Look at the two histograms below Each involves the same numb

Look at the two histograms below. Each involves the same number of data. The data are all whole numbers, so the height of each bar represents the number of values equal to the corresponding midpoint shown on the horizontal axis. Notice that both distributions are symmetric.

(a) Estimate the mode, median, and mean for each histogram.

(b) Which distribution has the larger standard deviation? Why?

Distribution (i), because more of the data are farther from the mean.Distribution (ii), because more of the data are farther from the mean.    Distribution (i), because more of the data are closer to the mean.Distribution (ii), because more of the data are closer to the mean.

Solution

a) Mode = most frequent entry, which is 7 in both data. Median is middle entry which is again 7 in both because equal number of poitns are before and after 7 in both. Mean is also 7 in both because of visible symmtery.

b) Distribution (i), because more of the data are farther from the mean.