Question

Find x, y and z in the below table.

$\begin{array}{ccc}Height\left(cm\right)& Frequency& CumulativeFrequency\\ 150-155& 12& 12\\ 155-160& x& 27\\ 160-165& y& 45\\ 165-170& 12& 57\\ 170-175& 3& z\end{array}$

• A. x = 18
  y = 12
  z = 60
• B. x = 15
  y = 18
  z = 54
• C. x = 15
  y = 18
  z = 60
• D. x = 15
  y = 42
  z = 60

Answer 1

The correct option is C x = 15

y = 18
z = 60
x is the frequency of the class interval 155-160. We know that cumulative frequency of a variable is the sum of all frequencies till the relevant variable. Here, cumulative frequency of this class interval is 27.
Therefore, x = 27 - 12 = 15.
Likewise, cumulative frequency of class interval 160-165 is 45. Hence, y = 45-27 = 18.
Finally, z is the cumulative frequency of class interval 170-175. That is, z = 57 + 3 = 60.