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Standard Deviation (Tabular Method) in Real World Problems: Worksheets, Online Test and Calculators

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Standard Deviation (Tabular Method) in Real World Problems

Name Grade School
Date Questions10 Score
1
Find the sample standard deviation of the following data. 8, 5, 2, 4, 10, 1, 7, 3, 6 and 9
2
Find the population standard deviation of the following data. 6, 8, 10, 12, 14, 16, 18, 20, 22 and 24
3
A teacher asked the students to complete 60 pages of a record notebook. Eight students have completed only 32, 35, 37, 30, 33, 36, 35 and 37 pages. Find the standard deviation of the pages yet to be completed by them.
4
Find the standard deviation of the wages of 9 workers given in ₹: 310, 290, 320, 280, 300, 290, 320, 310 and 280
5
Find the standard deviation of the first 10 natural numbers.
6
The amount of rainfall in a particular season for 6 days are given in centimeter are 17.8, 19.2, 16.3, 12.5, 12.8 and 11.4. Find its standard deviation.
7
Find the standard deviation of the average temperatures recorded over a five-day period last winter in celcius: 18, 22, 19, 25 and 12
8
Find the standard deviation of the highest temperatures recorded in eight specific states in celcius: 112, 100, 127, 120, 134, 118, 105 and 110
9
Find the standard deviation of the scores on the most recent reading test: 7.7, 7.4, 7.3 and 7.9
10
During a survey, 6 students were asked how many hours per day they study on an average? Their answers were as follows: 2, 6, 5, 3, 2 and 3. Evaluate the standard deviation.

Answers Key
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1
Find the sample standard deviation of the following data. 8, 5, 2, 4, 10, 1, 7, 3, 6 and 9
Sample Standard Deviation is 3.03
Solution

s=√∑ni=1(𝑥i − x̄)2(n-1)
where s = Sample Standard Deviation,
𝑥i = Terms Given in the Data,
x̄ = Mean,
n = Total number of Terms

xi(𝑥i − x̄)(𝑥i − x̄)2
82.56.25
5-0.50.25
2-3.512.25
4-1.52.25
104.520.25
1-4.520.25
71.52.25
3-2.56.25
60.50.25
93.512.25
∑𝑥i = 55∑(𝑥i − x̄)2 = 82.5
x̄ = 55/10 = 5.5

s=√∑ni=1(𝑥i − x̄)2(n-1)
s = √82.5(10 - 1)
s = √82.59
s = √9.17

∴ Sample Standard Deviation, s = 3.03
2
Find the population standard deviation of the following data. 6, 8, 10, 12, 14, 16, 18, 20, 22 and 24
Population Standard Deviation is 5.74
Solution

σ=√∑ni=1(𝑥i − μ)2N
where σ = Population Standard Deviation,
𝑥i = Terms Given in the Data,
μ = Mean,
N = Total number of Terms

xi(𝑥i − μ)(𝑥i − μ)2
6-981
8-749
10-525
12-39
14-11
1611
1839
20525
22749
24981
∑𝑥i = 150∑(𝑥i − μ)2 = 330
x̄ = 150/10 = 15


σ=√∑ni=1(𝑥i − μ)2N
σ = √33010
σ = √33
∴ Population Standard Deviation, σ = 5.74
3
A teacher asked the students to complete 60 pages of a record notebook. Eight students have completed only 32, 35, 37, 30, 33, 36, 35 and 37 pages. Find the standard deviation of the pages yet to be completed by them.
Standard Deviation is 2.34
Solution

σ=√∑ni=1(𝑥i − μ)2N
where σ = Population Standard Deviation,
𝑥i = Terms Given in the Data,
μ = Mean,
N = Total number of Terms

xi(𝑥i − μ)(𝑥i − μ)2
32-2.385.664
350.620.384
372.626.864
30-4.3819.184
33-1.381.904
361.622.624
350.620.384
372.626.864
∑𝑥i = 275∑(𝑥i − μ)2 = 43.878
x̄ = 275/8 = 34.38


