Question

4 is added to the data set 22, 25, 31, 33, 24. Answer true or false for the following statements.

The range and mean will increase
The mean and median will decrease
The mean will decrease but the median will stay the same
An outlier is more likely to change the median than the mean

Answer 1

Adding 4 to a data set affects the range and mean, but not the median. The statement regarding outliers is false.

Step-by-step explanation:

In this case, the data set is 22, 25, 31, 33, 24, and 4 is added to the data set. Let's analyze each statement:

1. The range is the difference between the maximum and minimum values in a data set. Since we're adding a smaller number (4) to all the values, the maximum and minimum values will increase, leading to an increase in the range. So, the statement is false because the range will increase.
2. The mean is the sum of all the values divided by the count of values. Adding 4 to each value will increase the sum, and since the count stays the same, the mean will increase. However, the median is the middle value when the data set is arranged in ascending order. Adding 4 to each value will not change the arrangement of the values or the middle value, so the statement is false because the median will stay the same.
3. An outlier is a value that is significantly different from the rest of the data set. When we add 4 to each value, no data point becomes an outlier because it retains its relative position in the data set. So, the statement is false.

Based on the above analysis, the correct statement is: The mean will increase but the median will stay the same.

Answer 2

The range and mean will increase - False

(because only range will increase, mean will decrease)

The mean and median will decrease - True

The mean will decrease but the median will stay the same - False

(Both of mean and median will decrease)

An outlier is more likely to change the median than the mean - False

(An outlier is more likely to change the mean than the median)