The weekly take-home pay (in dollars) for 20 graduate teaching assistants at University Z is as follows:

500.75, 217.43,488.25, 405.78
485.46, 495.48, 370.75, 435.40
479.65, 482.56, 470.28, 489.90
382.50, 500.75, 465.32, 481.25
506.43, 225.50, 504.38, 179.25

a. find the mean, median, and midrange weekly take-home pay for the assistants.

b. Which of these measures of central tendency is best represents typical weekly take-home pay for the assistants? explain.

Mean = (sum of scores)/number of scores

To find median, arrange scores in order of value. The median is that point which defines the higher 50% from the lower 50%.

Midrange = highest score-lowest score/2

The most central of these three measures (value in between the other two) would be the best measure of central tendency.

MIDRANGE actually = lowest + highest / 2

To answer these questions, we need to calculate the mean, median, and midrange of the weekly take-home pay for the assistants.

a. To find the mean, we add up all the values and divide by the total number of values. In this case, we have 20 values:

Mean = (500.75 + 217.43 + 488.25 + 405.78 + 485.46 + 495.48 + 370.75 + 435.40 + 479.65 + 482.56 + 470.28 + 489.90 + 382.50 + 500.75 + 465.32 + 481.25 + 506.43 + 225.50 + 504.38 + 179.25) / 20

Once you calculate this expression, you will find the mean.

To find the median, we need to arrange the values in increasing order. Then, we locate the middle value. If the number of values is odd, the median is the middle value. If the number of values is even, the median is the average of the two middle values.

Next, to find the midrange, we identify the minimum and the maximum values from the data set and compute the average of those two values.

b. To determine which measure of central tendency best represents the typical weekly take-home pay for the assistants, we need to consider the characteristics of each measure.

The mean is sensitive to outliers, as it considers all values equally. If there are extreme values in the data set (very high or very low), they can significantly influence the mean, potentially making it unrepresentative of the typical value.

The median, on the other hand, is not affected by extreme values, as it only considers the middle value(s). Therefore, it is a more robust measure of central tendency when dealing with skewed or asymmetric data.

The midrange is simply the average of the minimum and maximum values. It does not provide as much information about the distribution of the data.

Considering this, if the data set does not have any extreme values, the mean can be an appropriate measure of central tendency. However, if there are outliers present, the median would be a better representation of the typical weekly take-home pay for the assistants.

Note: To calculate the mean, median, and midrange of the given values, you can plug them into a statistical software or use mathematical formulas.