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Find the mean and the mode for the following frequency distribution :
Class
$30-35$ $35-40$ $40-45$ $45-50$ $50-55$
Frequency
$3$ $9$ $7$ $3$ $2$
Class
$30-35$ $35-40$ $40-45$ $45-50$ $50-55$
Frequency
$3$ $9$ $7$ $3$ $2$
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Solution:
Correct Table (1.5 Mark)
Let assumed mean be $42.5$
Mean = $A + \frac{\Sigma f_i u_i}{\Sigma f_i} \times h$
$= 42.5 + \frac{(-8)}{24} \times 5$ (1 Mark)
$= 40.84$ (0.5 Mark)
Mode = $l + \frac{f_1-f_0}{2f_1-f_0-f_2} \times h$
$= 35 + \frac{9-3}{18-3-7} \times 5$ (1.5 Mark)
$= 38.75$ (0.5 Mark)
Correct Table (1.5 Mark)
Let assumed mean be $42.5$
Mean = $A + \frac{\Sigma f_i u_i}{\Sigma f_i} \times h$
$= 42.5 + \frac{(-8)}{24} \times 5$ (1 Mark)
$= 40.84$ (0.5 Mark)
Mode = $l + \frac{f_1-f_0}{2f_1-f_0-f_2} \times h$
$= 35 + \frac{9-3}{18-3-7} \times 5$ (1.5 Mark)
$= 38.75$ (0.5 Mark)