NCERT Class 10 Mathematics

STATISTICS 265

Substituting the values of a, fidi and fi from Table 14.4, we get

x = 47.5^435 47.5 14.5 62

30

✁ ✂ ✁ ✂.

Therefore, the mean of the marks obtained by the students is 62.

The method discussed above is called the Assumed Mean Method.

Activity 1 : From the Table 14.3 find the mean by taking each of xi (i.e., 17.5, 32.5,
and so on) as ‘a’. What do you observe? You will find that the mean determined in
each case is the same, i.e., 62. (Why ?)

So, we can say that the value of the mean obtained does not depend on the
choice of ‘a’.

Observe that in Table 14.4, the values in Column 4 are all multiples of 15. So, if
we divide the values in the entire Column 4 by 15, we would get smaller numbers to
multiply with fi. (Here, 15 is the class size of each class interval.)

So, let ui = i

x a

h

✄

, where a is the assumed mean and h is the class size.

Now, we calculate ui in this way and continue as before (i.e., find fi ui and
then fiui). Taking h = 15, let us form Table 14.5.

Table 14.5

Class interval fi xi di = xi – a ui = i

x –a

h

fiui

10 - 25 2 17.5 –30 –2 –4

25 - 40 3 32.5 –15 –1 –3

40 - 55 7 47.5 0 0 0

55 - 70 6 62.5 15 1 6

70 - 85 6 77.5 30 2 12

85 - 100 6 92.5 45 3 18

Total fi = 30 fiui = 29

Let u = ii
i

fu

f

☎

☎

Here, again let us find the relation between u and x.