Measures of Center and Spread

"Average" of a set of numbers

​To calculate it:

1. Add up all the numbers in the data set.

2. Divide ​that total by the amount of numbers in the data set.

"Middle" number of a sorted list of numbers

​To calculate it:

1. Write the numbers in order from least to greatest.

2. Find the middle number.

3. If there are 2 "middle" numbers, the median will be the mean of those 2 numbers.

Difference between the largest & smallest values

in a set

​To calculate it:

1. Write the numbers in order from least to greatest.

2. Subtract (range = largest value – smallest value)

Divides the data in 4 equal parts

• 1st Quartile (Q1): the middle of the lower half of the data set

​

• 3rd Quartile (Q3): the middle of the upper half of the data set

Middle 50% of values when ordered from lowest to highest

​To calculate it:

1. Put the numbers in order from least to greatest.

2. Find the median.

3. Find the median of the lower and upper half of the data. These values are quartile 1 (Q1) and quartile 3 (Q3).

4. Find the difference between Q3 and Q1. (IQR = Q3 – Q1)

Measure of variation in a set of data (how far the data is away from the mean on average)

​To calculate it:

1. Find the mean of the numbers.

2. Calculate the difference between each number and the mean.

3. Take the absolute value of the differences.

4. Calculate the mean (average) of the absolute values.