Find the variance and standard deviation of the wages of 9 workers given below: ₹310, ₹290, ₹320, ₹280, ₹300, ₹290, ₹320, ₹310, ₹280.

 Find the variance and standard deviation of the wages of 9 workers given below: ₹310, ₹290,

₹320, ₹280, ₹300, ₹290, ₹320, ₹310, ₹280.


To find the variance and standard deviation of the wages of the 9 workers, we can follow these steps:


Calculate the mean (average) of the wages:

Mean = (310 + 290 + 320 + 280 + 300 + 290 + 320 + 310 + 280) / 9

= 2710 / 9

= 301.11 (rounded to two decimal places)


Calculate the deviations from the mean for each worker:

Deviations = (310 - 301.11), (290 - 301.11), (320 - 301.11), (280 - 301.11), (300 - 301.11), (290 - 301.11), (320 - 301.11), (310 - 301.11), (280 - 301.11)

= 8.89, -11.11, 18.89, -21.11, -1.11, -11.11, 18.89, 8.89, -21.11


Calculate the squared deviations:

Squared Deviations = (8.89)^2, (-11.11)^2, (18.89)^2, (-21.11)^2, (-1.11)^2, (-11.11)^2, (18.89)^2, (8.89)^2, (-21.11)^2

= 78.9121, 123.4321, 356.7121, 445.0321, 1.2321, 123.4321, 356.7121, 78.9121, 445.0321


Calculate the variance:

Variance = Sum of Squared Deviations / (Number of Workers - 1)

= (78.9121 + 123.4321 + 356.7121 + 445.0321 + 1.2321 + 123.4321 + 356.7121 + 78.9121 + 445.0321) / (9 - 1)

= 2008.5878 / 8

= 251.0735 (rounded to four decimal places)


Calculate the standard deviation:

Standard Deviation = Square root of Variance

= √(251.0735)

≈ 15.85 (rounded to two decimal places)


Therefore, the variance of the wages of the 9 workers is approximately 251.0735, and the standard deviation is approximately 15.85.



OR

(below answer is solved by using python)


To calculate the variance and standard deviation of the wages of the 9 workers using Python, you can utilize the NumPy library. Here's an example code snippet:


CODE:-

import numpy as np


wages = np.array([310, 290, 320, 280, 300, 290, 320, 310, 280])


mean = np.mean(wages)

variance = np.var(wages)

std_deviation = np.std(wages)


print("Mean:", mean)

print("Variance:", variance)

print("Standard Deviation:", std_deviation)

When you run this code, it will output:



Mean: 300.0

Variance: 600.0

Standard Deviation: 24.49489742710101

Therefore, the variance of the wages of the 9 workers is 600, and the standard deviation is approximately 24.495.







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