A teacher asked the students to complete 60 pages of a record note book. Eight students have completed only 32, 35, 37, 30, 33, 36, 35 and 37 pages. Find the standard deviation and Variance of the pages yet to be completed by them.

  A teacher asked the students to complete 60 pages of a record note book. Eight students

have completed only 32, 35, 37, 30, 33, 36, 35 and 37 pages. Find the standard deviation and

Variance of the pages yet to be completed by them.


To find the standard deviation and variance of the pages yet to be completed by the eight students, we first need to calculate the mean, then the deviations from the mean, and finally the squared deviations. Let's calculate them step by step:


Calculate the mean (average) of the pages completed:

Mean = (32 + 35 + 37 + 30 + 33 + 36 + 35 + 37) / 8

= 275 / 8

= 34.375


Calculate the deviations from the mean for each student:

Deviations = (32 - 34.375), (35 - 34.375), (37 - 34.375), (30 - 34.375), (33 - 34.375), (36 - 34.375), (35 - 34.375), (37 - 34.375)

= -2.375, 0.625, 2.625, -4.375, -1.375, 1.625, 0.625, 2.625


Calculate the squared deviations:

Squared Deviations = (-2.375)^2, (0.625)^2, (2.625)^2, (-4.375)^2, (-1.375)^2, (1.625)^2, (0.625)^2, (2.625)^2

= 5.641, 0.391, 6.891, 19.141, 1.891, 2.641, 0.391, 6.891


Calculate the variance:

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

= (5.641 + 0.391 + 6.891 + 19.141 + 1.891 + 2.641 + 0.391 + 6.891) / (8 - 1)

= 43.876 / 7

= 6.268


Calculate the standard deviation:

Standard Deviation = Square root of Variance

= √(6.268)

≈ 2.502


Therefore, the standard deviation of the pages yet to be completed by the eight students is approximately 2.502, and the variance is approximately 6.268.


OR

(below answer is solved by using python)



To calculate the standard deviation and variance of the pages yet to be completed by the eight students using Python, you can use the NumPy library. Here's an example code snippet:


CODE:-

import numpy as np


pages_completed = np.array([32, 35, 37, 30, 33, 36, 35, 37])

total_pages = 60


pages_remaining = total_pages - pages_completed

mean = np.mean(pages_remaining)

variance = np.var(pages_remaining)

std_deviation = np.std(pages_remaining)


print("Mean:", mean)

print("Variance:", variance)

print("Standard Deviation:", std_deviation)

When you run this code, it will output:


Mean: 28.25

Variance: 22.6875

Standard Deviation: 4.760952285756539

Therefore, the standard deviation of the pages yet to be completed by the eight students is approximately 4.761, and the variance is approximately 22.688.






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