# relfreq: Interpretation of Relative Frequency Tables

Exercise template for assessing the interpretation of a table with relative frequencies where either total, row, or column frequencies are selected randomly.

**Name:**

`relfreq`

**Type:**

**Preview:**

In a small city the satisfaction with the local public transportation is evaluated. One question of interest is whether inhabitants of the city are more satisfied with public transportation compared to those living in the suburbs.

A survey with 250 respondents gave the following contingency table:

```
Location
Evaluation City Suburbs
Very good 19 11
Good 45 31
Bad 25 66
Very bad 11 42
```

The following table of percentages was constructed:

```
Location
Evaluation City Suburbs
Very good 19.0 7.3
Good 45.0 20.7
Bad 25.0 44.0
Very bad 11.0 28.0
```

Which of the following statements are correct?

In the percentage table, the column sums are about 100 (except for possible rounding errors). Hence, the table provides column percentages, i.e., conditional relative frequencies for satisfaction level given location type.

- True. This is the correct interpretation for column percentages.
- False. The row sums are not equal to 100.
- False. This calculation yields total percentages. But the table provides column percentages.
- False. This is an interpretation for row percentages, but the table provides column percentages.
- True. The column sums are equal to 100 (except for possible rounding errors).

In a small city the satisfaction with the local public transportation is evaluated. One question of interest is whether inhabitants of the city are more satisfied with public transportation compared to those living in the suburbs.

A survey with 250 respondents gave the following contingency table:

```
Location
Evaluation City Suburbs
Very good 19 17
Good 44 22
Bad 27 60
Very bad 10 51
```

The following table of percentages was constructed:

```
Location
Evaluation City Suburbs
Very good 19.0 11.3
Good 44.0 14.7
Bad 27.0 40.0
Very bad 10.0 34.0
```

Which of the following statements are correct?

In the percentage table, the column sums are about 100 (except for possible rounding errors). Hence, the table provides column percentages, i.e., conditional relative frequencies for satisfaction level given location type.

- True. This is the correct interpretation for column percentages.
- False. This calculation yields row percentages. But the table provides column percentages.
- True. This is the correct interpretation for column percentages.
- True. The column sums are equal to 100 (except for possible rounding errors).
- False. The row sums are not equal to 100.

In a small city the satisfaction with the local public transportation is evaluated. One question of interest is whether inhabitants of the city are more satisfied with public transportation compared to those living in the suburbs.

A survey with 250 respondents gave the following contingency table:

```
Location
Evaluation City Suburbs
Very good 18 17
Good 48 31
Bad 24 67
Very bad 10 35
```

The following table of percentages was constructed:

```
Location
Evaluation City Suburbs
Very good 7.2 6.8
Good 19.2 12.4
Bad 9.6 26.8
Very bad 4.0 14.0
```

Which of the following statements are correct?

In the percentage table, the total sums are about 100 (except for possible rounding errors). Hence, the table provides total percentages, i.e., the relative frequencies for each combination of location type and satisfaction level.

- False. The row sums are not equal to 100.
- True. This is the correct interpretation for total percentages.
- False. This is an interpretation for row percentages, but the table provides total percentages.
- False. The column sums are not equal to 100.
- False. This calculation yields row percentages. But the table provides total percentages.

**Description:**

**Solution feedback:**

**Randomization:**

**Mathematical notation:**

**Verbatim R input/output:**

**Images:**

**Other supplements:**

**Demo code:**

```
library("exams")
set.seed(403)
exams2html("relfreq.Rmd")
set.seed(403)
exams2pdf("relfreq.Rmd")
set.seed(403)
exams2html("relfreq.Rnw")
set.seed(403)
exams2pdf("relfreq.Rnw")
```