Introduction to standard deviation practice problems:
The variance of a random variable or distribution is the expectation, or mean, of the deviation squared of that variable from its expected value or mean. ( Source - Wikipedia )
The standard deviation is nothing but the square root of its variance.
In this article of standard deviation practice problems, few example problems for finding standard deviation and several practice problems to find standard deviation are given.
Example Problems to Practice Standard Deviation:
Example 1:
Find the standard deviation for the given set of numbers:
{ 24, 20, 17, 31, 43 }
Solution:
Step 1: Mean
Mean = ` ( 24 + 20 + 17 + 31 + 43 ) / 5`
= ` 135 / 5`
= 27
Step 2: Variance
Variance = `( (24-27)^2 + (29-27)^2 + (17- 27)^2 + (31-27)^2 + (43-27)^2 )/5`
= `( (-3)^2 + (2)^2 + (- 10)^2 + (4)^2 + (16)^2 )/5`
= `(9+4+100+16+256)/5`
= `430/5`
= 86
Step 3:Standard deviation
Standard deviation = `sqrt ( 86 )`
= 9.27
Example 2:
Find the standard deviation for the given set of numbers:
{ 7, 4, 5, 1, 3 }
Solution:
Step 1: Mean
Mean = ` ( 7 + 4 + 5 + 1 + 3 ) / 5`
= ` 20 / 5`
= 4
Step 2: Variance
Variance = `( (7-4)^2 + (4-4)^2 + (5- 4)^2 + (1-4)^2 + (3-4)^2 )/5`
= `( (3)^2 + (0)^2 + (1)^2 + (-3)^2 + (-1)^2 )/5`
= `(9+0+1+9+1)/5`
= `20/5`
= 4
Step 3:Standard deviation
Standard deviation = `sqrt ( 4 )`
= 2
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Practice Problems for Finding Standard Deviation:
1) Find the standard deviation for the set of numbers: { 45, 67, 89, 24 }
2) Find the standard deviation for the data set: { 44, 67, 87, 90, 42 }
3) Find the standard deviation for the set of numbers: { 39, 21, 57, 61, 73 }
4) Find the standard deviation for the data set: { 207, 137, 316, 590 }
5) Find the standard deviation for the set of numbers: { 64, 80, 38, 40, 41 }
6) Find the standard deviation for the data set: { 12, 21, 60, 41 }
7) Find the standard deviation for the set of numbers: { 56, 24, 78, 29, 88 }
8) Find the standard deviation for the data set: { 41, 60, 77, 11, 63 }
9) Find the standard deviation for the set of numbers: { 12, 204, 717, 231 }
10) Find the standard deviation for the data set: { 245, 356, 343, 326, 460 }
11) Find the standard deviation for the set of numbers: { 16, 34, 68, 19, 78 }
12) Find the standard deviation for the data set: { 25, 50, 45, 17, 77 }
13) Find the standard deviation for the set of numbers: { 4, 4, 7, 6, 14 }
14) Find the standard deviation for the data set: { 45, 10, 45, 156, 27 }
15) Find the standard deviation for the set of numbers: { 216, 334, 566, 149 }
Answer key:
1) 24.26 2) 20.39 3) 18.23 4) 172.44 5) 16.66 6) 18.55 7) 25.52 8) 22.80
9) 260.04 10) 68.86 11) 25.44 12) 21.02 13) 3.69 14) 51.38 15) 158.68
The variance of a random variable or distribution is the expectation, or mean, of the deviation squared of that variable from its expected value or mean. ( Source - Wikipedia )
The standard deviation is nothing but the square root of its variance.
In this article of standard deviation practice problems, few example problems for finding standard deviation and several practice problems to find standard deviation are given.
Example Problems to Practice Standard Deviation:
Example 1:
Find the standard deviation for the given set of numbers:
{ 24, 20, 17, 31, 43 }
Solution:
Step 1: Mean
Mean = ` ( 24 + 20 + 17 + 31 + 43 ) / 5`
= ` 135 / 5`
= 27
Step 2: Variance
Variance = `( (24-27)^2 + (29-27)^2 + (17- 27)^2 + (31-27)^2 + (43-27)^2 )/5`
= `( (-3)^2 + (2)^2 + (- 10)^2 + (4)^2 + (16)^2 )/5`
= `(9+4+100+16+256)/5`
= `430/5`
= 86
Step 3:Standard deviation
Standard deviation = `sqrt ( 86 )`
= 9.27
Example 2:
Find the standard deviation for the given set of numbers:
{ 7, 4, 5, 1, 3 }
Solution:
Step 1: Mean
Mean = ` ( 7 + 4 + 5 + 1 + 3 ) / 5`
= ` 20 / 5`
= 4
Step 2: Variance
Variance = `( (7-4)^2 + (4-4)^2 + (5- 4)^2 + (1-4)^2 + (3-4)^2 )/5`
= `( (3)^2 + (0)^2 + (1)^2 + (-3)^2 + (-1)^2 )/5`
= `(9+0+1+9+1)/5`
= `20/5`
= 4
Step 3:Standard deviation
Standard deviation = `sqrt ( 4 )`
= 2
Please express your views of this topic how to convert a decimal to a fraction by commenting on blog.
Practice Problems for Finding Standard Deviation:
1) Find the standard deviation for the set of numbers: { 45, 67, 89, 24 }
2) Find the standard deviation for the data set: { 44, 67, 87, 90, 42 }
3) Find the standard deviation for the set of numbers: { 39, 21, 57, 61, 73 }
4) Find the standard deviation for the data set: { 207, 137, 316, 590 }
5) Find the standard deviation for the set of numbers: { 64, 80, 38, 40, 41 }
6) Find the standard deviation for the data set: { 12, 21, 60, 41 }
7) Find the standard deviation for the set of numbers: { 56, 24, 78, 29, 88 }
8) Find the standard deviation for the data set: { 41, 60, 77, 11, 63 }
9) Find the standard deviation for the set of numbers: { 12, 204, 717, 231 }
10) Find the standard deviation for the data set: { 245, 356, 343, 326, 460 }
11) Find the standard deviation for the set of numbers: { 16, 34, 68, 19, 78 }
12) Find the standard deviation for the data set: { 25, 50, 45, 17, 77 }
13) Find the standard deviation for the set of numbers: { 4, 4, 7, 6, 14 }
14) Find the standard deviation for the data set: { 45, 10, 45, 156, 27 }
15) Find the standard deviation for the set of numbers: { 216, 334, 566, 149 }
Answer key:
1) 24.26 2) 20.39 3) 18.23 4) 172.44 5) 16.66 6) 18.55 7) 25.52 8) 22.80
9) 260.04 10) 68.86 11) 25.44 12) 21.02 13) 3.69 14) 51.38 15) 158.68
