Question

The frequency distribution given below shows the heights of 60 students of a class. If mean of the data is 157, find the missing frequencies of x and y.
Height (in cm) 1144 - 148 148 - 152 152 - 156 | 156 - 160 160 - 164 164 - 1681
Number of students
8 T 15 y I 16
6​

Answer 1

x = 4 & y = 11  for distribution given of the heights of 60 students of a class with Mean 157

Step-by-step explanation:

Class             freq   Mean class   (mean - 154)/4

144 - 148        x         146              -2                             -2x

148 - 152       8          150              -1                              -8

152 - 156       15         154               0                              0

156 - 160       y           158               1                              y

160 - 164       16          162              2                             32

164 - 168        6          166              3                              18

            45 + x + y                                                      42 -2x + y

        45 + x + y     = 60

=> x + y = 15

Mean = 154  +   ( 42 -2x + y) * 4 / 60

=> 157 = 154  +   ( 42 -2x + y)  / 15

=> 42 -2x + y = 45

=> y - 2x  = 3

=> 15 - x - 2x = 3

=> -3x = -12

=> x = 4

y = 11

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Answer 2

The value of x is 4 and the value of y is 11