Classes |
xi |
fi |
fixi |
c.f. |
0−20 |
10 |
6 |
60 |
6 |
20−40 |
30 |
8 |
240 |
14 |
40−60 |
50 |
10 |
500 |
24 |
60−80 |
70 |
12 |
840 |
36 |
80−100 |
90 |
6 |
540 |
42 |
100−120 |
110 |
5 |
550 |
47 |
120−140 |
130 |
3 |
390 |
50 |
|
|
∑fi = 50 |
∑fixi = 3120 |
|
⇒ Mean = \(\frac{\sum f_ix_i}{\sum f_i} = \frac {3120}{50} = 62.4\)
⇒ N = 50 and \(\frac N2 = 25\)
∴ Median class = 60 − 80
l = lower limit of the modal class
h = size of the class intervals
f = frequency of the modal class
f1 = frequency of the class preceding the modal class
f2 = frequency of the class succeed in the modal class.
⇒ Here, l = 60, f = 12, cf = 24, h = 20
Median = \(l + \frac{\frac N2- cf}f \times h\)
\(= 60 + \frac{25 - 24}{12} \times 20\)
\(= 60 + \frac{20}{12} \)
\(= 61.66\)
Modal class = 60 − 80
⇒ l = 30, f = 12, f1 = 10, f2 = 6, h = 20
Mode = \(l + \frac{f - f_1}{2f - f_1 - f_2}\times h\)
\(= 60 + \frac{12 - 10}{2\times 12 - 10 - 6}\times 20\)
\(= 60+ \frac 2{8} \times 20\)
\(= 60 + 5\)
\(= 65\)