RDS Calculations and Formulae

Question 1

Mean

Answer 1

Sum of all data values divided by the number of data values

Sum (x) / n

Question 2

Median

Answer 2

Add 1 to the number of data values

Divide this by 2

Take the value associated with the data value found

e.g. 15 values, + 1 = 16/2 = 8

take value of 8th data point

For even values e.g. 16 +1 = 17/2 = 8.5

Take mean of 8th and 9th values

Question 3

Mode

Answer 3

Most frequently occurring data point

Question 4

Variance

Answer 4

Sum of (x - mean)² (each individual bracket is squared and then summed)

All divided by n (for population) or n-1 (for sample)

Given as σ² (population) or s² (sample)

Question 5

Standard deviation

Answer 5

Square root of the variance

Given as σ or s (population/sample)

Question 6

Standard error

Answer 6

Can only be calculated for a sample (not population)

s (standard dev) divided by square root of n

standard deviation of the sample divided by the square root of the number of values in the sample

Question 7

Interquartile range

Answer 7

Value for lower quartile subtracted from value for upper quartile (this is the range remember)

This is another measure of dispersion of data

Question 8

Example, you are given systolic blood pressure (in mmHg) for a sample of males and females. How would you go about using descriptive statistics to start describing the data?

Answer 8

Look for a measure of central tendency and of data dispersion.

Central tendency = mean

Dispersion = SD

Since it’s a sample it would be appropriate to also include the standard error of the mean

So in total, mean, SD, SEM