Compute three measures of central tendency and two measures of variability for the following data set: When asked their age, 10 college students responded: 21, 19, 20, 18, 18, 19, 33, 22, 19, and 18. Given this distribution, which measures of central tendency and variability are most appropriate? Explain your decision, drawing a graph or creating a frequency distribution as necessary.

What will be an ideal response?

Mode--most frequent value in a distribution; mode is 18 and 19; median--the position average or the point that divides a distribution; median is 19; mean--the arithmetic, or weighted average, computed by adding up the value of all the cases and dividing by the total number of cases; mean is 20.7; range--the true upper limit in a distribution minus the true lower limit; the range is 15; interquartile range--the range in a distribution between the end of the first quartile and the beginning of the third quartile; the first quartile is 18 and the third quartile is 21, therefore the interquartile range is 3; variance--a statistic that measures the variability of a distribution as the average squared deviation of each case from the mean; variance is 4.145; standard deviation--the square root of the average squared deviation of each case from the mean; standard deviation is 2.035.