Topic 3 - Numerical Summaries

Question 1

LO

Answer 1

LO3 Produce, interpret and compare graphical and numerical summaries, using base R and ggplot.

Question 2

Advantages of Numerical summaries

Answer 2

• Numerical summaries produce all the data to 1 simple number/ stat
• Loses lots of info, but is easy to comminicate

Question 3

Major features used to create a numeric summary

Answer 3

• Max
• Min
• Spread (stdev, range, IQR)
• Centre (mean, median)

Question 4

Mean

Answer 4

The average of the data
= sum of data / size of data

Question 6

Median

Answer 6

• The middle point when data is smallest to largest

Question 7

Robustness

Answer 7

• The median is said to be robust and is a good summary for skewed data, as it is not affected by outliers

Question 8

Comparing mean and median

Answer 8

Symetrical data:
- Excpect mean and median to be the same

Left skewed data:
- Mean expected to be smaller than median

Right skewed data:
- Expect mean to be larger than the median

Question 9

Limitations of mean and median

Answer 9

Both need to be paired with the spread of the data

Question 10

Standard deviation

Answer 10

• First define the Root Mean Square (RMS)
• Measures the average of a set of numbers, regardless of the signs
  1) root the #
  2) Mean the result
  3) square the result

Question 11

Stdev in terms of RMS

Answer 11

Stdev measures the spread of data
SDpop = RMS of gaps from the mean

Question 12

pop Vs sample SD

Answer 12

SDpop = SD sample x Root((n-1)/n)

Question 13

SD rule of thumb

Answer 13

1 SD = 68%
2 SD = 95%
3 SD = 99.7%

Question 14

Standard units

Answer 14

• ‘z’ score
• How many SD is a data point above or below the mean

Standard units = (Data Point - Mean) / SD

Question 15

IQR

Answer 15

• Another measure of spread
• Range of the middle 50% of the data
  IQR = Q3 - Q1

Question 16

Coefficient of Variation

Answer 16

• Combines the mean and SD into one summary
  CV = SD / Mean
• The higher the CV, the greater the spread around the mean