4.4 Measures of central tendency
4.4.1 Calculating the mean

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The mean can be calculated only for numeric variables, no matter if they are discrete or continuous. It’s obtained by simply dividing the sum of all values in a data set by the number of values. The calculation can be done from raw data or for data aggregated in a frequency table. Here are a few examples of calculation.

Example 1 – Soccer tournament at Mount Rival

Mount Rival hosts a soccer tournament each year. This season, in 10 games, the lead scorer for the home team scored 7, 5, 0, 7, 8, 5, 5, 4, 1 and 5 goals. What is the mean score of this player?

The sum of all values is 47 and there are 10 values. Therefore, the mean is 47 ÷ 10 = 4.7 goals per game.

Example 2 – Traffic fatalities

The following table lists the number of people killed in traffic accidents over a 10-year period. During this period, what was the average number of people having lost life every year? How many people died each day on average in traffic accidents?

Number of fatalities in traffic accidents
Table summary
This table displays the results of Number of fatalities in traffic accidents. The information is grouped by Year (appearing as row headers), Deaths (appearing as column headers).
Year Deaths
2009 623
2010 583
2011 959
2012 1,037
2013 960
2014 797
2015 663
2016 652
2017 560
2018 619
Total 7,453

The total number of deaths is presented in the table (7,453). To get the yearly average, the number of deaths is divided by 10 which gives 745.3 deaths per year. To get the daily average, the yearly average is divided by 365 which gives approximately 2 deaths per day.

For a larger data set, it can be easier to summarize data in a frequency table before calculating the mean. In this case, you need to weight each possible value by the frequency of the value to calculate the total.

Example 3 – Soccer tournament at Mount Rival

Let’s go back to Mount Rival soccer tournament. Suppose that five teams were competing, each of them including 10 players for a total of 50 players. The number of goals scored by each player was compiled and results were summarized in the frequency table below. For example, we can see that eight players scored only one goal during the tournament. What is the average number of goals scored by the players during the tournament?

Number of players by the number of goals scored
Table summary
This table displays the results of Number of players by the number of goals scored. The information is grouped by Number of goals scored (appearing as row headers), Number of players (appearing as column headers).
Number of goals scored Number of players
0 2
1 8
2 14
3 12
4 8
5 4
6 2

You first need to calculate the total number of goals scored. To do that, you take each observed value of the number of goals scored, which are values 0 to 6, and you multiply each value by the number of players:

0 × 2 + 1 × 8 + 2 × 14 + 3 × 12 + 4 × 8 + 5 × 4 + 6 × 2 = 136

Since there are 50 players, the average is 136 ÷ 50 = 2.72 goals per player.

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