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Find mean and mode of the following data:
Class $0-15 \quad 15-30 \quad 30-45 \quad 45-60 \quad 60-75 \quad 75-90 \quad 90-105$
Frequency $4 \quad 6 \quad 8 \quad 10 \quad 12 \quad 7 \quad 3$
Class $0-15 \quad 15-30 \quad 30-45 \quad 45-60 \quad 60-75 \quad 75-90 \quad 90-105$
Frequency $4 \quad 6 \quad 8 \quad 10 \quad 12 \quad 7 \quad 3$
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Solution:
Correct table (1 Mark)
Mean = $52.5 + 15 \times \frac{3}{50}$ (1 Mark)
$= 53.4$ (1/2 Mark)
Modal class is $60 - 75$
Mode = $60 + \frac{12-10}{(2\times 12-10-7)} \times 15$ (1 1/2 Mark)
$= 64.28$ (approx.) (1/2 Mark)
Correct table (1 Mark)
Mean = $52.5 + 15 \times \frac{3}{50}$ (1 Mark)
$= 53.4$ (1/2 Mark)
Modal class is $60 - 75$
Mode = $60 + \frac{12-10}{(2\times 12-10-7)} \times 15$ (1 1/2 Mark)
$= 64.28$ (approx.) (1/2 Mark)