Maths

266 MATHEMATICS
We have, u i
=
Therefore, u =
xi
✂f
h
i
a
( xi
a ✁ )
h 1 fx
i i
a ✄ f ☎
✂ ✁ ✂
✆
i
✞
✝
f h f
i
i
✂
✂
✟
✠
= 1 fx
i
✡
i
☛ f
☞
i ☞
✌ ✍
✎ a
☞
✏
✑
☞ h f f
1
✓ = ✒ x ✔ a
h
So, hu = x a ✕
i.e.,
x = a + hu
i
i
So, x =
a
fiu
✖
i
✗ ✘
h
✜ ✘f
✙ ✚ ✛
i
✢
Now, substituting the values of a, h, ✣f i
u i
and ✣f i
from Table 14.5, we get
x =
So, the mean marks obtained by a student is 62.
✤ ✥
✦ ✧ ★ ✩
✪
47.5 15
29
30
✫
= 47.5 + 14.5 = 62
The method discussed above is called the Step-deviation method.
We note that :
the step-deviation method will be convenient to apply if all the d ✬ i
’s have a
common factor.
✬ The mean obtained by all the three methods is the same.
The assumed mean method and step-deviation method are just simplified
✬
forms of the direct method.
The formula x = a + hu still holds if a and h are not as ✬ given above, but are
xi
✔ a
any non-zero numbers such that u i
= .
h
Let us apply these methods in another example.