3.1 Measures of Central tendency: Mode, Median, a

(c) If the highest number were decreased to a value smaller than B, what would be the effect on the median and mean?

Both the mean and median would decrease.

(b) If the highest number were decreased to a value still larger than B, what would be the effect on the median and mean?

The mean would decrease while the median would remain the same.

In this problem, we explore the effect on the mean, median, and mode of multiplying each data value by the same number. Consider the following data set. (c) Compare the results of parts (a) and (b). In general, how do you think the mode, median, and mean are affected when each data value in a set is multiplied by the same constant?

Multiplying each data value by the same constant c results in the mode, median, and mean increasing by a factor of c.

Consider a data set of 15 distinct measurements with mean A and median B. (a) If the highest number were increased, what would be the effect on the median and mean? Explain.

The mean would increase while the median would remain the same.

(c) Which average takes all the specific values into account?

mean

(a) Which average represents the middle value of a data distribution?

median

(b) If the numbers represented codes for the colors of T-shirts ordered from a catalog, which average(s) would make sense? (Select all that apply.)

mode

(b) Name of credit card (e.g., MasterCard, Visa, American Express, etc.).

mode

(b) Which average represents the most frequent value of a data distribution?

mode

(d) Suppose the numbers represent survey responses from 1 to 5, with 1 = disagree strongly, 2 = disagree, 3 = agree, 4 = agree strongly, and 5 = agree very strongly. Which average(s) make sense? (Select all that apply.)

mode, median

(c) Dollar amount due on next payment.

mode, median, mean

(c) If the numbers represented one-way mileages for trails to different lakes, which average(s) would make sense? (Select all that apply.)

mode, median, mean

Consider the following types of data that were obtained from a random sample of 49 credit card accounts. Identify all the averages (mean, median, or mode) that can be used to summarize the data. (Select all that apply.) (a) Outstanding balance on each account.

mode, median, mean

Consider the following numbers. 2 3 4 5 5 (a) Compute the mode, median, and mean.

mode: 5 Median: 4 mean: 3.8