Statistics 2

Question 1

What are the two types of data?

Answer 1

Discrete & continuous

Question 2

What is an example of discrete and continuous data?

Answer 2

Frequencies and weight

Question 3

What are the four scales of measurement?

Answer 3

Nominal, Ordinal, Interval and Ratio

Question 4

What is the nominal scale of measurement?

Answer 4

Discrete, mutually exclusive categories, if coded numerically then they have no numerical significance, no arithmetic possible

Question 5

What is the ordinal scale of measurement?

Answer 5

Discrete, categories are not mutually exclusive - instead they form a natural ordering/hierarchy, intervals in between categories are not uniform, no arithmetic possible

Question 6

What is the interval scale of measurement?

Answer 6

Continuous data, intervals are split equally allowing for simple arithmetic, however there is no absolute zero value which means there are no values below a certain point and it also prevents complex arithmetic

Question 7

What is the ratio scale of measurement?

Answer 7

Continuous data, interval data with an absolute zero point. all arithmetic possible

Question 8

What scales of measurement can a bar chart represent?

Answer 8

Discrete (nominal and ordinal) data

Question 9

How is data represented on the bar chart?

Answer 9

The length of the bar is proportional to frequency

Question 10

What is represented on the x and y axis of a bar chart?

Answer 10

X-axis = nothing just the names of the different categories
y-axis = frequency/measurement

Question 11

How would you order nominal and ordinal data on a bar chart along the x-axis?

Answer 11

Nominal: order from smallest category to the largest category
Ordinal: order from pre-determined way

Question 12

What data is represented on a histogram?

Answer 12

Continuous (ratio or interval) data

Question 13

How is data represented on the histogram?

Answer 13

The area is proportional to the size of the category

Question 14

If there is a change to the category size what axis is changed?

Answer 14

The x-axis

Question 15

Why is there no gaps between the different categories on the x-axis?

Answer 15

Because it is continuous data

Question 16

What is univariate analysis?

Answer 16

analysis of a single variable distribution

Question 17

How can distribution be described?

Answer 17

Visually (graphs and plots) or numerically (summary statistics)

Question 18

How is central tendency described?

Answer 18

Averages

Question 19

What is a bimodal distribution and how does it affect the central tendency?

Answer 19

it has two peaks so essentially there is no centre

Question 20

What is dispersion?

Answer 20

The spread of the data

Question 21

What are the two methods for representing and measuring dispersion?

Answer 21

Median and IQR & Standard deviation and variance

Question 22

When would you use the median and IQR as a method to represent dispersion?

Answer 22

Most suitable for non-normal distribution. Also when the sample size is small

Question 23

When would you use standard deviation and variance as a method to represent dispersion?

Answer 23

For normal distribution. (ratio and interval)

Question 24

What is standard deviation?

Answer 24

Summary statistic that characterises the spread of the distribution around the mean

Question 25

What happens as SD increases?

Answer 25

the spread of the data around the mean broadens/increases

Question 26

How much of the data is in 1 standard deviation of the mean?

Answer 26

68.26%

Question 27

How much of the data not within 1 SD is on either side of the mean?

Answer 27

15.87% on either side

Question 28

What happens to the shape of the normal curve at the point of 1SD?

Answer 28

It changes from a concave to convex shape

Question 29

What are important characteristics of a normal distribution?

Answer 29

It is spread equally and symmetrically

Question 30

What is variance?

Answer 30

Standard deviation squared

Question 31

What scales of measurement can variance not be used ?

Answer 31

nominal or ordinal

Question 32

What can the variance never be?

Answer 32

non-negative

Question 33

What is the name for values and calculations for a sample and a population?

Answer 33

Sample: statistic
Population: parameter

Question 34

What is the coefficient of variation?

Answer 34

It allows us to compare different variables of a distribution with different units or magnitude by standardising them.

Question 35

What scale of measurement is the coefficient of variation only valid for?

Answer 35

Ratio

Question 36

What is skewness?

Answer 36

The characterisation of shape in a normal distribution - measuring its symmetry

Question 37

If the skew is =, less than or more than 0 what does this mean?

Answer 37

= 0: No skew
<0: negative skew (more values concentrated to the right of mean)
>0: positive skew (more values concentrated to the left of mean)

Question 38

What is kurtosis?

Answer 38

A measure of peakedness

Question 39

What happens if kurtosis increases?

Answer 39

the mass of the data gets moved from the shoulders of the data distribution towards the centre

Question 40

What does it mean if the kurtosis is or = 3?

Answer 40

<3 means that it is platykurtic (not very peaked)
~3 means that it is mesokurtic (relatively peaked)
>3 means that it is leptokurtic (very peaked)

Question 41

What are the four moments of distribution?

Answer 41

1) Central value, 2) dispersion, 3) skewness, 4) kurtosis

Question 42

What is parametric data?

Answer 42

ratio or interval data that is normally distributed. n>30

Question 43

What is non-parametric data?

Answer 43

ordinal or nominal data OR ratio or interval data that is not normally distributed. n<30