# Lesson Worksheet: Statistical Analysis Mathematics

In this worksheet, we will practice choosing the suitable measure of central tendency to represent data, finding the margin of sampling error, and using the measure of variation to compare between sets of data.

**Q1: **

What is the denominator in the calculation of population standard deviation for a data set with items?

- A
- B
- C
- D
- E

**Q2: **

Which of the following sets of data has a mode of 48 and a median of 20?

- A20, 48, 48, 11, 11, 19
- B10, 16, 19, 21, 47, 47
- C48, 21, 11, 48, 20, 17
- D47, 47, 11, 48, 20, 17
- E21, 48, 19, 48, 17, 11

**Q3: **

Faisal wants to find out the average age of people who go swimming on a Saturday morning. He records the following data on a particular Saturday morning: 5, 12, 24, 19, 64, 38, 71, 13, 14, 41, 3.

Calculate the mean of the data giving your answer accurate to one decimal place.

Calculate the median of the data.

Calculate the mode of the data.

- A27.6
- B3
- C71
- D19
- EThere is no mode.

Calculate the range of the data.

**Q4: **

What does high sample variability mean?

- AThe means of the samples have large values.
- BA large variety of methods have been used to generate the samples.
- CGiven multiple samples from the same population, we should expect the sample statistics, for example, the calculated means, to have largely different values.
- DThere is a large number of samples.

**Q5: **

Using the data given in the table, calculate the standard deviation of the ages. Give your answer to three decimal places.

Ages (years) | 5 | 8 | 10 | 12 | 15 |
---|---|---|---|---|---|

Number of Students | 1 | 9 | 8 | 9 | 8 |

**Q6: **

Data Set 1 | 1 | 7 | 10 | 9 | 8 | 2 | 2 | 1 |
---|---|---|---|---|---|---|---|---|

Data Set 2 | 3 | 7 | 8 | 6 | 5 | 4 | 4 | 3 |

Calculate, to the nearest hundredth, the sample standard deviation for each data set.

- Adata set 1: 14.86, data set 2:3.43
- Bdata set 1: 3.85, data set 2: 1.85
- Cdata set 1: 3.61, data set 2: 1.73
- Ddata set 1: 1.85, data set 2: 3.85
- Edata set 1: 13.00, data set 2:3.00

What do these values reveal about the two data sets?

- AThe spread of the two data sets is very similar.
- BData set 2 is more widely spread than data set 1.
- CData set 2 is more variable than data set 1.
- DData set 1 is more widely spread than data set 2.
- EThe distributions of the two data sets are very similar.

**Q7: **

In general, what does a larger value of σ mean?

- AThe data is less spread out.
- BThe mean of the data is smaller.
- CThe data is more spread out.
- DThe mean of the data is larger.
- EThe median is larger than the mean.

**Q8: **

Using the data given in the table, calculate the standard deviation of the number of children. If necessary, give your answer to three decimal places.

Number of Children | 1 | 2 | 3 | 4 | 5 |
---|---|---|---|---|---|

Number of Families | 15 | 26 | 3 | 28 | 14 |

**Q9: **

The data set shown contains a potentially outlying value of 32. What effect would removing this value have on the standard deviation?

12 | 15 | 13 | 11 | 32 | 13 | 9 | 19 |

- AThe standard deviation would decrease.
- BThe standard deviation would increase.
- CThe standard deviation would not change.

**Q10: **

Calculate, to the nearest hundredth, the sample standard deviation for each of the shown data sets.

Data Set 1 | 25 | 22 | 28 | 51 | 26 | 28 | 29 | 32 |
---|---|---|---|---|---|---|---|---|

Data Set 2 | 21 | 27 | 19 | 26 | 24 | 23 | 28 | 25 |

- Adata set 1: , data set 2:
- Bdata set 1: , data set 2:
- Cdata set 1: , data set 2:
- Ddata set 1: , data set 2:
- Edata set 1: , data set 2:

Which of these statements helps explain the large difference between the sample standard deviations for the two data sets?

- AThe lowest value is in data set 2, so this makes the standard deviation smaller.
- BThe single large value of 51 in data set 1 causes the standard deviation to increase significantly.
- CThe median of data set 1 is greater, which explains why the standard deviation is greater.
- DThe mode of data set 1 value of 28 causes the standard deviation to increase significantly.
- EThe mean of data set 1 is greater, which explains why the standard deviation is greater.