σ=√∑ni=1(𝑥i − μ)2N
σ = √43.8788
σ = √5.485
∴ Population Standard Deviation, σ = 2.34
4
Find the standard deviation of the wages of 9 workers given in ₹: 310, 290, 320, 280, 300, 290, 320, 310 and 280
Standard Deviation is 14.91
Solution

σ=√∑ni=1(𝑥i − μ)2N
where σ = Population Standard Deviation,
𝑥i = Terms Given in the Data,
μ = Mean,
N = Total number of Terms

xi(𝑥i − μ)(𝑥i − μ)2
31010100
290-10100
32020400
280-20400
30000
290-10100
32020400
31010100
280-20400
∑𝑥i = 2700∑(𝑥i − μ)2 = 2000
x̄ = 2700/9 = 300


σ=√∑ni=1(𝑥i − μ)2N
σ = √20009
σ = √222.222
∴ Population Standard Deviation, σ = 14.91
5
Find the standard deviation of the first 10 natural numbers.
Standard Deviation is 2.87
Solution

σ=√∑ni=1(𝑥i − μ)2N
where σ = Population Standard Deviation,
𝑥i = Terms Given in the Data,
μ = Mean,
N = Total number of Terms

xi(𝑥i − μ)(𝑥i − μ)2
1-4.520.25
2-3.512.25
3-2.56.25
4-1.52.25
5-0.50.25
60.50.25
71.52.25
82.56.25
93.512.25
104.520.25
∑𝑥i = 55∑(𝑥i − μ)2 = 82.5
x̄ = 55/10 = 5.5


σ=√∑ni=1(𝑥i − μ)2N
σ = √82.510
σ = √8.25
∴ Population Standard Deviation, σ = 2.87
6
The amount of rainfall in a particular season for 6 days are given in centimeter are 17.8, 19.2, 16.3, 12.5, 12.8 and 11.4. Find its standard deviation.
Standard Deviation is 2.92
Solution

σ=√∑ni=1(𝑥i − μ)2N
where σ = Population Standard Deviation,
𝑥i = Terms Given in the Data,
μ = Mean,
N = Total number of Terms

xi(𝑥i − μ)(𝑥i − μ)2
17.82.87.84
19.24.217.64
16.31.31.69
12.5-2.56.25
12.8-2.24.84
11.4-3.612.96
∑𝑥i = 90∑(𝑥i − μ)2 = 51.22
x̄ = 90/6 = 15


σ=√∑ni=1(𝑥i − μ)2N
σ = √51.226
σ = √8.537
∴ Population Standard Deviation, σ = 2.92
7
Find the standard deviation of the average temperatures recorded over a five-day period last winter in celcius: 18, 22, 19, 25 and 12
Standard Deviation is 4.87
Solution

s=√∑ni=1(𝑥i − x̄)2(n-1)
where s = Sample Standard Deviation,
𝑥i = Terms Given in the Data,
x̄ = Mean,
n = Total number of Terms

xi(𝑥i − x̄)(𝑥i − x̄)2
18-1.21.44
222.87.84
19-0.20.04
255.833.64
12-7.251.84
∑𝑥i = 96∑(𝑥i − x̄)2 = 94.8
x̄ = 96/5 = 19.2

s=√∑ni=1(𝑥i − x̄)2(n-1)
s = √94.8(5 - 1)
s = √94.84
s = √23.7

∴ Sample Standard Deviation, s = 4.87
8
Find the standard deviation of the highest temperatures recorded in eight specific states in celcius: 112, 100, 127, 120, 134, 118, 105 and 110
Standard Deviation is 11.3
Solution

s=√∑ni=1(𝑥i − x̄)2(n-1)
where s = Sample Standard Deviation,
𝑥i = Terms Given in the Data,
x̄ = Mean,
n = Total number of Terms

xi(𝑥i − x̄)(𝑥i − x̄)2
112-3.7514.063
100-15.75248.063
12711.25126.563
1204.2518.063
13418.25333.063
1182.255.063
105-10.75115.563
110-5.7533.063
∑𝑥i = 926∑(𝑥i − x̄)2 = 893.504
x̄ = 926/8 = 115.75

