Types of Data Summary and Data Presentation

Question 1

What is term given to the data generated by an unordered categorical variable?

Answer 1

Nominal data

Question 2

What is the term given to the data generated by an ordered categorical variable?

Answer 2

Ordinal data

Question 3

What is a quantitative variable?

Answer 3

Represents a quantity which is counted or measured numerically (may be discrete or continuous)

Question 4

How do we visualise categorical data?

Answer 4

Bar chart or pie chart

Question 5

How do we visualise quantitative data?

Answer 5

Histogram or frequency polygon

Question 6

Key points about histograms

Answer 6

The x (horizontal) axis must be uniform with no breaks, and there are no spaces between the bars.

The y (vertical) axis always begins at zero - this is important because relative comparisons are being made.

The area of each bar represents the frequency (or relative frequency) in each group.

The width of each bar is the size of the interval for each group.

Question 7

Describe the properties of the mean

Answer 7

The mean is sensitive to outliers; the others are not. For example, a single data point with a very high value may increase the mean by an appreciable amount.

Question 8

Describe the mode

Answer 8

The mode may be affected by small changes in the data; the others are not. If two data values are almost equally common, slight changes in the data may affect which is the mode.

Question 9

Describe the mode

Answer 9

he mode and median may be found graphically. For example, the median can be found from a cumulative frequency plot.

Question 10

Describe the properties of mean, mode and median in symmetric versus skewed data

Answer 10

All three measures of location are equal for a symmetric distribution; in a skewed distribution they differ (see Figure 10).

Question 11

What is the better measure of location for skewed data?

Answer 11

Median

Question 12

What is the better measure of location for statistical analysis and inference?

Answer 12

Mean

Question 13

What is the best measure of location for significantly skewed data?

Answer 13

Transformations or non-parametric techniques

Question 14

List three ways to summarise the variability of a set of data

Answer 14

Range
Percentiles
Standard deviation

Question 15

What are the issues with using range as a measure of spread?

Answer 15

Reports extreme values and can only increase with sample size (unlike SD)

Question 16

What is the value of the average deviation?

Answer 16

Zero (mathematical certainty)

Question 17

What is the variance?

Answer 17

A measure of average deviation from the mean

Question 18

Why is n-1 used in the calculation of the variance/SD?

Answer 18

It is an accurate unbiased estimator (especially for small samples)

Question 19

What proportion of data lies within one standard deviation of the mean in a normally distributed dataset ?

Answer 19

68%

Question 20

What proportion of data lies within two standard deviations of the mean in a normally distributed dataset ?

Answer 20

95%

Question 21

What proportion of data lies within three standard deviations of the mean in a normally distributed dataset ?

Answer 21

99%