Question

Determine the mean, median, mode, and midrange for this collection of class test scores: 88 82 97 76 79 92 65 84 79 90 75 82 78 77 93 88 95 73 69 89 93 78 60 95 88 72 80 94 88 74 a. Mean is 84, median is 82, mode is 82, midrange is 77 b. Mean is 82, median is 88, mode is 88, midrange is 77 c. Mean is 82.4, median is 88, mode is 82, midrange is 78.5 d. Mean is 82.4, median is 82, mode is 88, midrange is 78.5

Answer 1

Mean of a given set of data = Sum of all observations ÷ Total number of observations

Mean of this data set = 88 + 82 + 97 + 76 + 79 + 92 + 65 + 84 + 79 + 90 + 75 + 82 + 78 + 77 + 93 + 88 + 95 + 73 + 69 89 + 93 + 78 + 60 + 95 + 88 + 72 + 80 + 94 + 88 + 74

Mean = 2729 ÷ 30

Mean = 82.4

Median = the middle observation in a given set of data

Median of these test scores = 60 , 65 , 69 , 72 , 73 , 74 , 75 , 76 , 77 , 78 , 78 , 79 , 79 , 80 , 82 , 82 , 84 , 88 , 88 , 88 , 88 , 89 , 90 , 92 , 93 , 93 , 94 , 95 , 95 , 97 .

Median = 82 + 82 / 2

= 164 ÷ 2

= 82

Median = 82

Mode = most frequently occurring number in a given set of data .

Mode of these test scores =

= 60 = 1 time

= 65 = 1 time

= 69 = 1 time

= 72 = 1 time

= 73 = 1 time

= 74 = 1 time

= 75 = 1 time

= 76 = 1 time

= 77 = 1 time

= 78 = 2 times

= 79 = 2 times

= 80 = 1 time

= 82 = 2 times

= 84 = 1 time

= 88 = 4 times

= 89 = 1 time

= 90 = 1 time

= 92 = 1 time

= 93 = 2 times

= 94 = 1 time

= 95 = 2 times

= 97 = 1 time

Mode = 88

Midrange = average of the largest and smallest number in a given set of data

Midrange of these test scores = 97 + 60 / 2

= 97 + 60 / 2

= 157 ÷ 2

= 78.5

Midrange = 78.5

Therefore , the correct option is :-

(d) Mean is 82.4 , median is 82 , mode is 88 , midrange is 78.5