Question

the distribution of golf scores for a class are represented by the dot - plot below.
a golf score of 84 was later added to the data set.
which of the following is not true about the data set when the new score is included?
a. the mean score increases.
b. the median score stays the same.
c. the standard deviation of the scores increases.
d. the interquartile range of the scores decreases.

Explanation:

Step1: Analyze the original data

The original dot - plot shows scores concentrated around 76 - 80.

Step2: Consider the new score of 84

The new score 84 is greater than most of the existing scores.

Step3: Analyze the mean

Since 84 is greater than the original mean, adding it will increase the sum of all scores and thus increase the mean. So, option A is true.

Step4: Analyze the median

If the original number of data points is odd, adding one more data point (84) may or may not change the median depending on the original data. But if the original number of data points is even, the median is the average of the two middle - ordered values. Since 84 is relatively large, it may not affect the middle - ordered values used to calculate the median. So, the median can stay the same. Option B can be true.

Step5: Analyze the standard deviation

The standard deviation measures the spread of the data. Adding a value (84) that is further from the mean than most of the original data points will increase the spread and thus increase the standard deviation. Option C is true.

Step6: Analyze the inter - quartile range

The inter - quartile range (IQR) is the difference between the third quartile ($Q_3$) and the first quartile ($Q_1$). Adding a large value (84) will not decrease the IQR. In fact, it may increase or have no effect on the IQR. So, option D is not true.

Answer:

D. The interquartile range of the scores decreases.