# Typologies, Indexes and Scales

## 15 important questions on Typologies, Indexes and Scales

### Which of the measures of central tendency is most informative for the variable polintr?

This is an ordinal variable and the most informative measure of central tendency for this type of variable is the median.

### Which of the measures of central tendency is most informative to summarize the results for the question?

This is a nominal variable, so only the mode makes sense.

### The ages of eight participants in a course: 35, 20, 20, 17, 33, 27, 31, 28

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### Where in the boxplot for variable V1 do you find the middle 50% of the observations?

### The ages of seven participants in a course: 35, 20, 20, 15, 30, 25, 30

Question

What is the (sample) standard deviation of these data?

Deviations from the mean are 10, 5, 5, 10, 0, 5, 5

Squared deviations are 100, 25, 25, 100, 0 , 25, 25

Summed squared deviations is 300

300 divided by the number of observations -1 = 50

Square root from 50 is about 7,1.

### Given

A study director wants to know which students should be enrolled in a 'star' program and which students need more support to finish the studies with much delay. He wants to compare a students’ grades in various courses. However, the teachers of the courses have used different ranges of grades (1-10 and 4-8) and the mean grades for the courses differ substantially.

**Question**

What can the study director do, to see whether some students are scoring systematically better or worse than other students? The study director should for each course grade...

subtract the mean score for that course and divide that outcome by the standard deviation of the grades for that course

### In the methods test, the student scored a 9. The mean score for the methods test is 7, the standard deviation of that test is 1.

In the statistics test, the student scored a 6. The mean score for the statistics test is 5,5, the standard deviation of that test is 2.

Question

What were the z-scores of this student?

### Two statements:

I. In normal distributions, the mean, median, and mode are equal.

II. Beyond -10 sd and + 10 sd from the mean, normal distributions are zero

Question

Which of these two statement(s) is/are correct?

in the normal distribution, the mode, median and mean are identical. Indeed, the normal distribution is never 'zero' (although it becomes extremely small).

### Given:

A normal distribution of a variable with µ = 0 and σ = 1.

Question:

what is the chance of finding an observation with a score lower than - 1,96?

How do you construct and interpret a bivariate table to test a bivariate hypothesis about the relationship between two dichotomies?

Dependent variable in the rows, independent variable in the columns, computing column percentages and comparing the percentages of two horizontally adjacent cells

### What type of data visualisation would you use to display the relationship between a ratio variable (a dependent variable) and a nominal variable?

A few box plots:

one for each of the values of the nominal variable is a nice way to display these data.

What would you conclude about the relationship between the two dichotomies shown in this table?

Relationship is positive, the effect is 20 percent points

The relationship between two nominal variables is to be examined. Which one of the following instruments could be used for this purpose?

### Which one of the following statements regarding Pearson’s correlation coefficient estimated for the relationship between X and Y is true?

There is a pattern, but it results in a Pearson correlation-coefficient close to zero

### Given

A researcher is interested in the effect of eating bread on the energy level among Dutch adults. He studies this relationship using a sample of Dutch individuals aged between 18 and 67.

Question

What is the main problem with the sample above, given the topic the researcher is interested in?

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