s=√∑ni=1(𝑥i − x̄)2(n-1)
s = √893.504(8 - 1)
s = √893.5047
s = √127.64

∴ Sample Standard Deviation, s = 11.3
9
Find the standard deviation of the scores on the most recent reading test: 7.7, 7.4, 7.3 and 7.9
Standard Deviation is 0.28
Solution

s=√∑ni=1(𝑥i − x̄)2(n-1)
where s = Sample Standard Deviation,
𝑥i = Terms Given in the Data,
x̄ = Mean,
n = Total number of Terms

xi(𝑥i − x̄)(𝑥i − x̄)2
7.70.1250.016
7.4-0.1750.031
7.3-0.2750.076
7.90.3250.106
∑𝑥i = 30.3∑(𝑥i − x̄)2 = 0.229
x̄ = 30.3/4 = 7.575

s=√∑ni=1(𝑥i − x̄)2(n-1)
s = √0.229(4 - 1)
s = √0.2293
s = √0.08

∴ Sample Standard Deviation, s = 0.28
10
During a survey, 6 students were asked how many hours per day they study on an average? Their answers were as follows: 2, 6, 5, 3, 2 and 3. Evaluate the standard deviation.
Standard Deviation is 1.64
Solution

s=√∑ni=1(𝑥i − x̄)2(n-1)
where s = Sample Standard Deviation,
𝑥i = Terms Given in the Data,
x̄ = Mean,
n = Total number of Terms

xi(𝑥i − x̄)(𝑥i − x̄)2
2-1.52.25
62.56.25
51.52.25
3-0.50.25
2-1.52.25
3-0.50.25
∑𝑥i = 21∑(𝑥i − x̄)2 = 13.5
x̄ = 21/6 = 3.5

s=√∑ni=1(𝑥i − x̄)2(n-1)
s = √13.5(6 - 1)
s = √13.55
s = √2.7

∴ Sample Standard Deviation, s = 1.64

Worksheet: Standard Deviation (Tabular Method) in Real World Problems

Standard deviation (tabular method) in real world problems worksheet is the largest collection of practice problems and solved exercises which can be served as homework, classwork or assignment problems for the students to learn, practice, assess, iterate and master the skills of how to solve such statistics problems in basic mathematics.

Online Test
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Find the standard deviation of the wages of 9 workers given in Rupees : 321, 263, 279, 262, 344, 326, 325, 331 and 264
The amount of rainfall in a particular season for 6 days are given in centimeter are 19.5, 15.6, 7.9, 19.7, 11.8 and 7.2. Find its standard deviation.
Find the sample standard deviation of the following data. 4, 25, 14, 3, 17, 2, 8, 12, 11 and 23
A teacher asked students to complete 60 pages of a record notebook. Eight students have completed only 33, 36, 34, 40, 35, 31, 30 and 39 pages. Find the standard deviation of the pages yet to be completed.
During a survey, 6 students were asked how many hours per day they study on an average? Their answers were as follows : 5, 3, 8, 9, 2 and 10. Evaluate the standard deviation.
Find the standard deviation of the first 6 natural numbers.
Find the standard deviation of the scores on the most recent reading test : 11.5, 6.8, 19.5, 12.9, 19 and 11.1
Find the population standard deviation of the following data. 25, 21, 19, 5, 7, 1, 20, 6, 11 and 3
Find the standard deviation of the average temperatures recorded over a five-day period last winter in celcius : 16, 13, 24, 12 and 26
Find the standard deviation of the highest temperatures recorded in eight specific states in celcius : 101, 114, 110, 111, 108, 109, 103 and 107
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Online Test: Standard Deviation (Tabular Method) in Real World Problems

This online test to find the standard deviation (tabular method) in real world problems is a formative assessment which can be used as homework, classwork or assignment problems to assess and improve the learner's math skills on statistics.

Standard Deviation Calculator

Calculation for
Mean35
Sample Variance350
Sample Standard Deviation18.708
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Standard deviation calculator is a key tool for users to generate step-by-step work to quickly understand the calculation, solve the homework problems, solve the classwork problems, prepare the answer key document for summative and formative assessments or immediately verify the entire calculation for the user supplied input values.