Exercise 5 Page 608

We want to identify the least value, first quartile, median, third quartile, and greatest value 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 least and greatest 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!

The least and greatest values are 15 and 70, respectively. Since the number of values in each half is even, the first and third quartile will be the averages of the two middle values in each half. First Quartile:&& 20+ 252= 22.5 Third Quartile:&& 55+ 602= 57.5 Moreover, since the number of values in the whole data set is even, the median is the average of the two middle values. Median: 30+ 402= 35

Box-and-Whisker Plot

We want to make a box-and-whisker plot using the obtained information. Least Value:& 15 First Quartile:& 22.5 Median:& 35 Third Quartile:& 57.5 Greatest Value:& 70 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 least value 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 greatest value.

Let's make our box-and-whisker plot! Ages of Family Members

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Box-and-Whisker Plot