Question

For a population of numbers 10, 8, 7 , 9 , 5, 12, 8, 6, 8 , 2 calculate variance and
standard deviation.

Answer 1

Given :- For a population of numbers 10, 8, 7 , 9 , 5, 12, 8, 6, 8 , 2 calculate variance and standard deviation.

Answer :-

→ Mean = (10 + 8 + 7 + 9 + 5 + 12 + 8 + 6 + 8 + 2) / 10 = 7.5

now, finding the sum of square of (each data - mean)² we get,

→ sum = (10 - 7.5)² + (8 - 7.5)² + (7 - 7.5)² + (9 - 7.5)² + (5 - 7.5)² + (12 - 7.5)² + (8 - 7.5)² + (6 - 7.5)² + (8 - 7.5)² - (2 - 7.5)² = 6.25 + 0.25 + 0.25 + 2.25 + 2.25 + 20.25 + 0.25 + 2.25 + 0.25 + 30.25 = 64.5 .

then,

→ Variance of population = sum / numbers of data = 64.5/10 = 6.45 .

therefore,

→ standard deviation = √(variance) = √(6.45) ≈ 2.54

Learn more :-

calculate the median and mode from the following income between (rs)100-200 100-300 100-400 100-500 100-600 no of person...

https://brainly.in/question/23585381

Some students of class X donated for the welfare of old age persons. The contributions are shown in the following distri...

https://brainly.in/question/17314012