The mean, median and mode of the given data set 7,12,24,20,26,x, y are 16, 15, and 7. Find the values of x and y, if x < y .

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Solution

The correct option is C 5
The mean, median and mode of the data set are given as 16,15 and 7.

The given data set is

7, 12, 24, 20, 26, x, y

The mode of the data set is the value or values that occur most often. All the values occur only one time. So, one of 'x' and 'y' will be 7.
Hence, let x = 7
The mean of the data set is the sum of the data divided by the number of data values

Mean = $\frac{s u m o f a l l d a t a}{n u m b e r o f d a t a}$

$16$ = $\frac{7 + 12 + 24 + 20 + 26 + 7 + y}{7}$

$16$ = $\frac{96 + y}{7}$

96 + y = 16 $\times$ 7

= 112

y = 112 - 96

= 16

It satisfies the condition x<y.

Hence, the values of x and y are 7 and 16.

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