1. Summary Statistics

Question 1

What is exploratory data analysis (ELA)?

Answer 1

the part of statistics concerned with taking a first look at some data

Question 2

what are two aspects of EDA

Answer 2

• summary statistics
• data visualisation

Question 3

What is meant by summary statistics?

Answer 3

Calculating numbers that briefly summarise the data
ie central values of the data, how spread out the data is, or about the relationship between two variables

Question 4

What is meant by data visualisation?

Answer 4

drawing a picture based on the data to show the shape (centrality and spread) of data, or the relationship between two variables

Question 5

What important questions should you ask about data before calculating summary statistics or drawing a plot?

Answer 5

• What is the data? “What variables were measured and how, how many datapoints etc”
• How was the data collected? “Sample or whole population?
• Are there any outliers?
• Ethical questions like are there any ethical or privacy issues, should the data be confidential?

Question 6

Two types of summary statistic

Answer 6

• Statistics of centrality, which tell us where the middle of the data is
• Statistics of spread, which tells us how far the data typically spreads out from the middle

Question 7

What is the mode of a dataset x?

Answer 7

the most common value of x(i)

Question 8

What is the median of a dataset x?

Answer 8

If the data is ordered, it is the central value in the ordered list
- if n is odd, this is x((n+1)/2)
- if n is even, this is 1/2(x(n/2) + x((n/2)+1

Question 9

What is the mean of a dataset x?

Answer 9

x(hat) = 1/n(x1 + x2 + … + xn)

= 1/n sum(x(i), 1,n)

Question 10

What quantile is the median

Answer 10

q(1/2)

Question 11

What quantile is the maximum

Answer 11

q(1)

Question 12

What quantile is the minimum

Answer 12

q(0)

Question 13

What is the lower quartile

Answer 13

q(1/4)

Question 14

What is the upper quartile

Answer 14

q(3/4)

Question 15

What is meant by the number of distinct observations

Answer 15

The number of different datapoints we have after removing any repeats

Question 16

What is the interquartile range?

Answer 16

Difference between the upper and lower quartiles

Question 17

What is the sample variance?

Answer 17

s^2(x) = 1/(n-1) ((x1- x(hat))^2 + … + (x(n) - x(hat))^2)

= 1/(n-1) sum((x(i) - x(hat))^2, 1, n)

Question 18

What is the standard deviation?

Answer 18

Square root of the sample variance

Question 19

What is the computational formula for sample variance?

Answer 19

s^2(x) = 1/(n-1) sum(x^2(i) - nx^2(hat), 1, n)