"Measures of Central Tendency" is one of the most important concepts in the study of descriptive statistics, a type of statistics used to describe and summarize values in a data set. Measures of central tendency do not provide information about the individual values of a data set. Rather, it is a set of numerical values that best represent or summarize the middle of the data set. The following measures can be used to determine the central tendency:
Range is often included when finding the measures of central tendency. However, the range is actually a measure of variation. A measure of variation describes the variability of the data-- or how spread out the data is in a data set.
As a member, you'll also get unlimited access to over 84,000 lessons in math, English, science, history, and more. Plus, get practice tests, quizzes, and personalized coaching to help you succeed.
Get unlimited access to over 84,000 lessons.
Try it risk-freeAlready registered? Log in here for access
The mean does not always provide the best measure of central tendency for a data set. When the data is in a symmetrical distribution, or bell-curve, the mean, median, and mode are all at the center of the distribution. If a data set contains outliers, or values that are significantly higher or lower than the rest of the values in the data set, it can look skewed when represented on a graph. A skewed distribution is when the tail of a distribution on a graph is longer than the other. If the tail is longer towards the negative side of a number line, it is left-skewed. If the tail is longer on the positive side of a number line, it is right-skewed. The more a distribution is skewed, either right or left, the less accurate the mean.
 |
Unlike the mean, the median is not calculated using all of the numbers in the data set, so the median is not impacted by extreme outliers or heavily skewed distributions.
The mode provides the value that occurs most frequently within a data set. The mode is frequently used with data sets that include categorical data, or data that can be organized into groups, but does not have mathematical meaning. Zip codes and phone numbers are types of numerical data that do not have a mathematical meaning because they do not indicate trends in a data set. Mode is useful for finding the most popular option in a categorical data set like the most favorite color.
Range is a numerical value that represents the spread of a data set. The range can be misleading if there are extreme outliers in the data set.
In mathematics, finding the mean is synonymous with finding the average of a set of numbers.
To calculate the mean:
 |
There are two ways to find the median of a data set. The correct method depends on the number of values within the set.
If the data set has an odd quantity of numbers in the set:
If the data set has an even quantity of numbers in the set:
The mode is the number that occurs the most in the data set. The mode may not be a unique value if no single number was repeated more than others.
The range is the numerical difference between the maximum and minimum.
The following is an example of how the mean, median, mode, and range can all be drawn from the same data set.
American Tiger University recorded the following ages for their 2021-2022 academic year roster:
| Student's Name | Age |
| Mindy | 19 |
| Cameron | 22 |
| Tony | 19 |
| Keith | 23 |
| Lauren | 19 |
| Tommy | 21 |
| Pilar | 25 |
| Mike | 19 |
| Carla | 27 |
| Kira | 25 |
| Marcus | 21 |
To find the mean of the American Tiger University roster, or "data set,":
$$\large \frac{19+22+19+23+19+21+25+19+27+25+21}{11} = \frac{240}{11}=21.\bar{81} $$
The average age of a member on the swim team is approximately 21.81.
To find the median of the data set:
 |
21 is the single number directly in the center, and the median of the swim team is therefore 21.
Jordan is eighteen years old and freshman who's just joined the American Tiger University swim team, and the roster has changed. Now the second method for finding the median is necessary. Now to find the median:
 |
3. To find a single value for the median, calculate the average of these two values. The median age of a member on the swim team is 21 years old.
$$\large \frac{21 + 21}{2}= 21\ $$
 |
The value (age) 19 occurs four times and most often in the data set. The most common age of the team members is 19 years. The mode is therefore 19.
The graph below demonstrates the distribution of the data set. The distribution is slightly skewed right ("positive skewness").
 |
This distribution is slightly skewed right and indicates that the mean is only slightly greater than the median. The mean is not heavily impacted by a possible outlier.
For this data set, the mode (19 years) is the lowest measure of central tendency and the mean (21.5 years) is the highest. The median (21 years) is the value in the middle. Since the mean and median only differ by 0.5 years, both could be considered the best representation of this data set.
To find the range of the data set:
$$\large 27 - 18 = 9 $$
The range of ages of the members on the swim team is 9 years.
This lesson covers the following regarding how to find measures of central tendency:
This lesson has covered the following vocabulary words:
To unlock this lesson you must be a Study.com Member.
Create your account
In mathematics the mean is considered to be the same thing as the average. Both are calculated by finding the sum of the total values in the set, then dividing that number by the number of values within the set.
Range is a measure of variability and represents the spread of the values in a data set. Mode is the number or value that occurs most often in the data set, or the most popular value. Mean is the average, or center of a normal distribution. The mean may not be as accurate in data sets with outliers or skewed distributions.
The mean of a data set can be found by adding the values together and dividing that sum by the total number of values in the set. The median can be found by organizing the values from least to greatest and locating the value that is directly in the center of the set. If there are two values, the mean can be found by adding those two values and dividing that sum by two. The mode is the value that occurs most frequently within a set of data.
Already a member? Log In
BackAlready registered? Log in here for access
