Question

The number of school related extracurricular activities per student find the mean the variance and standard deviation of the probability distribution do you do

This Question: 1 pt Use the probability distribution to complete parts (a) and (b) below. The number of school-related extracurricular activities per student Activities 0 1 2 3 4 5 6 7 Probability 0.059 0.123 0.162 0.178 0.212 0.129 0.084 0.053 (a) Find the mean, variance, and standard deviation of the probability distribution. The mean is 3.3. (Round to one decimal place as needed.) The variance is (Round to one decimal place as needed.) Q The standard deviation is (Round to one decimal place as needed.) (b) Interpret the results.

Answer 1

X	P(X)	X*P(X)	(X-Mean)^2	P(X)*(X-Mean)^2
0	0.059	0	10.890000	0.64251
1	0.123	0.123	5.290000	0.65067
2	0.162	0.324	1.690000	0.27378
3	0.178	0.534	0.090000	0.01602
4	0.212	0.848	0.490000	0.10388
5	0.129	0.645	2.890000	0.37281
6	0.084	0.504	7.290000	0.61236
7	0.053	0.371	13.690000	0.72557

I have used above table to show the calculation of Mean,Variance and Standard deviation of the probability distribution.

a)Mean(μ) = ∑xP(x) = 0+0.123+0.324+0.534+0.848+0.645+0.505+0.371

   Mean = 3.3

Variance = ∑(x−μ)2P(x) = 0.64251+0.65067+0.27378+0.16002+0.10388+0.37381+0.61236+0.72557

Variance = 3.4

Standard Deviation(σ) = sqrt(variance)= √ 3.4

Standard Deviation = 1.8

b)Both standard deviation and variance are calculated using the mean of a set of numbers concerned. The mean is the average of a group of numbers, and the variance measures the average degree of difference between each number and the mean. The average number of extracurricular activities related to school per student is 3.3.
The variance calculates the average degree at which each point differs from the mean — the sum of all data points. By using the square root of the variance, the average degree of each point varies by mean is 3.4.Standard deviation is a metric that looks at how far from the mean a number group is. Variance calculation uses squares, as it weighs outliers heavier than data closer to the mean. Standard deviation looks at how a group of numbers is distributed from the mean by looking at the square root of the variance. As per this problem, spread of extracurricular activities data is 1.8. Standard deviation seems closer to the mean.