# Worksheet: Variance and Standard Deviation

In this worksheet, we will practice finding and interpreting the variance and the standard deviation.

**Q3: **

The table shows the distribution of goals scored in the first half of a football season.

Number of Goals | 0 | 1 | 3 | 4 | 6 |
---|---|---|---|---|---|

Number of Matches | 5 | 2 | 7 | 7 | 4 |

Find the standard deviation of the number of goals scored. Give your answer to three decimal places.

**Q5: **

Without calculating the exact standard deviations, determine which of the following datasets has the highest standard deviation.

- A100, 200, 300, 400, 500, 500
- B3, 31, 53, 63, 63, 63
- C1,000, 2,000, 3,000, 4,000, 5,000, 6,000
- D10, 10, 10, 10, 10, 11
- E100, 100, 100, 100, 100, 100

**Q6: **

What is the name of a quantity expressing by how much the members of a group differ from the mean value for the group?

- Astandard deviation
- Bmedian
- Carithmetic mean
- Drange

**Q7: **

Michael has gathered in the table below his last jogging times in minutes.

96 | 97 | 98 | 100 | 101 | 108 | 81 | 114 | 83 | 116 |

85 | 113 | 119 | 120 | 86 | 89 | 91 | 87 | 94 |

If the jogging times were converted into hours, what would be the variance of the data set? Give your answer correct to two decimal places.

**Q8: **

The table represents the time, in minutes, that several people took to finish a race.

100 | 101 | 104 | 106 | 109 | 110 | 112 | 113 | 82 | 115 |

116 | 117 | 86 | 119 | 120 | 87 | 90 | 91 | 89 |

If the data was instead given in hours, calculate its standard deviation to two decimal places.

**Q9: **

Calculate the standard deviation of the values . Give your answer to three decimal places.

**Q10: **

Find, to two decimal places, the variance of the following scores obtained in a quiz by 92 students.

Score | 0–20 | 20–40 | 40–60 | 60–80 | 80–100 |
---|---|---|---|---|---|

Frequency | 26 | 10 | 24 | 5 | 27 |

**Q12: **

By calculating the standard deviation, determine which of the sets , , or has the largest dispersion.

- A
- B
- C

**Q13: **

Determine (without calculating the standard deviation exactly) which of the following data sets has the lowest standard deviation.

- A100, 200, 300, 400, 500, 600
- B0, 18, 37, 49, 49, 49
- C50, 50, 50, 50, 50, 1,000
- D149, 149, 149, 149, 149, 150
- E10, 20, 30, 40, 50, 60

**Q14: **

Without calculating exact standard deviation values, determine which of the following data sets has the highest standard deviation.

- A75, 75, 75, 75, 75, 75
- B900, 1,800, 2,700, 3,600, 4,500, 5,400
- C10, 20, 30, 40, 50, 50
- D18, 31, 32, 55, 55, 55
- E144, 144, 144, 144, 144, 145

**Q15: **

The set of data 47, 51, 47, 51, 47, 51, 47, 51, 47, 51 has a mean of 49. Use this to decide (without calculating the exact answer) which of the following is closest to the standard deviation of the data.

- A10
- B2
- C1
- D5

**Q16: **

Using the given table and assuming an approximate normal distribution of grades in both schools, determine which student has the higher grade when compared to his school peers.

Student | GPA | School Mean GPA | Standard Deviation |
---|---|---|---|

Daniel | 3.02 | 2.85 | 0.29 |

William | 2.37 | 2.88 | 0.59 |

- ADaniel
- BWilliam

**Q17: **

If the dispersion of a set of values is equal to zero, then which of the following are true?

- AThe difference between the individuals is great.
- BAll the values are equal.
- CThe difference between the individuals is small.
- DThe arithmetic mean of these values is zero.
- EAll the values are negative.