Question

The following table gives the literacy rate (in percentage) of 35 cities. Find the mean literacy rate.
Literacy rate (in %):
45−55
55−65
65−75
75−85
85−95
Number of cities:
3
10
11
8
3

Answer 1

STEP DEVIATION METHOD:

Step deviation method is used in the cases where the deviation from the assumed mean 'A' are multiples of a common number. If the values of ‘di’ for each class is a multiple of ‘h’ the calculation become simpler by taking ui= di/h = (xi - A )/h

Here, h is the class size of each class interval.

★★ Find the class marks of class interval. These class marks would serve as the representative of whole class and are represented by xi.  

★★ Class marks (xi)  = ( lower limit + upper limit) /2

★★ We may take Assumed mean 'A’ to be that xi which lies in the middle of x1 ,x2 …..xn

MEAN = A + h ×(Σfiui /Σfi) , where ui =  (xi - A )/h

[‘Σ’ Sigma means ‘summation’ ]

FREQUENCY DISTRIBUTION TABLE IS IN THE ATTACHMENT  

From the table : Σfiui = -2 ,  Σfi = 35

Let the assumed mean, A = 70,  h = 10

MEAN = A + h ×(Σfiui /Σfi)

Mean = 70 + 10(-2/35)

= 70 - 4/7

= 70 - 0.571

= 69.428

Mean = 69.428 ≈ 69.43%

Hence, the Mean literacy rate is approximately is 69.43%.

HOPE THIS ANSWER WILL HELP YOU….

Answer 2

$\bf \huge{Answer :}$

We can find the class mark by using the formula :

X =( Upper class limit + lower class limit )/2

Class size ( h ) for the given data is 10.

Now, taking 70 as the assumed mean (a) ( wrong )

Calculate d¡, u¡ , f¡u¡ as given in the table.

We get,

N = 35

Sum = -2

Hence,
$\sf{{ \: \bar {x}} = a + \frac{sum}{N} \times h}$

$\sf{= 70 + ( - 2/35)} \\ \\ \sf{ = 70 - 4/7} \\ \\ \sf{ = 70 - 0.57}$

$\sf{= 69.43}$

Hence,

Mean literacy rate is 69.43 %

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