Descriptive Statistics

Question 1

What are the 3 measures of central tendency?

Answer 1

-Mean
-Median
-Mode

Question 2

What are the 3 measures of disperison?

Answer 2

-Interquaritle Range (IQR)
-Variance
-Standard Deviation

Question 3

What are the measures of association?

Answer 3

-Chhi-Squared
-Correlation

Question 4

Define Central tendency

Answer 4

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

Question 5

What is Cenral tendency useful for?

Answer 5

-Useful for comparisons between datasets or groups within a dataset
-Can be tracked over time to monitor increases/decreases in key metrics
-Used in many statistical tests

Question 6

What is the Mean?

Answer 6

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

Question 7

Features of the Mean

Answer 7

-For ordinal and scale data
-Statistically powerful (uses all data points)
-Not robust (can be distorted by outliers)

Question 8

Define the Median (M)

Answer 8

The middle value when values of a variable are arranged in order of magnitude

Question 9

Features of the Median

Answer 9

-For ordinal and scale data
-Robust to outliers, so more appropriate than mean when dealing with extreme values
-Lacks statistical power

Question 10

Define the Mode

Answer 10

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

Question 11

Features of the Mode

Answer 11

-Only measures suitable for nominal data
-Can be used with ordinal and scale data but other options are generally prefrable

Question 12

How is the Mode useful?

Answer 12

• Categorical data: The only measure of central tendency suitable for nominal variables
• Visualisation and reporting: Grouping numerical data can simplify communication and involves trade-off between detail and user-friendliness
• Aggregated or transformed data

Question 13

Define dispersion

Answer 13

Dispersion measures how far, on average, each observation lies from the central tendency. Represents the variation in values within a variable.

Question 14

Interquartile Range

Answer 14

IQR is the range of values within the middle 50% of data points, calculated as the difference between Q1 and Q3, with Q1 located at position (n+1)/4 and Q3 at 3(n+1)/4

Question 15

What is comparing the range and IQR useful for?

Answer 15

-Useful for understanding the dispersion of a variable and identifying outliers
-Box plots are the easiest way to do this

Question 16

Define Variance

Answer 16

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

Question 17

Define Standard Deviation

Answer 17

The square root of the variance, representing how far, on average we can expect an individual observation to deviate above or below the mean

Question 18

How to calculate Standard Deviation

Answer 18

1. Find the mean
2. Find the difference between value and the mean
3. Square each difference
4. Find the sum of the squared differences
5. Find the variance: the mean of the squared differecnes
6. Find the SD: the square root of the variance

Question 19

What is Kurtosis?

Answer 19

The ‘flatness’ of the distribution of values

Question 20

What does a Large SD/ flat distribution mean?

Answer 20

Data are fairly dispersed around the mean, with more values in the tails of the distribution

Question 21

What does a Small SD/ narrow distributiin mean?

Answer 21

Has a ‘peak’ in values clustered around the mean.

Question 22

What do we use the coefficient of variation (CV) to do?

Answer 22

To measure the relative variability. This is typically expressed as a percentage.

Question 23

What is the Coefficient of Variation useful for comparing?

Answer 23

-Different variables
-The same variable
-International comparisons

Question 24

What do measures of association consider?

Answer 24

The relationship between two variables

Question 25

Chi-Squared

Answer 25

Tests for association based on the frequency of two variables' co-occurence, comparing the expected frequency if there was no association with the observed frequency in the sample data.

Question 26

Correlation

Answer 26

Represents the strength and magnitude of the association between two variables. The correlation coefficient r ranges from -1 to 1.

Question 27

What is a Contingency table?

Answer 27

Contingency tables list the possible values of x and y, and the frequency of each combination. This is known as cross-tabulation.

Question 28

What does a Positive covariance indicate?

Answer 28

Indicates variables that tend to 'move together' away from their means: if we observe a high value of x, we also expect to see a high value of y

Question 29

What does a Negative Covariance indicate?

Answer 29

Indicates variables that move in opposite directions: if we oberve a high value of x, we expect to see a value of y below its mean.

Question 30

What is the correlation coefficient?

Answer 30

It transforms the covariance to a scaled, interpretable representation of the strength and direction of this relationship. It ranges from -1 to 1.

Question 31

What are Scatter Plots?

Answer 31

They show if there is a linear relationship between two variables.

Question 32

Skewness

Answer 32

Skewness refers to an imbalance, asymmetry, or distortion in the distribution of various organizational, economic, or behavioral factors.

Question 33

What is a skewed distribution?

Answer 33

Skewed distributions have a relatively higher proportion of their values at the low (positive skew) or high (negative skew) end of the range

Question 34

What is Normal distribution?

Answer 34

When the mean and median are approximately the same (PCS close to 0), the data is symetrically distributed around the central tendency.

Question 35

What are normal distributions always?

Answer 35

1. Symetric 2. Asymptotic