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Question

The scores of a team in a competition is given. 60, 90, 80, 100, 70, 110, 120, x, y Find the value of x and y, if the mean, median and mode of the data are 95, 90 and 80 and x < y.

A
80 and 120
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B
90 and 120
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C
80 and 110
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D
80 and 145
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Solution

The correct option is D 80 and 145The given data set is, 60, 90, 80, 100, 70, 110, 120, x, y. Given: Mean of the data set = 95 Median = 90 Mode = 80 Since, each value occurs one time in the given data set, and since mode =80, x or y value should be 80. It is given x < y. Let x = 80 Mean = sum of all datanumber of data Mean of the data = 60+90+80+100+70+110+120+80+y9 = 710+y9 It is given that, mean of the data = 95 ⟹ 95 = 710+y9 ⟹ 9 × 95 = 710 + y ⟹ 855 = 710 + y ⟹ 855 - 710 = y ⟹ y = 145 If x and y are 80 and 145, the data set is 60, 90, 80, 100, 70, 110, 120, 80, 145 Let us arrange the data in ascending order. We get 60, 70, 80, 80, 90, 100, 110, 120, 145 For a set with an odd number of values, the median is the middle value of the data set when it is arranged in an ascending or descending order. Hence, median = 90 Hence, mean, median and mode are 95, 90 and 80 respectively. This satisfies the given data. Hence, x and y values are 80 and 145 respectively.

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