Question

Using the assumed - 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.

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

Mean,
$\overline{x}\text{=A +}\frac{\sum ({\text{f}}_i\times {\text{d}}_i)}{\sum {\text{f}}_i}$

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

=(68 + 0.88) = 68.88

Hence, mean height = 68.88 cm