Exercise 1

Find the standard deviation for the following data series:

12, 6, 7, 3, 15, 10, 18, 5.

Exercise 2

Find the standard deviation for the following series of numbers:

2, 3, 6, 8, 11.

12, 6, 7, 3, 15, 10, 18, 5.

Exercise 3

Find the standard deviation for the series:

3, 5, 2, 7, 6, 4, 9.

3, 5, 2, 7, 6, 4, 9, 1.

Exercise 4

Given the statistical distribution of the table.

xi 61 64 67 70 73
fi 5 18 42 27 8

Calculate the standard deviation.

Exercise 5

A statistical distribution is given by the following table:

  [10, 15) [15, 20) [20, 25) [25, 30) [30, 35)
fi 3 5 7 4 2

Calculate the standard deviation.

Exercise 6

The heights of the players (in centimeters) from a basketball team are represented by the table:

Height [170, 175) [175, 180) [180, 185) [185, 190) [190, 195) [195, 2.00)
No. of players 1 3 4 8 5 2

Calculate:

Exercise 1.

The standard deviation.

Exercise 2.

How many players are above the mean plus one standard deviation?

Exercise 7

Given the absolute cumulative frequency table:

Age Fi
[0, 2) 4
[2, 4) 11
[4, 6) 24
[6, 8) 34
[8, 10) 40

Calculate the standard deviation.

Solution of exercise 1

Find the standard deviation for the following data series:

12, 6, 7, 3, 15, 10, 18, 5.

Solution of exercise 2

Find the standard deviation for the following series of numbers:

2, 3, 6, 8, 11.

Standard Deviation

12, 6, 7, 3, 15, 10, 18, 5.

Standard Deviation

Solution of exercise 3

Find the standard deviation for the series:

3, 5, 2, 7, 6, 4, 9.

Standard Deviation

3, 5, 2, 7, 6, 4, 9, 1.

Standard Deviation

Solution of exercise 4

Given the statistical distribution of the table.

xi 61 64 67 70 73
fi 5 18 42 27 8

Calculate standard deviation.

xi fi xi · fi x · fi
61 5 305 18 065
64 18 1152 73 728
67 42 2814 188 538
71 27 1890 132 300
73 8 584 42 632
  100 6745 455 803

Standard Deviation

Solution of exercise 5

A statistical distribution is given by the following table:

  [10, 15) [15, 20) [20, 25) [25, 30) [30, 35)
fi 3 5 7 4 2

Calculate the standard deviation.

  xi fi xi · fi x · fi
[10, 15) 12.5 3 37.5 468.75
[15, 20) 17.5 5 87.5 1537.3
[20, 25) 22.5 7 157.5 3543.8
[25, 30) 27.5 4 110 3025
[30, 35) 32.5 2 65 2112.5
    21 457.5 10681.25

Standard Deviation

Solution of exercise 6

The heights of the players (in centimeters) from a basketball team are represented by the table:

Height [170, 175) [175, 180) [180, 185) [185, 190) [190, 195) [195, 2.00)
No. of players 1 3 4 8 5 2

Calculate:

3. The standard deviation.

4. How many players are above the mean plus one standard deviation?

  xi fi Fi xi · fi x · fi
[1.70, 1.75) 1.725 1 1 1.725 2.976
[1.75, 1.80) 1.775 3 4 5.325 9.453
[1.80, 1.85) 1.825 4 8 7.3 13.324
[1.85, 1.90) 1.875 8 16 15 28.128
[1.90, 1.95) 1.925 5 21 9.625 18.53
[1.95, 2.00) 1.975 2 23 3.95 7.802
    23   42.925 80.213

1

2

x + σ = 1.866+ 0.077 = 1.943

This value belongs to a percentile that is in the penultimate interval.

There are only 3 players above x + σ.

Solution of exercise 7

Given the absolute cumulative frequency table:

Edad Fi
[0, 2) 4
[2, 4) 11
[4, 6) 24
[6, 8) 34
[8, 10) 40

1. Calculate the arithmetic mean and standard deviation.

2. Calculate the difference between the values that are the 10 central ages?

3. Create the respective absolute cumulative frequency polygon.

  xi fi Fi xi · fi x · fi
[0, 2) 1 4 4 4 4
[2, 4) 3 7 11 21 63
[4, 6) 5 13 24 65 325
[6, 8) 7 10 34 70 490
[8, 10) 9 6 40 54 486
    40   214 1368

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Emma

I am passionate about travelling and currently live and work in Paris. I like to spend my time reading, gardening, running, learning languages and exploring new places.

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