Question

Using the aasumed - mean method, find the mean height of the plants from the following frequency-distribution table:

$\begin{array}{cccccc}\text{Height (in cm)}{x}_i& 60& 64& 68& 72& 76\\ \text{Number of plants}{f}_i& 5& 16& 40& 30& 9\end{array}$
[4 MARKS]

Answer 1

Tabular form: 1 Mark
Concept: 1 Mark
Application: 2 Marks

Let the assumed mean be A = 68

Now, we may arrange the given data as under.

$\begin{array}{cccc}\text{Height (in cm)}{x}_i& \text{Frequency}& d_i=(x_i-A)=(x_i-68)& f_i\times d_i\\ x_i& f_i& =(x_i-68)& \\ 60& 5& -8& -40\\ 64& 16& -4& -64\\ 68=A& 40& 0& 0\\ 72& 30& 4& 120\\ 76& 9& 8& 72\\ & \sum f_i=100& & \sum (f_i\times d_i)=88\end{array}$

Mean, $\overline{x}=A+\frac{\sum (f_i\times d_i)}{\sum f_i}$

$=(68+\frac{88}{100})$

=(68 + 0.88) = 68.88

Hence, mean height = 68.88 cm