Exercise 17 Page 488

We want to make a box-and-whisker plot for the given data. 180,175,205,160,210,175,190,205,190,160,165,195 To do this, we need to identify the minimum, the first quartile, the median, the third quartile, and the maximum of the given data set. Let's do these things one at a time. Quartiles are values that divide a data set into four equal parts.

• The median, which is also called the second quartile, separates the data into upper and lower halves.
• The first quartile is the median of the lower half of the data.
• The third quartile is the median of the upper half of the data.

  These three quartiles together with the least and greatest values are often called the five-number summary of the data set. Let's identify the five-number summary of the given data set. First, we will order the data from least to greatest.

  

  The minimum and maximum values are 160 and 210, respectively. Because the number of values is even, the median is the average of the two middle values. Median: 180+ 190/2= 185 The median splits our data set into two even parts. The first quartile is the average value of the two middle values of the lower half and the third quartile is the average of the two middle values of the upper half. Let's find them! &First Quartile: 165+ 175/2= 170 &Third Quartile: 195+ 205/2= 200 Let's list all of the information we have found for our plot. Minimum:& 160 First Quartile:& 170 Median:& 185 Third Quartile:& 200 Maximum:& 210 Now we are ready to make the box-and-whisker plot. 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!