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? press to hear a reminder or hint for this problem.

Explanation:

Step1: Understand the effect on mean

The mean is affected by extreme values. The value 150 is an out - lier. Removing it will decrease the sum of the data values and the number of data points. Since the mean is $\frac{\text{Sum of data values}}{\text{Number of data points}}$, the mean will decrease.

Step2: Understand the effect on median

The median is the middle - value when the data is arranged in ascending or descending order. With $n = 10$ data points, the median is the average of the 5th and 6th ordered values. Removing one value ($n=9$) will change the position of the middle value, but since 150 is an outlier, the median is less likely to be affected significantly. It may or may not change much.

Step3: Understand the effect on mode

The mode is the most frequently occurring value. Since 150 is not the mode (mode is 72), removing it will not change the mode.

Step4: Understand the effect on range

The range is $\text{Maximum value}-\text{Minimum value}$. Currently, the range is 75. Removing the maximum value (150) will decrease the range.

Step5: Understand the effect on IQR

The inter - quartile range (IQR) is the difference between the third quartile ($Q_3$) and the first quartile ($Q_1$). An outlier like 150 is less likely to affect the quartiles as they are based on the middle 50% of the data. So, the IQR is not likely to change much.

The two statements most likely true are: The mean will decrease and the range will decrease.

Answer:

The mean will decrease; The range will decrease.