Question

the following were calculated from the times (in minutes) that 10 individuals reported spending on the internet each day. mean: 87 median: 72 mode: 72 range: 75 iqr: 30 there was one individual in this group who reported spending 150 minutes per day on the internet. if you removed this individuals time from the data set, which two statements are most likely true?

Explanation:

Step1: Understand the effect of an out - lier

The value 150 is an out - lier. The mean is affected by outliers as it takes into account all values in the data set. The median and mode are less affected by outliers.

Step2: Analyze the mean

When the outlier (150) is removed, the sum of the remaining 9 values will be smaller than the sum of all 10 values. Since the mean is $\text{Mean}=\frac{\text{Sum of values}}{\text{Number of values}}$, with a smaller sum and one less value, the mean will decrease.

Step3: Analyze the range

The range is calculated as $\text{Range}=\text{Max}-\text{Min}$. The out - lier 150 is the maximum value. When it is removed, the new maximum value will be smaller, so the range will decrease.

Step4: Analyze the median and mode

The median is the middle value when the data is ordered. Since the median is 72 and there are 10 values originally, removing one value (the out - lier) may not change the middle value (or the middle two values' average in case of an even - numbered data set before removal) if the out - lier is at the extreme end. The mode is the most frequently occurring value. Removing one value (the out - lier) is unlikely to change the most frequently occurring value.

Answer:

The mean will decrease and the range will decrease.