How to Find the Measures of Central Tendency? (+FREE Worksheet!)

Median: The middle value that separates the higher half from the lower half. Numbers are arranged in either ascending or descending order. The middle number is then taken.

Mode: the most frequent value. It is used to show the most popular option and is the highest bar in the histogram.

To decide which one to use, the following should be considered:

• The mean gives all values the same importance, even very large or very small values, while the median focuses more on the values that are in the middle of the data set; So, the mean can use the data more fully. However, as mentioned, the mean can be strongly influenced by one or two very large or very small values.
• There is always only one value for the median or mean on a data set, but a set can have more than one mode.
• Among the Measures of Central Tendency, the mode is less used than the mean and median. However, in some cases, the mode can be significantly useful.

Finding the Measures of Central Tendency: Example 1:

Find the mean, median, and mode of the data set. \(10, 11, 25, 16, 16, 46, 29, 35\)

Solution: Mean: first add the values \(10+11+25+16+16+46+29+35=188\)

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Divide by \(8\), the number of values. Mean\(=\frac{188}{8}=23.5\)

Median: Order the data from least to greatest. \(10, 11, 16, 16, 25, 29, 35, 45\)

Average the two middle values. \(=\frac{16+25}{2}=20.5\)

 So, \(20.5\) is median.

Mode: the value \(16\) occurs two times. So, \(16\) is the mode.

Finding the Measures of Central Tendency Example 2:

Find the mean, median, and mode of the data set. \(22, 35, 45, 53, 52, 35, 11, 16, 35, 11\)

Solution: Mean: first add the values \(22+35+45+53+52+35+11+16+35+11=315\)

Divide by \(10\), the number of values. Mean\(=\frac{315}{10}=31.5\)

Median: Order the data from least to greatest. \(11, 11, 16, 22, 35, 35, 35, 45, 52, 53\)

Average the two middle values. \(=\frac{35+35}{2}=35\)

 So, \(35\) is median.

Mode: the value \(35\) occurs three times. So, \(35\) is the mode.

Finding the Measures of Central Tendency Example 3:

Find the mean, median, and mode of the data set. \(9, 2, 5, 21, 16, 5, 36, 13, 10\)

Solution: Mean: first add the values \(9+2+5+21+16+5+36+13+10=117\)

Divide by \(9\), the number of values. Mean\(=\frac{117}{9}=13\)

Median: Order the data from least to greatest. \(2, 5, 5, 9, 10, 13, 16, 21, 36\)

The middle value is the median. So, median\(=10\)

Mode: the value \(5\) occurs two times. So, \(5\) is the mode.

Finding the Measures of Central Tendency Example 4:

Find the mean, median, and mode of the data set. \(25, 36, 39, 8, 17, 45, 60, 1, 36, 42, 10\)

Solution: Mean: first add the values \(25+36+39+8+17+45+60+1+36+42+10=319\)

Divide by \(11\), the number of values. Mean\(=\frac{319}{11}=29\)

Median: Order the data from least to greatest. \(1, 8, 10, 17,25, 36, 36, 39, 42, 45, 60 \)

The middle value is the median. So, median\(=36\)

Mode: the value \(36\) occurs two times. So, \(36\) is the mode.

Exercises for Finding the Measures of Central Tendency

Calculate the mean, median, and mode for the following data sets.

1. Points scored by a basketball player: {\(8, 3, 17, 26, 13, 3, 30\)}
2. Marks on a set of tests: {\(64, 88, 95, 75, 69, 88, 70, 77\)}
3. Waiting time, in minutes: {\(13, 19, 11, 19, 7, 32, 45, 33\)}
4. Monthly rent \($\): {\(630, 585, 670, 710, 670, 600, 590\)}

1. Mean: \(14.29\) Median: \(13\) Mode: \(3\)
2. Mean: \(78.25\) Median: \(76\) Mode: \(88\)
3. Mean: \(22.38\) Median: \(19\) Mode: \(19\)
4. Mean: \(636.43\) Median: \(630\) Mode: \(670\)

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For a complete grade-level workbook that covers data and statistics alongside the rest of pre-algebra, Pre-Algebra for Beginners walks you through statistics topics with clear examples and try-it-yourself problems. For more practice with data and probability at middle-school level, Mastering Grade 6 Math includes plenty of worked exercises.

Frequently Asked Questions

How do you find measures of central tendency?

Find the mean by adding all values and dividing by how many there are, the median by sorting the data and taking the middle value, and the mode by finding the value that appears most often. For 4, 7, 7, 9, 13, the mean is 40 ÷ 5 = 8, the median is 7 and the mode is 7.

How do you find the best measure of central tendency?

Look at the shape of the data and check for outliers. Use the mean for fairly symmetric data without extreme values, the median for skewed data or data with outliers, such as home prices, and the mode for categories, such as the most popular shoe size. When the mean and median differ a lot, the median is usually the safer choice.

How do you calculate measures of central tendency for grouped data?

For grouped data, use each class midpoint as a stand-in for the values in that class. Multiply each midpoint by its frequency, add the products, and divide by the total frequency to estimate the mean. The median falls in the class containing the middle position, and the modal class is the one with the highest frequency.

How do you find measures of central tendency in Excel?

Enter your data in a column, then use built-in functions. For values in cells A1 to A10, type =AVERAGE(A1:A10) for the mean, =MEDIAN(A1:A10) for the median and =MODE.SNGL(A1:A10) for the mode. If several values tie for most frequent, =MODE.MULT returns all of them.

How do you find the range in measures of central tendency?

The range is not a measure of central tendency; it measures spread. To find it, subtract the smallest value from the largest. For 12, 15, 18, 22, 30, the range is 30 − 12 = 18. Reporting the range alongside the mean or median shows both the typical value and how spread out the data is.

Related EffortlessMath Lessons

If a topic on this page feels rusty, these short lessons go deeper:

• How to find mean, median, mode, and range
• How to find mean absolute deviation
• How to find range, quartile, and IQR
• How to interpret histograms
• How to graph a box plot