The radio music listener market is diverse. Listener formats might include adult contemporary, album rock, top 40, oldies, rap, country and western, classical, and jazz. In targeting audiences, market researchers need to be concerned about the ages of the listeners attracted to particular formats. Suppose a market researcher surveyed a sample of 170 listeners of country music radio stations and obtained the following age distribution.

Age .......Frequency

15–under 20 ....... 9

20–under 25 .....16

25–under 30 .....27

30–under 35 ....44

35–under 40 ......42

40–under 45 ......23

45–under 50 ....... 7

50–under 55 ...... 2

a. What are the mean and modal ages of country music listeners?

b. What are the variance and standard deviation of the ages of country music listeners?