Calculate the mean, variance and standard deviation for the following distribution:Class 30-40 40-50 50-60 60-70 70-80 80-90 90-100Frequency 3 7 12 15 8 3 2

Question

Calculate the mean, variance and standard deviation for the following distribution:Class       30-40    40-50      50-60      60-70      70-80      80-90       90-100Frequency   3             7             12          15             8            3               2

Filo · Accepted Answer

Solution: With the given distribution ,

x_{i} = 35, 45, 55, 65, 75, 85, 95

f_{i} = 3, 7, 12, 15, 8, 3, 2

∴ x_{i} f_{i} = 105, 315, 660, 975, 600, 255, 190

∴ \sum f_{i} = 50

\sum x_{i} f_{i} = 3100

∴ M e a n (\overline{X}) = \frac{\sum x _{i} f _{i}}{\sum f _{i}} = \frac{3100}{50} = 62

Now,

∣ x_{i} - \overline{x} ∣ = 27, 17, 7, 3, 13, 23, 33

∣ x_{i} - \overline{x} ∣^{2} = 729, 289, 49, 9, 169, 529, 1089

∴ ∣ x_{i} - \overline{x} ∣^{2} f_{i} = 2187, 2023, 588, 135, 1352, 1587, 2178

∴

Variance,

(σ)^{2} = \frac{\sum ∣ x _{i} - x ∣ ^{2} f _{i}}{\sum f _{i}} = \frac{10050}{50} = 201

Standard deviation,

(σ) = 201 = \sim 14.177 .

Question Text	Calculate the mean, variance and standard deviation for the following distribution:Class 30-40 40-50 50-60 60-70 70-80 80-90 90-100Frequency 3 7 12 15 8 3 2
Answer Type	Text solution:1
Upvotes	150

Calculate the mean, variance and standard deviation for the following distribution:Class 30-40 40-50 50-60 60-70 70-80 80-90 90-100Frequency 3 7 12 15 8 3 2

Text solutionVerified

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