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Find mean and mode of the following frequency distribution :
Class: $5-15$ $15-25$ $25-35$ $35-45$ $45-55$ $55-65$
Frequency: $11$ $20$ $25$ $22$ $12$ $10$
Class: $5-15$ $15-25$ $25-35$ $35-45$ $45-55$ $55-65$
Frequency: $11$ $20$ $25$ $22$ $12$ $10$
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Sol. Correct table (I) (2 Marks)
$\therefore \text{Mean} = \bar{x} = 30+10 \times \frac{34}{100}$ (II) ($\frac{1}{2}$ Mark)
$= 33.4$ (III) ($\frac{1}{2}$ Mark)
Modal Class $= 25 - 35$ (IV) ($\frac{1}{2}$ Mark)
$\therefore \text{Mode} = 25 + \frac{25-20}{2\times25-20-22} \times 10$ (V) (1 Mark)
$= 25 + \frac{50}{8}$
$= 31.25$ (VI) ($\frac{1}{2}$ Mark)
$\therefore \text{Mean} = \bar{x} = 30+10 \times \frac{34}{100}$ (II) ($\frac{1}{2}$ Mark)
$= 33.4$ (III) ($\frac{1}{2}$ Mark)
Modal Class $= 25 - 35$ (IV) ($\frac{1}{2}$ Mark)
$\therefore \text{Mode} = 25 + \frac{25-20}{2\times25-20-22} \times 10$ (V) (1 Mark)
$= 25 + \frac{50}{8}$
$= 31.25$ (VI) ($\frac{1}{2}$ Mark)