Question

The table below gives the percentage distribution of female teachers in the primary schools of rural areas of various states and union territories (U.T.) of India. Find the mean percentage of female teachers using all the three methods.
Percentage of female teachers 15 - 25 25 - 35 35 – 45 45 - 55 55 - 65 65 - 75 75 – 85
Number of States/U.T. 6 11 7 4 4 2 1

Answer 1

Answer:

Given:-

$distribution \: table \: \: \: \: \: \: \: \: \: num \: of \: states \\ \: \: \: 15 - 25 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: 6 \\ \: \: \: 25 - 35 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: 11 \\ \: \: \: 35 - 45 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: 7 \\ \: \: \: 45 - 55 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: 4 \\ \: \: \: 55 - 65 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: 4 \\ \: \: \: 65 - 75 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: 2 \\ \: \: 75 - 85 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: 1$

To find :-

• mean percentage of female teachers using all three method..

Solution:-

• as we all know three method to find means
• direct method
• short cut method
• step deviation method

firstly we will find by

Direct method:-

steps

• prepare a frequency table with three coloum:

1. in the first column from left write the values of the varient (x)
2. in the 2nd column from the left write the corresponding frequency(f)of each varient in column in column
3. in thr 3 rd column write the product of each x with the frequency (f) i.e write each value of fx

• add all the entries in the secound column to get Σ f
• add all the entries in the third columm to get Σfx
• then put the formula n solve it

For table plzz refere the diagram

here

$Σfx = 1390 \\ Σf = 35$

$mean = \frac{Σfx}{Σf} \\ \\ mean \: = \frac{1390}{35} \\ \\ \: \: \: \: \: \: \: \: \: \: \: = 39.71$

2:- short cut method:-

• prepare a frequency table with three coloum:
• in the first column from left write the values of the varient (x)

1. in the 2nd column from the left write the corresponding frequency(f)of each varient in column in column
2. take number A ( preferably from given values of varies x in the first column) here the number A is call assume mean
3. from each value of variate x in the first column substact assume means A to get deviation d.( d =x - A)
4. multiply the frequency f to the deviation d
5. find Σ fd
6. then solve with formula
7. plzz refere picture for table.

$here \\ a = 50 \\ Σfd = - 360 \\ Σf = 35$

$mean \: = a + \frac{fd}{d} \\ \\ man \: = 50 + \frac{ - 360}{35} \\ \\ mean = 50 - 10.29 \\ \\ \: \: \: \: \: \: \: \: \: \: \: = 39.71$

now for

step deviation method:-

• prepare a frequency table with three coloum:
• in the first column from left write the values of the varient (x)
• in the 2nd column from the left write the corresponding frequency(f)of each varient in column in column
• take number A ( preferably from given values of varies x in the first column) here the number A is call assume mean
• from each value of variate x in the first column substact assume means A to get deviation d.( d =x - A)
• choose the large number i which may divide each value of d in 3rd column .divide each value of d by i to get d /i = x -A /i. denoted value obtaim by t ans the write 4th column.
• multiplt the f and. d
• addd the value of Σft. and value of Σf.
• the solve by formula

$here \\ \\ a = 50 \\ Σft = - 36 \\ Σf = 35 \\ i = 10$

$mean \: = a \: + \frac{Σft}{Σf} \times i \\ \\ mean \: = 50 + \frac{ - 36}{35} \times 10 \\ \\ mean = 50 - 10.29 \\ \\ mean = 39.71$

Answer 2

Answer:

39.71

Step-by-step explanation:

Mean= 50+10×-36/35

x= 50-10.29

x= 39.71

Therefore, the mean percentage of female teacher's is 39.71

Hope it helps you.............