Question

A researcher selects a sample of 6 males and 11 females. She asks participants to rate the likelihood they would do female-stereotyped jobs (such as nursing or school teaching) on a scale from 1 = not likely at all to 5 = very likely. Men indicated that they would be less likely to do these jobs (M = 2.1) compared with women (M = 4.3). What is the weighted mean for this entire sample of 17 participants?

Answer 1

Answer:

3.5234 is the average likelihood the sample would do female-stereotyped jobs on a scale from 1 = not likely at all to 5 = very likely.

Explanation:

The weighted mean is a statistical measure, which is used to assign different weights to a set of data (some data is more important than others). This is obtained by the product of the data by the weights assigned and then the sum of the results, the result of this is divided by the sum of the weights.

First we have to define out weights, because there are more females in our sample then we should assigned a bigger weight to females than mens, this is obtained by finding the % that females represents in the sample:

$\frac{11}{17} = 0.647$    Females represent 64.7% of the sample

$\frac{6}{17} = 0.353$  Males represent 35.3% of the sample

Now that we have our weight we just have to use the formula for the weighted mean (WM)

WM = $\frac{2.1 * 0.353 + 4.3 * 0.647}{0.353 + 0.647} = 0.647$

WM = $\frac{0.7413 + 2.7821}{1} = 3.5234$

which means that the weighted mean for the entire sample of 17 participants if 3.5234