Question

Make a box-and-whisker plot for the data. What is the lower quartile value? 42 48 43 65 58 47 60 56 52 64 51 66 56 62

Answer 1

First we sort our fourteen points:

42 43 47 48 51 52 56 56 58 60 62 64 65 66

With fourteen points the median is the average of the 7th and the 8th, the lower quartile is the fourth and the upper quartile the 11th.

The median is the middle, 56. The Upper quartile is 62 and the lower quartile is, drumroll,

answer: 48

The minimum is 42 and the max is 66. So our box and whiskers plot has left whisker at 42, left box edge at 48, median line at 56, right box edge 62, right whisker 66.

Answer 2

Answer: 48

Step-by-step explanation:

The given data : 42 48 43 65 58 47 60 56 52 64 51 66 56 62

Arrange in ascending order : 42, 43, 47, 48, 51, 52, 56, 56, 58, 60, 62, 64, 65, , 66

Since , the lower quartile is the median of the lower half.

lower half of data : 42, 43, 47, 48, 51, 52, 56

Median of lower half = 48

Hence, the lower quartile = 48

Upper quartile is the median of the upperhalf.

Upper half of data :  56, 58, 60, 62, 64, 65, , 66

Median of lower half = 62

Hence, the upper quartile = 48

Since number of data values is 14

Then , the median = mean of the middlemost numbers.

Median of data : $\dfrac{56+56}{2}=56$

Least value = 42

largest data value = 66