Standard Deviation Problems

1Find the standard deviation for the following data series:

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

2Find the standard deviation for the following series of numbers:

2, 3, 6, 8, 11.

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

3Find the standard deviation for the series:

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

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

4Given the statistical distribution of the table.

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

Calculate the standard deviation.

5A 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.

6The 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:

1. The standard deviation.

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

7Given 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.


1

Find the standard deviation for the following data series:

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


Standard Deviation Operations

Standard Deviation Operations

Standard Deviation Solution


2

Find the standard deviation for the following series of numbers:

2, 3, 6, 8, 11.

Standard Deviation Operations

Standard Deviation Problems

Standard Deviation

Standard Deviation


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

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varianza

Standard Deviation

Standard Deviation


3

Find the standard deviation for the series:

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


Standard Deviation Operations

Standard Deviation Operations

Standard Deviation

Standard Deviation Exercise


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

Standard Deviation Operations

Standard Deviation

Standard Deviation

Standard Deviation Solution


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 xi2 · 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 Operations

Standard Deviation Operations

Standard Deviation

Standard Deviation


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 xi2 · 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 Operations

Standard Deviation Operations

Standard Deviation

Standard Deviation Solution


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 xi2 · 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

Standard Deviation Operations

1

Standard Deviation Operations

2

x + σ = 1.866+ 0.077 = 1.943

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

Standard Deviation Operations

Standard Deviation Operations

There are only 3 players above x + σ.


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 xi2 · 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

Standard Deviation Operations

Standard Deviation Problem




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