Week 4

Question 1

Can a median be obtained for nominal variables?

Answer 1

Median cannot be obtained for nomimal variables, it can be obtained only on ordered variables – ordinal, interval, ratio

Question 2

What types of data can the mode be used for

Answer 2

Can be used for all types of variables – and often used for nominal and ordinal variables e.g. the most frequent answer was ‘extremely satisfied.’

Question 3

Can there be multiple modes

Answer 3

Yes

Question 4

What variables can mean be defined in

Answer 4

Ratio and interval

Question 5

Difference between mean and median

Answer 5

Mean depends on the actual values, whike median is not affected e.g. one extreme outlier can hugley affect mean but not median

Question 6

How would you go about creating equal sections of data (use coins)

Answer 6

Divide coins into sections containing the same number of data and report where the sections are located
The cut off points dividing these sections are called quantiles
if there were 200 coins - 20 sections of 10 coins each

Question 7

When there are 4 sections, they are called _____, and the median is the ____

Answer 7

quartiles (1sr-3rd)
2nd quartile

Question 8

When there are 100 sections, they are ______ (1st-99th) and the median is the ___

Answer 8

percentiles
50th percentile

Question 9

What is the 2nd moment

Answer 9

(distance from mean)^2 to each data point / number of data points
This is the variance
How hard it would be to spin the coins around the mean (torque)

Question 10

What does a small variance mean

Answer 10

This is when the data has a small spread
Its concentrated more towards the mean

Question 11

What is standard deviation

Answer 11

Square root of variance is called the standard deviation (SD)
The standard distance from the mean

Question 12

What do z scores enable

Answer 12

Fair comparisons of deviations

Question 13

What does skewness measure

Answer 13

The degree of asymmetry

Question 14

Skewness and the 3rd moment

Answer 14

3rd moment = (distance from mean)^3 to each data point / no of data points
To make it dimensionless, this is divided by SD^3 ie. Skewness = 3rd moment/ SD^3

Question 15

What does zero and high skewness mean

Answer 15

Zero skewness means data are symmetrically distributed, high skewness means distribution is highly asymmetrical.

Question 16

What does positive and negative skewness indicate

Answer 16

-Positive/negative skewness indicates which direction data are skewed (see graphs for reference)

Question 17

What does kurtosis meaure

Answer 17

Kurtosis meaures the sharpness

Question 18

Kurtosis and the 4th moment

Answer 18

4th moment = (distance from mean)^4 to each data point / no of data points
To make it dimensionless, this is divided by SD^4 ie. Kurtosis= 4th moment/ SD^4

Question 19

What do we do to the kurtosis

Answer 19

Kurtosis is always positive, but we normally subtract 3 (the kurtosis of the normal distribution). This is called the excess kurtosis

Question 20

Reasons for outliers

Answer 20

Can be due to inaccuracies in data processing, problems with the methodology (e.g. measurements, instruments, participants not following instructions, an actual extreme value from an unusual participant

Question 21

2 ways of measuring an outlier

Answer 21

1. Based on z score – outlier if z score is more than 3 or less than –3 I.e. when the distance from the mean is more than 3 times of SD
2. based on the IQR; width between the 1st and 3rd quartile – outlier if value is greater than 1.5 IQR above the 3rd quartule or smaller than 1.5 IQR below the 1st quartie

Question 22

Cumulative probability

Answer 22

Using bionomial distribution, you can also calculate the probability that you get heads in a certain range e.g. what is the probability you get no more than 3 heads in 10 tosses?

Question 23

What is the IQR

Answer 23

width of between the 1st and the 3rd quartile

Question 24

Two tailed cumulative probability

Answer 24

Sometimes you may want to check the probability that a data is deviated from the centre or mean.

In this case, you need to take the cumulative probability at both ends. Checking this probability is called the two tailed probability

Question 25

What do you need to use to describe a distribution of a continuous variable

Answer 25

Continuous distribution

Question 26

In continuous distribution, what indicates the probability

Answer 26

And the area under the distribution in that range indicates the probability

Question 27

Y axis on continuous distribution

Answer 27

Probability density