Question

The leader of two postpartum women’s support groups is interested in the depression levels of the women in her groups. She administers the Center for Epidemiologic Studies Depression Scale (CES-D) screening test to the members of her groups. The CES-D is a 20-question self-test that measures depressive feelings and behaviors during the previous week.
The mean depression level from the screening test for the 6 women in the first group is μ1= 16; the mean depression level for the 10 women in the second group is μ2=12.

Without calculating the weighted mean for the combined group, you know that the weighted mean is:

a. Midway between 16 and 12
b. Closer to 16 than to 12
c. Closer to 12 than to 16

Answer 1

Answer:

The answer is "Option a".

Step-by-step explanation:

$\text{Weighted mean} = \frac{(6\times 16+10 \times 12)}{16}$

                         $= \frac{( 96 +120)}{16}\\\\ = \frac{(216)}{16}\\\\ = 13.5$

$\text{Weighted mean} = \frac{( 6\times 18+10\times 14)}{16}$

                        $= \frac{( 6\times 18 +10\times 14)}{16}\\\\= \frac{( 108+140)}{16}\\\\= \frac{( 248)}{16}\\\\= 15.5$