Question

Construct a box plot from the given data. Use the approximation method. Diameters of Cans in an Assembly Line: 5.7,5.2,5.7,5.6,5.1,5.3,5.5,5.3,5.6 Answer Draw the box plot by selecting each of the five movable parts to the appropriate position.

Answer 1

For the box plot, 5 numbers are needed.

Minimum, Q1, Q2, Q3 and maximum.

Q1, Q2, and Q3 are the quartiles of the data.

First, arrange the observations in increasing order.

The observations in increasing order are,

5.1, 5.2, 5.3, 5.3, 5.5, 5.6, 5.6, 5.7, 5.7

Minimum = 5.1

The quartiles divide the data into 4 equal parts.

First, find median that is Q2

Q2 is the middlemost observation of the data set.

there are 9 observations, so fifth observation from the arranged data set is the median

Q2 = fifth observation = 5.5

Q2 = 5.5

Now divides the data into two equal parts including the median. The median of first-half data set is nothing but Q1 and the median of second-half data set is Q3

The first-half data set is, 5.1, 5.2, 5.3, 5.3, 5.5

The third observation is the middlemost that is 5.3

Q1 = 5.3

The second-half data set is 5.5, 5.6, 5.6, 5.7, 5.7

The third observation is the middlemost that is 5.6

Q3 = 5.6

Maximum = Largest observation = 5.7

The five numbers to draw box plot are,

Minimum = 5.1

Q1 = 5.3

Q2 = 5.5

Q3 = 5.6

Maximum = 5.7

The box plot is,