# Problems of Frequency Tables and Charts

## Exercise 1

Classify the following variables

- Daily hours of exercise.
- Nationality.
- Blood pressure.
- Severity of illness.
- Number of sport injuries in a year.
- Daily calorie intake.
- Size of clothing.
- Subjects passed in a course.

- Quantitative continuous.
- Qualitative nominal.
- Quantitative continuous.
- Qualitative ordinal.
- Quantitative discrete.
- Quantitative continuous.
- Qualitative ordinal.
- Quantitative discrete.

## Exercise 2

The number of injuries suffered by the members of a soccer team in a league were

```
0 1 2 1 3 0 1 0 1 2 0 1 1 1 2 0 1 3 2 1 2 1 0 1
```

Compute:

- Construct the frequency distribution table of the sample.
- Draw the bar chart of the sample and the polygon.
- Draw the cumulative frequency bar chart and polygon.

Injuries | $n_i$ | $f_i$ | $N_i$ | $F_i$ |
---|---|---|---|---|

0 | 6 | 0.2500 | 6 | 0.2500 |

1 | 11 | 0.4583 | 17 | 0.7083 |

2 | 5 | 0.2083 | 22 | 0.9167 |

3 | 2 | 0.0833 | 24 | 1.0000 |

## Exercise 3

A survey about the daily number of medicines consumed by people over 70 shows the following results:

```
3 1 2 2 0 1 4 2 3 5 1 3 2 3 1 4 2 4 3 2 3 5 0 1 2 0 2 3 0 1 1 5 3 4 2 3 0 1 2 3
```

- Construct the frequency distribution table of the sample.
- Draw the bar chart of the sample and the polygon.
- Draw the cumulative relative frequency bar chart and polygon.

Medicines | $n_i$ | $f_i$ | $N_i$ | $F_i$ |
---|---|---|---|---|

1 | 8 | 0.200 | 13 | 0.325 |

2 | 10 | 0.250 | 23 | 0.575 |

3 | 10 | 0.250 | 33 | 0.825 |

4 | 4 | 0.100 | 37 | 0.925 |

5 | 3 | 0.075 | 40 | 1.000 |

## Exercise 4

In a survey about the dependency of older people, 23 persons over 75 years were asked about the help they need in daily life. The answers were

```
B D A B C C B C D E A B C E A B C D B B A A B
```

where the meanings of letters are:

A No help. B Help climbing stairs. C Help climbing stairs and getting up from a chair or bed. D Help climbing stairs, getting up and dressing. E Help for almost everything.

Construct the frequency distribution table and a suitable chart.

Help | $n_i$ | $f_i$ | $N_i$ | $F_i$ |
---|---|---|---|---|

A | 5 | 0.2174 | 5 | 0.2174 |

B | 8 | 0.3478 | 13 | 0.5652 |

C | 5 | 0.2174 | 18 | 0.7826 |

D | 3 | 0.1304 | 21 | 0.9130 |

E | 2 | 0.0870 | 23 | 1.0000 |

## Exercise 5

The number of people treated in the emergency service of a hospital every day of November was

```
15 23 12 10 28 7 12 17 20 21 18 13 11 12 26 30 6 16 19 22 14 17 21 28 9 16 13 11 16 20
```

- Construct the frequency distribution table of the sample.
- Draw a suitable chart for the frequency distribution.
- Draw a suitable chart for the cumulative frequency distribution.

People | $n_i$ | $f_i$ | $N_i$ | $F_i$ |
---|---|---|---|---|

[5,10] | 4 | 0.1333 | 4 | 0.1333 |

(10,15] | 9 | 0.3000 | 13 | 0.4333 |

(15,20] | 9 | 0.3000 | 22 | 0.7333 |

(20,25] | 4 | 0.1333 | 26 | 0.8667 |

(25,30] | 4 | 0.1333 | 30 | 1.0000 |

## Exercise 6

The following frequency distribution table represents the distribution of time (in min) required by people attended in a medical dispensary.

$$ \begin{array}{|c|c|c|c|c|} \hline \mbox{Time} & n_{i} & f_{i} & N_{i} & F_{i}\newline \hline \left[ 0,5\right) & 2 & & & \newline \hline \left[ 5,10\right) & & & 8 & \newline \hline \left[ 10,15\right) & & & & 0.7 \newline \hline \left[ 15,20\right) & 6 & & &\newline \hline \end{array} $$

- Complete the table.
- Draw the ogive.

$$ \begin{array}{|c|c|c|c|c|} \hline \mbox{Time} & n_{i} & f_{i} & N_{i} & F_{i}\newline \hline \left[ 0,5\right) & 2 & 0.1 & 2 & 0.1 \newline \hline \left[ 5,10\right) & 6 & 0.3 & 8 & 0.4 \newline \hline \left[ 10,15\right) & 6 & 0.3 & 14 & 0.7 \newline \hline \left[ 15,20\right) & 6 & 0.3 & 20 & 1\newline \hline \end{array} $$

## Exercise 7

The following table represents the frequency distribution of the yearly uses of a health insurance in a sample of clients of a insurance company.

uses | clients |
---|---|

0 | 4 |

1 | 8 |

2 | 6 |

3 | 3 |

4 | 2 |

5 | 1 |

7 | 1 |

Draw the box plot. Study the symmetry of the distribution.

## Exercise 8

The box plots below correspond to the age of a sample of people by marital status.

- Which group has higher ages?
- Which group has lower central dispersion?
- Which groups have outliers?
- At which group is the age distribution more asymmetric?

- Widowers.
- Divorced.
- Widowers and divorced.
- Divorced.