Question

The following is a dataset of salaries for a company in thousands). Find the mean and median and determine if the meanor median is the better measure of central tendency.

Answer 1

Option a is correct; the mean is 80, the median is 92, and the median is the better measure of central tendency for this dataset.

To find the mean and median of the given dataset (11, 87, 85, 95, 92, 93, 97), let's first arrange the numbers in ascending order:

11, 85, 87, 92, 93, 95, 97

Mean Calculation:

`\[ \text{Mean} = (11 + 85 + 87 + 92 + 93 + 95 + 97)/(7) = (560)/(7) = 80 \]`

Median Calculation:

Since there are 7 numbers, the median is the fourth number, which is 92.

Now, comparing the calculated mean and median with the provided options:

a. Mean = 80, Median = 92

This matches the calculated values.

Conclusion:

The correct answer is option a. The mean is 80, and the median is 92. In this case, the median (92) is the better measure of central tendency as it is less influenced by extreme values. The dataset has a relatively symmetrical distribution, and the median is less affected by the presence of outliers, making it a more robust measure in this context.

Answer 2

Mean = 80, Median = 92

Mean is the better measure of central tendency

Step-by-step explanation:

Given the following dataset

11, 87, 85, 95, 92, 93, 97

Find the mean

Mean = sum of data/sample size

Mean = 11+87+85+95+92+93+97/7

Mean = 560/7

Mean = 80

Median is the value of middle after re-arranging either in ascending or descending order

Rearrange

11, 85, 87), 92, (93, 95, 97

Since the value at the middle is 92, hence the median is 92

out of the measure of central tendency, mean is better than median

Mean = 80, Median = 92

Mean is the better measure of central tendency