Question

please remember to submit your workbook. the following table shows the number of electoral votes for the president. which measure of central tendency best represents the data? median mean, median, and mode mean

Explanation:

Step1: Arrange data in order

18, 20, 20, 23, 23, 24, 25, 26, 29, 32, 34, 38

Step2: Calculate mean

Mean = $\frac{18 + 20+20 + 23+23 + 24+25 + 26+29 + 32+34 + 38}{12}=\frac{312}{12} = 26$

Step3: Calculate median

Since there are 12 data points (even number), median is the average of the 6th and 7th values. Median = $\frac{24 + 25}{2}=24.5$

Step4: Analyze mode

The mode is the value that appears most frequently. Here, 20 and 23 both appear twice.

Step5: Evaluate outliers

There are no extreme outliers that would skew the mean. But the data has two - mode (bimodal) which makes mode less representative. The mean is 26 and median is 24.5. Since the data is relatively symmetric (no extreme skewness) and there is no strong reason to prefer median over mean (as in case of extreme outliers), and mode is bimodal, the mean is a good measure. However, if we consider that the data has two values (20 and 23) repeating, but overall spread is not too large and mean is a commonly used measure for such data (no extreme skewness), mean is a reasonable choice. But if we check the difference between mean and median (26 - 24.5=1.5), it's not very large. But if we consider that the formula for mean uses all data points and in the absence of strong skewness, mean is a good measure of central tendency.

Answer:

mean