Question

Calculate the missing frequency when mean is 67.45:

Answer 1

Answer:

The complete data is,

findout the missing frequencies from the following data,given that A.M=67.45 inches :height(inches)-60-62| 63-65|66-68|69-71|72-74|Total|

no.of student- 5 | 18 |f3 |f4 |8 |100 |

N = 100

5 + 18 + f3 + f4 + 8 = 100

31 + f3 + f4 = 100

f3 + f4 = 100 - 31

f3 + f4 = 69 .........(1)

d = \dfrac{x_i - A}{c} = \dfrac{x_i - 67}{3}d=

c

x

i

−A

=

3

x

i

−67

Class Interval Frequency Mid-Value fidi

60-62 5 61 -2 -10

63-65 18 64 -1 -18

66-68 f3 67 0 0

69-71 f4 70 1 f4

72-74 8 73 2 16

Total ∑f = N = 31 + f3 + f4 A = 67 - ∑ fd = –12 + f4

Arithmetic mean

\bar{x}

x

ˉ

= 67.45 (given)

A + [\dfrac{\sum {fd}}{N} \times c] = 67.45A+[

N

∑fd

×c]=67.45

67 + [\dfrac{ {-12+f_4}}{100} \times 3] = 67.4567+[

100

−12+f

4

×3]=67.45

(-12 + f4) × 3 = (67.45 - 67) × 100

-12 + f4 = 15

f4 = 15 + 12

∴ f4 = 27

Using (1) we have,

f3 + 27 = 69

f3 = 69 - 27

∴ f3 = 42

Therefore, the missing frequencies are 27 and 42