- Name and compare the measures of center shown in a graph
Calculating Mean and Median
Mean and median are two different ways to define the center of a data set. Depending on the data and its distribution, one measure of center might be most informative or most representative of the “typical” value. In analyzing quantitative data, the measure of center will be one key component.
Mean & Median
mean
The mean of a data set is also commonly known as the average of a data set.
The symbol we use to denote mean differs depending on whether we are discussing a sample or a population.
- Notation for mean of a population: [latex]{\mu}[/latex] (pronounced “mu”)
- Notation for mean of a sample of observations: [latex]\stackrel{¯}{x}[/latex] (pronounced “x-bar”)
To calculate the mean, we add all the data values and divide by the number of data points.
Formula for mean: [latex]{\mu}\text{ or }\bar{x}=\dfrac{\sum{x}}{n}[/latex]
where [latex]{\mu}\text{ or }\bar{x}[/latex] is the mean, [latex]\sum[/latex] is the symbol for sum (add up the data values), [latex]x[/latex] represents the data values, and [latex]n[/latex] represents the number of data values.
median
The median of a data set is the value “in the middle” after all of the values have been arranged in ascending order.
- If there are an odd number of terms, take the one in the middle as the median.
- If there are an even number of terms, take the mean of the two in the middle.
Let’s consider this small set of data that represents the cost per day of snacks for one individual:
[latex]$3.30\qquad $0.80\qquad $5.80\qquad $10.00\qquad $3.60\qquad $8.70\qquad $0[/latex]
a) Calculate the mean of the data set.
Mean = [latex]$4.60[/latex]
b) Calculate the median of the data set.
Median = [latex]$3.60[/latex]