Astudent takes 10 exams during a semester and receives the following grades 90 85 97 76 89 58 82 102 70 and 67 what would the five number summary used in a boxplot

Formula using a boxplot

Minimum = the lowest element of set

First Quartile = (n+1)/4

Median = (n+1)/2

Third Quartile = 3(n+1)/4

Maximum = the highest element of set.

Solution:

Arrange the given in order. (58, 67, 70, 76, 82, 85, 89, 90, 97, 102),

The five number summary of (90, 85, 97, 76, 89, 58, 82, 102, 70, and 67) is,

Minimum = 58

First Quartile = (10+1)/4 = 2.75 (or 3) getting this answer you need to go back to the arranged given numbers and look for the 3rd number which is 70

Median:  = (82+85)/2 = 83.5

Third Quartile = 3(10+1)/4 8.25 or 8th which is 90 in the arranged numbers.

Maximum = 102

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so, converting firstly the mixed fractions to improper fractions and then "adding".