NCERT Class 10 Mathematics

264 MATHEMATICS

The third step is to find the product of di with the corresponding fi, and take the sum
of all the fi di’s. The calculations are shown in Table 14.4.

Table 14.4

Class interval Number of Class mark di = xi – 47.5 fidi

students (fi) (xi)

10 - 25 2 17.5 –30 –60

25 - 40 3 32.5 –15 –45

40 - 55 7 47.5 0 0

55 - 70 6 62.5 15 90

70 - 85 6 77.5 30 180

85 - 100 6 92.5 45 270

Total fi = 30 fidi = 435

So, from Table 14.4, the mean of the deviations, d = ii

i

fd

f

✁

✁

.

Now, let us find the relation between d and x.

Since in obtaining di, we subtracted ‘a’ from each xi, so, in order to get the mean

x, we need to add ‘a’ to d. This can be explained mathematically as:

Mean of deviations, d = ii

i

fd

f

✂

✂

So, d =

ii()

i

f xa

f

✁ ✄

✁

= ii i

ii

fxfa

f f

✂ ✂

☎

✂ ✂

= i

i

f

xa

f

✂

☎

✂

= x✆a

So, x =a + d

i.e., x = ii
i

fd

a

f

✂

✝

✂