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Find the median and the mode for the following data :
Class
Frequency
0-20
15
20-40
18
40-60
21
60-80
29
80-100
17
Class
Frequency
0-20
15
20-40
18
40-60
21
60-80
29
80-100
17
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Ans.
Class
$f_i$
$cf$
0-20
15
15
20-40
18
33
40-60
21
54
60-80
29
83
80-100
17
100
(Correct Table: 1 Mark)
$N = \frac{100}{2} = 50$ (1 1/2 Marks)
Median $= 40 + \frac{50-33}{21} \times 20$ (1/2 Mark)
$= 56.19$ (1 1/2 Marks)
Mode $= 60 + \frac{29-21}{58-21-17} \times 20$ (1/2 Mark)
$= 68$
Class
$f_i$
$cf$
0-20
15
15
20-40
18
33
40-60
21
54
60-80
29
83
80-100
17
100
(Correct Table: 1 Mark)
$N = \frac{100}{2} = 50$ (1 1/2 Marks)
Median $= 40 + \frac{50-33}{21} \times 20$ (1/2 Mark)
$= 56.19$ (1 1/2 Marks)
Mode $= 60 + \frac{29-21}{58-21-17} \times 20$ (1/2 Mark)
$= 68$