Question

Draw a box-and-whisker plot of the data. \(48,10,48,25,40,42,44,23,21,13,50,17\)

Short answer

The box-and-whisker plot for the given data set will have the minimum value at 10, the lower quartile (Q1) at 17, the median (Q2) at 32.5, the upper quartile (Q3) at 44 and the maximum value at 50.

Step-by-step solution

Organize the Data

The first step is to arrange the data in ascending order which is: \[10, 13, 17, 21, 23, 25, 40, 42, 44, 48, 48, 50\]

Calculate Quartiles

Then, calculate Q1, Q2, and Q3 using the formula for location of a percentile, \(L_p = 1 + (n-1) * p\). n is the total number of data, p is the percentile in decimal form. If the location is a fraction, take the average of the two surrounding numbers. For this data set, the lower quartile (Q1) is 17, the median (Q2) is 32.5, and the upper quartile (Q3) is 44.

Find Minimum and Maximum

The minimum value is the smallest number which is 10 and the maximum value is the largest number which is 50.

Draw Box-and-Whisker Plot

Draw a number line from roughly a little before the smallest value to a little after the largest value. Mark each of Q1, Q2, Q3, the minimum and the maximum values on this line. Draw your box starting at Q1 and ending at Q3. Draw a line at Q2 to denote the median. Finally, draw lines (whiskers) from the box out to the minimum and maximum.