Question

a highway patrol officer measures the speed of cars on the freeway. the speeds of the first 20 cars are shown on the line - plot below.
freeway driving speeds
the next car that drives past is going 69 miles per hour. how does this car change the statistics that summarize the data?
a the mean increases.
b the range increases.
c the median increases.
d the interquartile range increases.

Explanation:

Step1: Recall mean formula

The mean $\bar{x}=\frac{\sum_{i = 1}^{n}x_{i}}{n}$. Adding a larger - valued data point (69 is larger than most of the existing data points) will increase the sum $\sum_{i = 1}^{n}x_{i}$ while $n$ increases by 1. So the mean will increase.

Step2: Analyze range

The range is the difference between the maximum and minimum values. If the new value 69 is not the new maximum (assuming the previous maximum was already 70), the range will not change.

Step3: Analyze median

For $n = 20$ (even number of data - points), the median is the average of the 10th and 11th ordered data - points. Adding one more data - point may or may not change the position of the 10th and 11th ordered data - points in a way that increases the median.

Step4: Analyze inter - quartile range

The inter - quartile range (IQR) is $Q_{3}-Q_{1}$. Adding one data - point may not change the values of $Q_{1}$ and $Q_{3}$ in a way that increases the IQR.

Answer:

A. The mean increases