Question

Draw a box-and-whisker plot of the data. Attendance at early showing of a movie: \(48,60,40,68,51,47,57,41,65,61,20,65,49,34,63,53,52,35,45,35,65,65,48,36,24,53,64,48,40\)

Short answer

The box-and-whisker plot has a lower whisker extending from 20 (minimum) to 40 (Q1), a box from 40 (Q1) to 60 (Q3) with a line at 48 (median), and an upper whisker extending from 60 (Q3) to 68 (maximum).

Step-by-step solution

Arrange the data in ascending order

Start by arranging the dataset in ascending order which yields: 20,24,34,35,35,36,40,40,41,45,47,48,48,48,49,51,52,53,53,57,60,61,63,64,65,65,65,65,68

Find the Median (Q2)

The median is the number that falls exactly in the middle of the ordered list. Since there are 29 numbers in the dataset, the median will lie at the 15th position. From the ordered data, the median is 48.

Find the First quartile (Q1)

The first quartile is the median of the first half of the ordered list. Since there are 14 numbers before the median, Q1 lies at the 7th position which is 40.

Find the Third quartile (Q3)

The third quartile is the median of the second half of the ordered list. Since there are 14 numbers after the median, Q3 lies at the 7th position in the second half which is 60.

Identify the minimum and maximum

From the ordered data, the minimum value in the dataset is 20 and the maximum value is 68.

Draw the box-and-whisker plot

The resulting box-and-whisker plot would have a 'box' from 40 (Q1) to 60 (Q3), with a line inside the box at 48 (the median). There would be two 'whiskers', one reaching from 40 to 20 (the minimum) and the other reaching from 60 to 68 (the maximum).