 2 . 0- 150 200 250 300 350 Listeners (1000s) Start Value |0 Interval 25 Use Custom 10 frequency 5- 0- 150 200 250 300 350 Listeners (1000s) Start Value |0 Interval |25) Figure 1