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Find median and mode of the following distribution :
Class Interval 0-15 15-30 30-45 45-60 60-75 75-90 90-105
Frequency 15 10 12 9 8 10 6
Class Interval 0-15 15-30 30-45 45-60 60-75 75-90 90-105
Frequency 15 10 12 9 8 10 6
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Sol. Class Interval f cf
0-15 15 15
15-30 10 25
30-45 12 37
45-60 9 46
60-75 8 54
75-90 10 64
90-105 6 70
Correct table (I) (1)
$ \frac{70}{2} = 35$, Median class is 30 - 45 (II) (1/2)
Median = $30 + \frac{35-25}{12} \times 15$ (III) (1)
$= \frac{85}{2} = 42.5$ (IV) (1/2)
Modal class is 0 – 15 (V) (1/2)
Mode = $0 + \frac{15-0}{30-0-10} \times 15$ (VI) (1)
$= \frac{45}{4} = 11.25$ (VII) (1/2)
0-15 15 15
15-30 10 25
30-45 12 37
45-60 9 46
60-75 8 54
75-90 10 64
90-105 6 70
Correct table (I) (1)
$ \frac{70}{2} = 35$, Median class is 30 - 45 (II) (1/2)
Median = $30 + \frac{35-25}{12} \times 15$ (III) (1)
$= \frac{85}{2} = 42.5$ (IV) (1/2)
Modal class is 0 – 15 (V) (1/2)
Mode = $0 + \frac{15-0}{30-0-10} \times 15$ (VI) (1)
$= \frac{45}{4} = 11.25$ (VII) (1/2)