Using the aasumed - mean method- find the mean height of the plants from the following frequency-distribution table-WlineHeight in - cm - X - i - 60 - 64 - 68 - 72 - 76 wllhline Number of - plants f - i - 5 - 16 - 40 - 30 - 9 end array -4 MARKS-

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Standard VIII

Mathematics

Mean

Using the aas...

Question

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

$\begin{matrix} H e i g h t (i n c m) x_{i} & 60 & 64 & 68 & 72 & 76 N u m b e r o f p l a n t s f_{i} & 5 & 16 & 40 & 30 & 9 \end{matrix}$
[4 MARKS]

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Solution

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.

$\begin{matrix} H e i g h t (i n c m) x_{i} & F r e q u e n c y & d_{i} = (x_{i} - A) = (x_{i} - 68) & f_{i} \times d_{i} x_{i} & f_{i} & = (x_{i} - 68) 60 & 5 & - 8 & - 40 64 & 16 & - 4 & - 64 68 = A & 40 & 0 & 0 72 & 30 & 4 & 120 76 & 9 & 8 & 72 \sum f_{i} = 100 & \sum (f_{i} \times d_{i}) = 88 \end{matrix}$

Mean, $¯ x = A + \frac{\sum (f_{i} \times d_{i})}{\sum f_{i}}$

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

=(68 + 0.88) = 68.88

Hence, mean height = 68.88 cm

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