Question

1. generalize does deleting a data point always change the median of a data set? explain. no, deleting a data point does not always change the median of a data set because if the deleted data point is not the median and its removal does not shift the middle value if the remaining ordereddata then the median remains the same. assessment practice 13. the table shows the number of home runs hit by eight baseball players last season. a ninth player hits only 6 home runs last season. select the statements that best describe the data. home runs hit 42 31 35 34 43 42 53 57 there is now an outlier in the data set. the mean increases when the ninth player is added. the mode increases when the ninth player is added. the median is the same when the ninth player is added. the distribution becomes more skewed when the ninth player is added.

Explanation:

1. Outlier: The values for the first eight players range from 31 - 57. The ninth - player has only 6 home runs, which is far from the other values, so it is an outlier.
2. Mean: The mean of the first eight values is $\frac{42 + 31+35 + 34+43+42+53+57}{8}=\frac{337}{8}=42.125$. When we add the ninth value (6), the new mean is $\frac{337 + 6}{9}=\frac{343}{9}\approx38.11$, so the mean decreases.
3. Mode: The mode of the first eight values is 42. Adding the value 6 does not change the mode (still 42).
4. Median: First, order the first eight values: 31, 34, 35, 42, 42, 43, 53, 57. The median of 8 values is the average of the 4th and 5th values, $\frac{42 + 42}{2}=42$. When we add the value 6 and re - order: 6, 31, 34, 35, 42, 42, 43, 53, 57. The median of 9 values is the 5th value, which is 42. So the median is the same.
5. Skewness: The distribution of the first eight values is relatively symmetric. Adding the outlier 6 makes the distribution more left - skewed.

Answer:

There is now an outlier in the data set.
The median is the same when the ninth player is added.
The distribution becomes more skewed when the ninth player is added.