Question

Find the unknown entries a, b, c, d, e and f in the following distribution of heights of students in a class
$\begin{array}{ccc}Height\left(incm\right)& Frequency& Cumulativefrequency\\ 150-155& 12& a\\ 155-160& b& 25\\ 160-165& 10& c\\ 165-170& d& 43\\ 170-175& e& 48\\ 175-180& 2& f\\ Total& 50& \end{array}$

Answer 1

$\begin{array}{cccc}Height\left(incm\right)& Frequency& Cumulativefrequency\left(given\right)& Cumulativefrequency\\ 150-155& 12& a& 12\\ 155-160& b& 25& 12+b\\ 160-165& 10& c& 22+b\\ 165-170& d& 43& 22+b+d\\ 170-175& e& 48& 22+b+d+e\\ 175-180& 2& f& 24+b+d+e\\ Total& 50& & \end{array}$
On comparing last two columns of the table, we get
a = 12 ------(1)
and 12 + b = 25
$\Rightarrow$ b = 25 - 12 = 13-----(2)
and 22 + b = c
$\Rightarrow$ c = 22 + 13 = 35-----(3)
and 22 + b + d = 43
$\Rightarrow$ 22 + 13 + d = 43
$\Rightarrow$ d = 43 - 35 = 8-------(4)
and 22 + b + d + e = 48
$\Rightarrow$ e = 48 - 43 = 5------(5)
and 24 + b + d + e = f
$\Rightarrow$ 24 + 13 + 8 + 5 = f
$\therefore$ f = 50---------(6)