Question

Given that the mean height of a group of students is 67.45 inches. Find out the missing frequencies for that following Incomplete distribution of height of 100 students.

Answer 1

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)

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

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

$\bar{x}$ = 67.45  (given)

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

$67 + [\dfrac{ {-12+f_4}}{100} \times 3] = 67.45$

(-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

Answer 2

Answer:

Go through the attachment for reference