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. outliers affect which measures of center or dispersion the most? a the iqr will increase. b the median will increase. c the range will decrease. d the mean will decrease.

Explanation:

Step1: Understand the effect of an outlier

The value 150 is an outlier as it is much larger than other values likely in the data - set. The range is calculated as the difference between the maximum and minimum values. Removing the largest value (the outlier 150) will reduce the difference between the maximum and minimum values.

Step2: Understand the effect on the mean

The mean is the sum of all values divided by the number of values. The outlier 150 is a large value, and when it is removed, the sum of the values will decrease while the number of values also decreases by 1. Since the outlier is large, the mean will decrease.

Step3: Analyze the effect on median and IQR

The median is the middle - value (for an odd - numbered data set) or the average of the two middle - values (for an even - numbered data set). The IQR is the difference between the third quartile and the first quartile. These measures are less affected by outliers.

Answer:

C. The range will decrease., D. The mean will decrease.