Question

Draw a box-and-whisker plot of the data. \(85,61,55,78,79,86,30,76,76,87,68,82\)

Short answer

The box-and-whisker plot will have a box ranging from 61 to 85 with a line to mark the median at 77. The whiskers extend from the box to the maximum and minimum data values, which are 87 and 30 respectively.

Step-by-step solution

Order the Data

The first step is to put the given data in ascending order. The data when arranged in ascending order will be \(30, 55, 61, 68, 76, 76, 78, 79, 82, 85, 86, 87\)

Find the Quartiles

Next, find the quartiles of the data. The lower quartile (Q1) is the median of the lower half of the data. The upper quartile (Q3) is the median of the upper half of the data. The median is the middle value. With 12 data points, it falls between 6th and 7th numbers, so calculate the arithmetic mean of these twos.\nSo, we get Q1 as 61, median as 77 and Q3 as 85.

Calculate the Minimum and Maximum

The minimum and maximum numbers are the smallest (30) and largest (87) numbers in the dataset respectively.

Draw the Box-and-Whisker Plot

The final step is to draw the box-and-whisker plot. The 'whiskers' are the lines that extend from the box indicating variability outside the upper and lower quartiles, hence they are set at the minimum and maximum data values. The 'box' is drawn from Q1 to Q3 with a line drawn in the middle to mark the median. So, the box stretches from 61 to 85 with a line at 77, and the whiskers go from 30 to 87.