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Find mean and mode of the following data:
| Class | $10-20$ | $20-30$ | $30-40$ | $40-50$ | $50-60$ | $60-70$ | $70-80$ |
|---|---|---|---|---|---|---|---|
| Frequency | $5$ | $4$ | $10$ | $13$ | $12$ | $10$ | $6$ |
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Solution:
Correct table (1
frac{1}{2} Marks)
Assumed Mean = $45$
Mean = $45 + \frac{17}{60} \times 10 = 45 + \frac{17}{6} = 45 + 2.83 = 47.83$ (approx) (1 Mark)
Modal class is $40 - 50$ (
frac{1}{2} Mark)
Mode = $L + \frac{f_1 - f_0}{2f_1 - f_0 - f_2} \times h = 40 + \frac{13-10}{2\times 13-10-12} \times 10$ (1
frac{1}{2} Marks)
$= 40 + \frac{3}{26-22} \times 10 = 40 + \frac{3}{4} \times 10 = 40 + 7.5 = 47.5$ (
frac{1}{2} Mark)
Correct table (1
frac{1}{2} Marks)
Assumed Mean = $45$
Mean = $45 + \frac{17}{60} \times 10 = 45 + \frac{17}{6} = 45 + 2.83 = 47.83$ (approx) (1 Mark)
Modal class is $40 - 50$ (
frac{1}{2} Mark)
Mode = $L + \frac{f_1 - f_0}{2f_1 - f_0 - f_2} \times h = 40 + \frac{13-10}{2\times 13-10-12} \times 10$ (1
frac{1}{2} Marks)
$= 40 + \frac{3}{26-22} \times 10 = 40 + \frac{3}{4} \times 10 = 40 + 7.5 = 47.5$ (
frac{1}{2} Mark)