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 173 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 oldies listeners?

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