Answer to Question #102433 in Statistics and Probability for Hasana Rochelle

Question

The measures of central tendency are given for 3 data sets.In each case,identify a likely distribution for the data. Explain.

a. mean = 34.5 mode = 34.5 median = 34.5
b. mean = 31.5 mode = 38.5 median = 34.5
c. mean = 34.5 mode = 30.5 median = 32.5

Answer 1

When a data distribution is bell-shaped symmetrical, the values for the mean, median, and mode are the same or almost the same.

For left-skewed distributions, the mean is less than the median and the median is less than the mode. For right-skewed distributions, the mode is the smallest value, the median is the next largest, and the mean is the largest.

a. mean = 34.5 = mode = median

All three measures are identical in a normal distribution.

b. mean = 31.5 < 34.5=median < 38.5=mode

The mean is less than the median and the median is less than the mode in a left-skewed distribution.

c. mode=30.5 < 32.5=median < 34.5=mean.

The mode is the smallest value, the median is the next largest, and the mean is the largest in a right-skewed distribution.