10 Descriptive Statistics

Question 1

What do stats allow us to do?

Answer 1

• understand world phenomena with use of available data
• obtain tools to summarise and interpret data
• make proper inference/ forecasting

Question 2

Descriptive statics

Answer 2

Used to summarise information which would otherwise be too complex to take in

Question 3

Statistical inference

Answer 3

The drawing of lessons about a population from studying a sample of data drawn from that population

Question 4

Variable

Answer 4

A specific characteristic of a unit

Question 5

What are the two different types of variable?

Answer 5

Numerical- where each observation takes a numerical value

Categorical- records which of a series of categories are observed

Question 6

What are the types of numerical variables

Answer 6

Discrete- possible values are limited to a sequence of number (usually natural numbers)
Continuous- can take on any value within a range of real numbers

Question 7

What are the types of categorical values

Answer 7

Nominal- the categories have no ordering or ranking

Ordinal- the categories have a ranking

Question 8

Types of data

Answer 8

Cross section data- data on several units at one point in time
Time series data- data on one unit across several points in time
Panel data- data on several units across several points in time

Question 9

Population

Answer 9

Describes the complete set of all units of interest to an investigator (N)

Question 10

Sample

Answer 10

An observed subset of the population (n)

Question 11

Simple random sampling

Answer 11

• each member of the population is chosen strictly by chance
• each member of the population is equally likely to be chosen
• every possible sample of n objects is equally to be chosen

Question 12

Xi

Answer 12

An observation in a sample

Question 13

Sigma

Answer 13

The sum of the values

Question 14

Frequency distribution

Answer 14

A list or table containing groupings and corresponding frequencies for days within each group

Question 15

K

Answer 15

Possible groups which data could fall in

Question 16

Absolute frequency

Answer 16

The number of observations belonging to a group

Question 17

Relative frequency

Answer 17

The proportion of observations belonging to that group

Question 18

Cumulative frequency

Answer 18

The total number of observations in that and any previous class

Question 19

Cumulative relative frequency

Answer 19

The proportion of observations in that and any previous class

Question 20

Arithmetic mean

Answer 20

The sum of all the values divided by the number of values

Question 21

Median

Answer 21

The middle observation. If the number of values is even, the median is the mean of the tie middle values

Question 22

Mode

Answer 22

Most common value

Question 23

Which one out of mean, median and mode is most affected by outliers?

Answer 23

Mean

Question 24

Left skewed data

Answer 24

When the mean is less than the median

Question 25

Right skewed data

Answer 25

When the mean is greater than the median

Question 26

Geometric mean

Answer 26

Used to measure the rate of change of a variable over time. It is the nth root of a product of n numbers

Question 27

Range

Answer 27

The difference between the smallest and largest value of the data

Question 28

Interquartile range

Answer 28

Calculates the range of the middle 50% of the data Q3-Q1

Question 29

Variance

Answer 29

The average of squared deviations of values from the mean.

Question 30

What is the sample variance divided by and why?

Answer 30

n-1 because the sample variance is an estimation and is underestimated since extreme values are rare and are unlikely to be included in the data

Question 31

Standard deviation

Answer 31

The square root of the variance

Question 32

Why is standard deviation more useful than variance

Answer 32

Standard deviation allows us to measure the spread from the men’s in units

Question 33

Advantages of variance and standard deviation

Answer 33

• each value of the data set is used in the calculations

* values far from the mean are given extra weight

Question 34

Coefficient variation

Answer 34

Measures the relative variation and can be used to compare two or more sets of data. It is always given as a percentage

Question 35

Covariance

Answer 35

Measures the joint variability of two variables

Question 36

What does the sign of the covariance indicate

Answer 36

The direction of the relationship between the two variables.
Cov(x,y)>0 x and y have positive correlation
Cov(x,y)<0 x and y have negative correlation

Question 37

Coefficient of correlation

Answer 37

Measures the relative strength of the linear relationship between two variables

Question 38

What values does the coefficient of correlation take?

Answer 38

-1 to 1

Question 39

Why is coefficient of correlation more useful than covariance?

Answer 39

It gives both the direction and strength of the relationship