Exercise 2 Page 749

We want to identify the minimum, first quartile, median, third quartile, and maximum of the given data set. Then we will make a box-and-whisker plot using these values. Let's do these things one at a time.

Values

Quartiles are values that divide a data set into four equal parts. When quartiles are combined with the minimum and maximum values, it is often called the five-number summary of the data set.

• The median, which can also be known as the second quartile (Q_2), separates the data into upper and lower halves.
• The first quartile (Q_1) is the median of the lower half of the data.
• The third quartile (Q_3) is the median of the upper half of the data.

Let's identify the five-number summary of the given data set. Do not forget to arrange the data from least to greatest first! Given Data Set 29 24 28 32 30 31 26 33 Arranged Data Set 24 26 28 29_(lower half) 30 31 32 33_(upper half) The minimum and maximum values are 24 and 33, respectively. Since the number of values in each half is even, the first quartile is the average of the two middle values in the lower half. Q_1: 26+ 282= 27 Analogously, the third quartile is the average of the two middle values in the upper half. Q_3: 31+322=31.5 Since the number of values is even, the median is the average of the two middle values. Median: 29+ 302= 29.5 The first quartile is 27 and the third quartile is 31.5. The median of the data is 29.5.

Box-and-Whisker Plot

We want to make a box-and-whisker plot using the obtained information. Minimum:& 24 First Quartile:& 27 Median:& 29.5 Third Quartile:& 31.5 Maximum:& 33 This type of graph summarizes a set of data by displaying it along a number line. It consists of three parts, a box and two whiskers.

• The left whisker extends from the minimum to the first quartile.
• The box extends from the first to the third quartile and has a vertical line through the median.
• The right whisker extends from the third quartile to the maximum.

Let's make our box-and-whisker plot! Daily Attendance