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Find mean and mode of the following distribution :
Class: $0-15$ $15-30$ $30-45$ $45-60$ $60-75$ $75-90$ $90-105$
Frequency: $4$ $8$ $11$ $14$ $10$ $7$ $6$
Class: $0-15$ $15-30$ $30-45$ $45-60$ $60-75$ $75-90$ $90-105$
Frequency: $4$ $8$ $11$ $14$ $10$ $7$ $6$
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Correct table (2 Marks)
$\therefore \text{Mean} = \bar{x} = 52.5 + 15\times \frac{3}{60}$ (1/2 Mark)
= $53.25$ (1/2 Mark)
Modal Class = $45 - 60$ (1/2 Mark)
$\therefore \text{Mode} = 45 + \frac{14-11}{28-11-10} \times 15$ (1 Mark)
= $45 + \frac{3 \times 15}{7}$
= $51.4$ (approx.) (1/2 Mark)
$\therefore \text{Mean} = \bar{x} = 52.5 + 15\times \frac{3}{60}$ (1/2 Mark)
= $53.25$ (1/2 Mark)
Modal Class = $45 - 60$ (1/2 Mark)
$\therefore \text{Mode} = 45 + \frac{14-11}{28-11-10} \times 15$ (1 Mark)
= $45 + \frac{3 \times 15}{7}$
= $51.4$ (approx.) (1/2 Mark)