The height of a group of 100 adults has an average height of

The height of a group of 100 adults has an average height of 66 inches, a median of 68 inches and a standard deviation of 3 inches. The height of a second group of 100 adults has an average height of 70 inches, a median of 68 inches and a standard deviation of 3 inches.

Is either group symmetric?   Explain.

If the two groups are combined find the average and median of the combined group.

If the two groups are combined will the standard deviation of the combined group be less than 3, more than 3, or 3?   Explain

Solution

The height of a group of 100 adults has an average height of 66 inches, a median of 68 inches and a standard deviation of 3 inches. The height of a second group of 100 adults has an average height of 70 inches, a median of 68 inches and a standard deviation of 3 inches.

Is either group symmetric?   Explain.

Group1 mean 66 < median 68, slightly left skewed

Group2 mean 70 > median 68, slightly right skewed

If the two groups are combined find the average and median of the combined group.

combined average   = (100*66+100*70)/200 =68

combined median   = 68

If the two groups are combined will the standard deviation of the combined group be less than 3, more than 3, or 3?   Explain

combined standard deviation of the combined group be more than 3.

One group mean is 66 and other group mean is 70, deviation from the combined mean is larger than the individual group deviations.