Question

2. Consider the following distribution of teen birth rates (per 1,000 females age 15-19) by state according to the CDC (2016). State Teen Birth Rate 15.9 aryland assachusetts ew York a. Calculate the values of the mean and the median. 8.5 13.2 21.8 Mean- orth Carolina 15.8 ennsylvania Median- 4 b. Now imagine that you added in Mississippi which had a teen birth rate of 32.6. Recalculate the values of the mean and median including this state with the ones in the table above. Mean - Median- c. How did adding the new state change the values of the mean and the median? In other words, which is more susceptible to extreme values: the mean or the median?

Answer 1

2)

a)

Mean =

= 75.2 = 15.04

Arranging in ascending order:

8.5, 13.2, 15.8, 15.9, 21.8

Since the number of observations is odd, so Median =

hterm- term - 15.8 n +1 thterm term 3dterm 15.8 2rd

b)

Mean =

Σ x 75.2 + 32.6 17.9667 6

Arranging in ascending order:

8.5, 13.2, 15.8, 15.9, 21.8, 32.6

Since the number of observations is even, so Median =

er m 15.85

c)

Adding the new state increased the value of the mean by a greater margin as compared to increase in the value of the median.

Hence mean is more susceptible to extreme values.