Chapters

- Exercise 1
- Exercise 2
- Exercise 3
- Exercise 4
- Exercise 5
- Exercise 6
- Exercise 1.
- Exercise 2.
- Exercise 7
- Solution of exercise 1
- Solution of exercise 2
- Standard Deviation
- Standard Deviation
- Solution of exercise 3
- Standard Deviation
- Standard Deviation
- Solution of exercise 4
- Standard Deviation
- Solution of exercise 5
- Standard Deviation
- Solution of exercise 6
- 1
- 2
- Solution of exercise 7

## 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.

x_{i } | 61 | 64 | 67 | 70 | 73 |

f_{i} | 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) | |

f_{i} | 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 | F_{i} |

[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.

x_{i } | 61 | 64 | 67 | 70 | 73 |

f_{i} | 5 | 18 | 42 | 27 | 8 |

Calculate standard deviation.

x_{i } | f_{i} | x_{i} · f_{i} | x_{i² } · f_{i } |

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) | |

f_{i} | 3 | 5 | 7 | 4 | 2 |

Calculate the standard deviation.

x_{i } | f_{i} | x_{i} · f_{i} | x_{i² } · f_{i } | |

[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?

x_{i } | f_{i } | F_{i } | x_{i} · f_{i} | x_{i² } · f_{i } | |

[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 | F_{i} |

[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.

x_{i } | f_{i} | F_{i} | x_{i} · f_{i} | x_{i² } · f_{i } | |

[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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