Topic 1 - Data, Samples and Descriptive Statistics

Question 1

Define population

Answer 1

The entire/complete group we are interested in

Question 2

Define sample

Answer 2

Smaller group on which data is collected

Question 3

Define parameter

Answer 3

Numerical measures which describe specific characteristics of a POPULATION (remember p parameter for p population)

Question 4

Define statistics

Answer 4

Numerical measures computed from a sample (remember s statistics for s sample)

Question 5

How many areas can statistical analysis be divided into?

Answer 5

2 areas

Question 6

What are the areas that statistical analysis can be divided into?

Answer 6

1) Descriptive statistics
2) Inferential statistics

Question 7

What are descriptive statistics?

Answer 7

Numerical and graphical methods used to summarise and present info in a meaningful way

Question 8

What are inferential statistics?

Answer 8

When you make inferences or predictions about the population based on the findings from your sample
e.g. things like hypothesis testing

Question 9

Describe the general process in statistics

Answer 9

1) From the population you collect data to form your sample
2) Using descriptive statistics you can describe the sample (statistics)
3) Using the statistics found you can use inferential statistics to make estimates about the parameters (features) of the population
4) This can then allow you to draw conclusions about the population

Question 10

What is simple random sampling?

Answer 10

Each unit of population has an equal probability of being chosen to be part of sample- each individual chosen randomly (entirely by chance)
- good, unbiased representation of population

Question 11

What are the variations of simple random sampling?

Answer 11

1) With replacement- sample unit drawn and then returned to population after characteristics recorded
2) Without replacement- sample drawn is not returned to population after characteristics recorded- … each unit can be only be drawn once (NOTE here sample values not independent as sample drawn can affect next sample- as you cannot draw the unit you drew previously)

Question 12

How could you describe a distribution of a histogram or potentially even other graphical representations of data?

Answer 12

1) Symmetric distribution- if there is symmetry or balance when data is presented
2) Positively skewed- skewed to the right- where distribution is higher to the left and lower on the right
3) Negatively skewed- skewed to the left- where distribution is higher to the right and lower on the left

Question 13

How many ways can you summarise the data of one variable?

Answer 13

2 ways

Question 14

What are the ways in which you can summarise the data of one variable and briefly describe or give examples of each way?

Answer 14

1) Frequency distribution e.g. ordered list or table
2) Histograms- graph summarising the data in a frequency distribution- vertical axis either frequency, relative frequency or percentage

Question 15

In how many ways can you display the relationship between two variables?

Answer 15

2 general ways

Question 16

How can you display the relationship between two variables?

Answer 16

1) Categorical (qualitative) variables e.g. cross tables
2) Numerical (quantitative) variables e.g. scatter plots/diagrams

Question 17

What is the Simpson’s Paradox?

Answer 17

For example say you have 2 people who sell 2 products A and B
The aggregate data (sales of both products looked at together where you see the total sales and sales effectiveness as a percentage)- the aggregate data shows the person 2 is more affective in sales

BUT when you look at the sales for the 2 products separately, you see that person 1 is more effective in selling each individual product than person 1

… the 2 contradicting pictures are known as the Simpson’s paradox

See last slide of topic 01 pre recorded lecture if need be for visual

Question 18

Give examples of descriptive statistics

Answer 18

4 main types:
1) Measures of Frequency- count, percent, frequency
2) Measures of Central Tendency- mean, median or mode
3) Measures of Variation or Dispersion- range, variance, standard deviation
4) Measures of Position- percentile ranks, quartile ranks

Question 19

Give examples of inferential statistics

Answer 19

1) Hypothesis Testing
2) Point Estimate

Question 20

In a positively skewed distribution how does the mean, median and mode compare?

Answer 20

In a positively skewed distribution (skewed to the right- where distribution is higher on the left and lower on the right side)
REMEMBER the order is always mode, median mean OR mean, median, mode (mode is always the highest peak BUT we are interested in the x-axis position of that measure of central tendency) … as it is mode, median, mean from left to right, the mode is the smallest, then the median is slightly larger and the mean is the largest out of the 3

Question 21

In a negatively skewed distribution how does the mean, median and mode compare?

Answer 21

In a negatively skewed distribution (skewed to the left- where distribution is higher on the right and lower on the left side)
REMEMBER the order is always mode, median, mean OR mean, median, mode (mode is always the highest peak BUT we are interested in the x-axis position of that measure of central tendency) … as it is mean, median, mode from left to right, the mode is the smallest, then median is slightly larger and the mean is the largest out of the 3

Question 22

What is an independent event?

Answer 22

When the first draw doesn’t effect the second
I.e. draw is done with replacement so that all units can be drawn including the one/ones drawn previously

Question 23

What is a dependent event?

Answer 23

When the first draw does effect the second … the second does depend on the first
I.e. draw is done without replacement so that a unit drawn previously cannot be drawn again- also the total number of units that can be drawn falls