Lecture 3

Question 1

Why is knowing the dispersion of data important?

Answer 1

Two different data sets may share the same mean, but the dispersion (spread) of that data may be entirely different

Question 2

Measures of Dispersion

Answer 2

Range (IQR or Median), Variance and Standard Deviation

Question 3

Range

Answer 3

Calculated by subtracting the smallest value from the largest value. Strongly affected by outliers

Question 4

IQR x 1.5 rule

Answer 4

We call an observation a suspected outlier if it falls more than 1.5 x IQR above the third quartile or below the first quartile. Can be used to justify excluding outlier data.

Question 5

Variance

Answer 5

The overall degree to which data points differ from the mean and each other

Question 6

How to calculate variance?

Answer 6

1. Find the difference between each value and the mean.
2. Square these differences
3. Add these differences together
4. Divide by the number of data points minus 1 (if working with a sample – if working with the population simply divide by the number of data points)

Question 7

Why do we calculate standard deviation rather than variance?

Answer 7

Variance: we square the differences between the individual data points and the mean, which means the units of measurement are less intuitive

Question 8

Standard Deviation

Answer 8

A very useful measure of dispersion IF our data is normally distributed. Nearly all values/observations fall within 2 standard deviations either side of the mean.

Question 9

The 68-95-99.7 Rule

Answer 9

68% of data will lie 1SD away from the mean. 95% of data will lie 2DS’s away from the mean. 99.7% of data will lie 3SD’s away from the mean