Descriptive Statistics (Lecture 8)

Question 1

What is the aim of descriptive statistics?

Answer 1

To summarise the key features of data to make it understandable for humans, identifying characteristics/patterns.

Question 2

What are our measures of central tendency?

Answer 2

Mean (x̄)
Median (M)
Mode (Z)

Question 3

What are our measures of dispersion?

Answer 3

Interquartile Range (IQR)
Variance
Standard Deviation (SD)

Question 4

What are our measures of association?

Answer 4

Chi-Squared (2)
Correlation (r)

Question 5

What’s the central tendency?

Answer 5

A single number that aims to represents the ‘typical’
value of a variable (the average), somewhere between the highest and lowest value of the observations.

Question 6

What’s the mean?

Answer 6

Calculated by summing all values of a variable and dividing by the number of observations.

Question 7

What’s the Median (M)

Answer 7

The middle value when the values of a variable are arranged in order of smallest-largest.

Question 8

What’s the Mode (Z)?

Answer 8

The most commonly occurring value (may be more than one mode for a single variable)

Question 9

What data is the mean used for?

Answer 9

Ordinal and scale data

Question 10

What data is the Median used for?

Answer 10

Ordinal and scale data

Question 11

What data is the Mode used for?

Answer 11

Nominal data

Question 12

What data is the mode useful for?

Answer 12

Categorical data

Question 13

What two types of visuals are used for illustrating the central tendency?

Answer 13

Bar charts (for categorical data) and histograms (for continuous data)

Question 14

What type of data are bar charts used for?

Answer 14

Categorical data

Question 15

What type of data are histograms used for?

Answer 15

Continuous data

Question 16

What do lower values in skewness indicate?

Answer 16

The median is lower than the mean (positive skew)

Question 17

What’s a negative skew?

Answer 17

More high values create this.

Question 18

What do lower values in the measure of central tendency suggest?

Answer 18

It is a better representation of the ‘typical’ value of a variable.

Question 19

What do range and interquartile range provide in dispersion?

Answer 19

A basic measure, useful
for visualization and identifying outliers.

Question 20

What are the preferred measures used in further analysis in dispersion?

Answer 20

Variance and standard deviation

Question 21

What’s the interquartile range (IQR)?

Answer 21

The range of the middle 50% of values (i.e. between the ‘median’ of the upper and lower halves).

Question 22

What plot is the most useful for the IQR?

Answer 22

Box plots

Question 23

What is Variance?

Answer 23

The mean of the squared differences between each
value and the mean.

Question 24

What is Standard Deviation?

Answer 24

Square root of the variance

Question 25

What does SD represent?

Answer 25

How far, on average we can expect an individual observation to deviate above or below the mean.

Question 26

What is kurtosis

Answer 26

The visual representation of measures and dispersion

Question 27

What does a large standard deviation in a graph mean?

Answer 27

Flat distribution

Question 28

What does a small standard deviation in a graph mean?

Answer 28

Narrow distribution

Question 29

What does it mean when the SD is small in a graph?

Answer 29

The mean is a better representation of the average value

Question 30

What do we use descriptive statistics for?

Answer 30

To summarise our sample data and use statistical inference to generalise about population parameters.