Question

Conduct a survey at population in your locality taking a sample of atleast 50 families prepare a project report with respect to the following points: 1 represent the data showing age using class interval. 2 compute the average income of the families. 3 literacy level of the population in term of elementary, secondary, senior secondary, graduation and above. 4find the variance of the income of the families. 5 represent the data in part 3 with the help of bar graph

Answer 1

The Answers for Q1, Q2, Q3, and Q5 are given in images.

The average income of the families is 6.9 lakhs.

The variance of the incomes is 3.2736

Given,

Number of families = 50

Total Number of people = 200

To Find,

Mean and variance of the Family Incomes.

Solution,

2) Mean = ∑ (xi*fi) / ∑ (fi)

x1*f1 = 2.5 * 17 = 42.5

x2*f2 = 7.5 * 25 = 187.5

x3*f3 = 12.5 * 5 = 62.5

x4*f4 = 17.5 * 3 = 52.5

∑ (xi*fi) = 42.5 + 187.5 + 62.5 + 52.5

∑ (xi*fi) = 345

∑ (fi) = Total Number of families = 50

Mean = $\frac{345}{50}$

Mean = μ =  6.9 lakhs

4) Variance = σ² = (Σ (X - μ)²)/N

(X₁ - μ)² = (2.5 - 6.9)² = (- 4.4)² = 19.6

(X₂ - μ)² = (7.5 - 6.9)² = (0.6)² = 0.36

(X₃ - μ)² = (12.5 - 6.9)² = (5.6)² = 31.36

(X₄ - μ)² = (17.5 - 6.9)² = (10.6)² = 112.36

N = Total Number of families = 50

Σ (X - μ)² = 19.6 + 0.36 + 31.36 + 112.36

Σ (X - μ)² = 163.68

σ² = (Σ (X - μ)²)/N

σ² = (163.68)/50 = 3.2736

Thus, the variance is 3.2736.

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