Question

question #13 ian surveyed his friends about the number of televisions in their homes. their responses are shown in the list. he will make a box - and - whisker plot of his data. to do so, he must first calculate the minimum, maximum, median, lower quartile, and upper quartile. 4, 3, 2, 4, 3, 7, 2, 1, 4, 4, 6, 2 select all of the following that are one of the 5 values needed to create the box - and - whisker plot. a 1 b 2 c 2.5 d 3.5 e 4

Explanation:

Step1: Recall box - and - whisker plot components

A box - and - whisker plot is based on the five - number summary: minimum, first quartile (lower quartile), median, third quartile (upper quartile), and maximum.

Step2: Analyze the data set

The data set is \(4,3,2,4,3,7,2,1,4,4,6,2\). First, we need to order the data set: \(1,2,2,2,3,3,4,4,4,4,6,7\).
The minimum value is \(1\).
To find the median (second quartile), since \(n = 12\) (an even - numbered data set), the median is the average of the \(\frac{n}{2}\)th and \((\frac{n}{2}+1)\)th ordered values. \(\frac{12}{2}=6\) and \(\frac{12}{2}+1 = 7\), so the median is \(\frac{3 + 4}{2}=3.5\).
The lower half of the data is \(1,2,2,2,3,3\). The median of the lower half (first quartile) is \(\frac{2+2}{2}=2\).
The upper half of the data is \(4,4,4,4,6,7\). The median of the upper half (third quartile) is \(\frac{4 + 4}{2}=4\).
The maximum value is \(7\).

Answer:

A. 1, B. 2, C. 3.5, D. 4, E. 7