Question

19. Jessica’s Spanish test scores are 98, 74, 88, 83, 91, and 85. Find the range, median, first and third quartiles, and interquartile range of her scores. Use the measures of variation to describe the data.

Answer 1

First arrange the data in ascending order

74,83,85,88,91,98

Range = maximum value - minimum value

= 98 - 74

= 24

Median = middle of all values

We have even number of data values, so median will be the center or average of two middle values

= (85+88)/2

= 173/2

= 86.5

First quartile is the median for first half (74,83,85)

Q1 = middle value or

= (3+1)/2th term

= 83 (because middle can be found directly in case of odd number of data value)

Third quartile is the median for second half (88,91,98)

Q3 = middle value or

= (3+1)/2th term

= 91 (because middle can be found directly in case of odd number of data value)

Inter quartile range = Q3-Q1

= 91 - 83

= 8

50% of data values lies between 83 and 91

25 % of data values are below 83

and 75% of data values are below 91