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Addition and subtraction Multiplication and division Decimals Fractions RoundingHere you will learn about the measures of central tendency, which is the mean, median and mode of data sets, including what they are and how to find them.

Students first learn about measures of central tendency in the 6 th grade and expand this knowledge as they move through middle school and high school statistics.

The **mean, median and mode** are different measures of center of a numerical data set. They are a way of summarizing a data set with a single number.

The mean is the average of a numerical data set.

To calculate the mean, find the **total of the values** and **divide the total by the number of values**.

The “number of values” is sometimes referred to as the “number of numbers”.

Let’s find the mean of this data set.

The **mean** is 4.57 (rounded to 2 decimal places)

The median is the middle number of a numerical data set.

To find the median, we need to arrange the values in numerical order, from the smallest value to the highest value, and find the **middle value**.

The middle value is the median value.

Let’s find the **median** of the same data set.

The **median** is 5 because it is the middle number of data points.

The mode is the most common number. To find the mode, we need to find the value in the data set that occurs the most number of times.

Let’s find the mode of the data set.

The number that occurs the most or is most frequent is 6.

The **mode** is 6.

Use this quiz to check your 6th grade students’ understanding of mean, median, and mode. 10+ questions with answers covering a range of 6th grade topics on mean, median, and mode to identify areas of strength and support!

DOWNLOAD FREEUse this quiz to check your 6th grade students’ understanding of mean, median, and mode. 10+ questions with answers covering a range of 6th grade topics on mean, median, and mode to identify areas of strength and support!

DOWNLOAD FREEThe range is the difference between the greatest value and the least value of a data set. It is a measure of variability not a measure of center.

Let’s find the range of the data set.

7 - 1 = 6

The range is 6.

How does this apply to 6 th grade math?

**Grade 6 – Statistics and Probability 6.SP.A.3**

Recognize that a measure of center for a numerical data set summarizes all of its values with a single number, while a measure of variation describes how its values vary with a single number.

**Grade 6 – Statistics and Probability 6.SP.A2**

Understand that a set of data collected to answer a statistical question has a distribution which can be described by its center, spread, and overall shape.

**Grade 6 – Statistics and Probability 6.SP.B.5c**

Giving quantitative measures of center (median and/or mean) and variability (interquartile range and/or mean absolute deviation), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context in which the data were gathered.

In order to find the mean, median or mode:

**List the numbers in order from least to greatest.****To find the mean, find the total of the numbers in the data set and divide by the number of values in the data set.****To find the median, find value(s) in the middle of the data set.****To find the mode, look for the value(s) that occur the most; there may be more than one mode.****To find the range, find the difference between the largest value and the smallest value.**

Find the mode for the given data set.

**List the numbers in order from least to greatest.**

4**To find the mode, look for the value(s) that occur the most; there may be more than one mode.**

7 occurs the most, so the mode is 7.

Find the median for the given data set.

**List the numbers in order from least to greatest**

**To find the median, find values in the middle of the data set.**

The value in the middle is 9. The median is 9.

Find the median of the given data set.

**List the numbers in order from least to greatest.**

Find the middle of the data set. There is an even number of values, so we have a middle pair. To find the median, find the average of the two middle numbers or the midpoint of 4 and 6.

The average of 4 and 6 or the midpoint between 4 and 6 is 5. So, the median is 5.

Find the mean of the given data set.

**List the numbers in order from least to greatest.**

Although not necessary, it can be helpful to put the values in order.

**To find mean, find the total of the numbers in the data set and divide by the number of values in the data set.**

The mean is 7.6.

Find the mean, median, and mode of the data set.

**List the numbers in order from least to greatest.**

**To find the mean, find the total of the numbers in the data set and divide by the number of values in the data set.**

The mean is 13.

**To find the median, find values in the middle of the data set.**

There are an even number of data points in the data set, so there are two values in the middle, 12 and 13. To find the median, find the average of the two numbers of the midpoint.

The median is 12.5.

**To find the mode, look for the value(s) that occur the most; there may be more than one mode.**

12 is the value that occurs the most which means it is the mode.

Find the mean, median, and mode of the data set.

**List the numbers in order from least to greatest.**

The mean is 4.875.

**To find the median, find values in the middle of the data set.**

There are an even amount of values in the data set, 4 and 6 are in the middle. To find the median find the average of 4 and 6 or find the midpoint of 4 and 6.

The median is 5.

**To find the mode, look for the value(s) that occur the most; there may be more than one mode.**

3 and 6 both occur twice, so there are two modes, 3 and 6. Since there are two modes, the data is bimodal.

The modes are 3 and 6.

**To find the range, find the difference between the largest value and the smallest value.**

8 - 2 = 6

The range is 6.

- Incorporate project based data science learning activities where students have opportunity to collect their own data, as well as do data analysis/statistical analysis on the collected data.

- Although worksheets and paper-based quizzes have their place, consider alternate forms of formative assessments that engage students to gain a global perspective by having them summarize data in real time with real world data points.

**Mixing up the measures of center**For example, if a student is asked to find the median and they find the mean.

**Listing the numbers in descending order instead of ascending order**When summarizing data, the best way to list the data is in ascending order (from least to greatest) not descending order (greatest to least).

**Thinking that the mean and median have to be a whole number**

When summarizing data, the mean and median do not necessarily have to be whole numbers. For example, for this data set, the mean is not a whole number.10, \, 8, \, 5, \, 5, \, 6, \, 7, \, 5, \, 11, \, 4, \, 9, \, 3

In this data set, the median is not a whole number.

12 and 13 are the middle numbers so to find the median, find the average between the two numbers.

Median = 12.5

- Averages and range
- Range in math
- Mean in math
- Mode in math
- Median

1. Find the mode of the given data set.

12

17

18

16

The value that occurs the most in the data set is 18. The other numbers only occur once.

2. Find the mode of the given data set.

19

21

23

19 and 23

The most common values are 19 and 23. These two values occur twice within the data set. The other values only occur once.

3. Find the median of the given data set.

18

19

17

31

Put the numbers in order from the smallest number to largest number. Then find the middle value.

The middle value is 17, so this is the median.

4. Find the median of the given data set.

35

36

37

38

Put the numbers in order from the smallest to largest. Then find the middle value.

The middle pairs of values are 35 and 37. The average of these is 36. The median is 36.

5. Find the mean of the given data set.

17

12.5

16.4

15.5

To find the mean, add up all the values in the data set and divide by the number of values in the data set.

6. Find the mean, median, mode, and range for the given data set (round to two decimal places when necessary).

Mean = 6.23, Median = 7.2, Mode = 7.2, Range = 7.9

Mean = 6, Median = 6.2, Mode = 7.2, Range = 8

Mean = 7, Median = 7.2, Mode = 7.2, Range = 7

Mean = 6.2, Median = 7, Mode = 7, Range = 7.2

List the numbers in order from least to greatest.

The value in the middle is 7.2.

The median is 7.2.

The value that occurs the most is 7.2. The mode is 7.2.

Range = 9.1-1.2 = 7.9

Range = 7.9

Yes, data sets can be made up of whole numbers (odd numbers and even numbers), integers, decimals, and fractions.

The arithmetic mean is the mean (average value) where you add all the values and divide by the number of values in the set of data.

An outlier is an extremely high or low data point in relation to the rest of the set of numbers in the data set.

The geometric mean is the square root of a product of two numbers.

The standard deviation is a statistical measure that measures the dispersion of data points relative to the mean.

Descriptive statistics is a method of summarizing data. Measures of central tendency are descriptive statistics.

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