Exercise 1 Page 340

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 14 16 20 5 22 30 16 28 Arranged Data Set 5 14 16 16_(lower half) | 20 22 28 30_(upper half) The minimum and maximum values are 5 and 30, respectively. Since the number of values is even, the median is the average of the two middle values. Median: 16+ 202= 18 Moreover, 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: 14+162=15 Analogously, the third quartile is the average of the two middle values in the upper half. Q_3: 22+282=25 The first quartile is 15 and the third quartile is 25.

Box-and-Whisker Plot

We want to make a box-and-whisker plot using the obtained information. Minimum:& 5 First Quartile:& 15 Median:& 18 Third Quartile:& 25 Maximum:& 30 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! Scores