Find standard deviation. Expenditure 10 30 30 50 50 70 70 90 90 110 : : : : : : Individual 3 2 4 3 3

Solution: Standard Deviation of Expenditure Step 1: Find the Midpoints (xᵢ) of Each Class Interval The given data is grouped, so we calculate the midpoint of each class interval. Expenditure (Class) Midpoint (xᵢ) 10–30 10+302 = 20 30–50 30+502 = 40 50–70 50+702 = 60 70–90 70+902 = 80 90–110 90+1102 = 100 Step 2: Calculate the Frequency (fᵢ) and fᵢxᵢ The frequency (fᵢ) is given in the table. Midpoint (xᵢ) Frequency (fᵢ) fᵢxᵢ 20 3 60 40 2 80 60 4 240 80 3 240 100 3 300 Step 3: Compute the Mean (μ) = f i x i f i = 60 + 80 + 240 + 240 + 3003 + 2 + 4 + 3 + 3 = 92015 = 61.33 Step 4: Calculate (xᵢ − μ)² and fᵢ(xᵢ − μ)² array c c c c x i & f i & (x i )^2 & f i(x i )^2 \\ 20 & 3 & (20 61.33)^2 = 1774.49 & 5323.47 \\ 40 & 2 & (40 61.33)^2 = 454.49 & 908.98 \\ 60 & 4 & (60 61.33)^2 = 1.77 & 7.08 \\ 80 & 3 & (80 61.33)^2 = 344.49 & 1033.47 \\ 100 & 3 & (100 61.33)^2 = 1474.49 & 4423.47 \\ array f i(x i )^2 = 5323.47 + 908.98 + 7.08 + 1033.47 + 4423.47 = 11696.47 Step 5: Compute Variance (σ²) ^2 = f i(x i )^2N = 11696.4715 = 779.76 Step 6: Find Standard Deviation (σ) = 779.76 = 27.93 Final Answer: The standard deviation of the given expenditure data is 27.93 .

Find standard deviation. Expenditure 10 30 30 50 50 70 70 90 90 110 : : : : : :… – Economics NEB 2074 (old course) Solution

Solution: Standard Deviation of Expenditure

Step 1: Find the Midpoints (xᵢ) of Each Class Interval

The given data is grouped, so we calculate the midpoint of each class interval.

Expenditure (Class)	Midpoint (xᵢ)
10–30	$\frac{10 + 30}{2} = 20$
30–50	$\frac{30 + 50}{2} = 40$
50–70	$\frac{50 + 70}{2} = 60$
70–90	$\frac{70 + 90}{2} = 80$
90–110	$\frac{90 + 110}{2} = 100$

Step 2: Calculate the Frequency (fᵢ) and fᵢxᵢ

The frequency (fᵢ) is given in the table.

Midpoint (xᵢ)	Frequency (fᵢ)	fᵢxᵢ
20	3	60
40	2	80
60	4	240
80	3	240
100	3	300

Step 3: Compute the Mean (μ)

$μ = \frac{\sum f _{i} x _{i}}{\sum f _{i}} = \frac{60 + 80 + 240 + 240 + 300}{3 + 2 + 4 + 3 + 3} = \frac{920}{15} = 61.33$

Step 4: Calculate (xᵢ − μ)² and fᵢ(xᵢ − μ)²

$x_{i} 20406080100 f_{i} 32433 (x_{i} - μ)^{2} (20 - 61.33)^{2} = 1774.49 (40 - 61.33)^{2} = 454.49 (60 - 61.33)^{2} = 1.77 (80 - 61.33)^{2} = 344.49 (100 - 61.33)^{2} = 1474.49 f_{i} (x_{i} - μ)^{2} 5323.47 908.98 7.08 1033.47 4423.47$

$\sum f_{i} (x_{i} - μ)^{2} = 5323.47 + 908.98 + 7.08 + 1033.47 + 4423.47 = 11696.47$

Step 5: Compute Variance (σ²)

$σ^{2} = \frac{\sum f _{i} ( x _{i} - μ ) ^{2}}{N} = \frac{11696.47}{15} = 779.76$

Step 6: Find Standard Deviation (σ)

$σ = 779.76 = 27.93$

Final Answer: The standard deviation of the given expenditure data is 27.93.