## Measures of Center and Variability

#### Aligned To Common Core Standard:

**Grade 7 Statistics** - 7.SP.B.4

What are Measures of Center and Variability?
Do you know what central tendency and its measures are? Let's take a look!
**Central Tendency** - A single value that describes a set of data by identifying the central position in a given set of data is known as the central tendency. There are three measures of central tendency; mean, median, and mode.
**Mean** - The average of all the values in the data set is known as mean. The formula for mean is the total sum of terms divided by the number of terms.
**Median** - The number that falls in the exact center of the given data is known as the median. For finding the median, the data is arranged from the smallest to the biggest number to see which number falls in the middle.
**Mode** - Calculating the mode is pretty easy. It is the number that occurs the most frequently in the given data. Let's say that in a data set, which represents 12 students borrowing books from the library. Some took one, some two, but most books taken were three. So the mode will be 3 since it is the most frequently appearing number.
**Variability** - Variability is defined as how much a group of data is spread. Variability helps you to understand the variation in data sets. It also helps in comparing the statistics of your data with other data. The measures for variance are standard deviation and range.
**Standard deviation** - A figure that represents how far each number is from the mean is known as standard deviation. When the standard deviation is low, it implies that most of the values are near the mean. If the values are present far from the mean, the standard deviation is high.
**Range** - The range is defined as the difference between the highest and lowest numbers in the data set. These statistics worksheets will have students use data pools and learn to calculate measures of center and the degree to which the data differs.

### Printable Worksheets And Lessons

- Median and Mean Step-by-step
Lesson- Use the bar graph to determine the data.

- Guided Lesson -
Find out how additional data changes your current conditions. Then
take a look at Orange Airlines.

- Guided Lesson Explanation
- I lead the students to the answers with this one. It just made
more sense with this skill.

- Practice Worksheet
- We focus mostly on central tendencies and determine data's affect
on it.

- Matching Worksheet - See if you have any trouble following what I am driving at with this one.

#### Homework Sheets

These sheets will really help students start to make sense of large pools of data.

- Homework 1 - On Sports Day students wear different color T-shirts. Find the median and mean of the data.
- Homework 2 - 5 students had their science project graded. Their scores are as follows: 40, 35, 37, 48, and 46 respectively. Find the mean (or average) of their scores?
- Homework 3 - Look at this set of 9 numbers: How would the range change if the number 6 replaced one of the 2s in the set?

#### Practice Worksheets

We work on skills that are most commonly used in Science to fudge data; as my old college professor reminded me.

- Practice 1 - Find the mean, median and mode of this data.
- Practice 2 - How would the range change if the number 3 is replaced one of the 1 in the set?
- Practice 3 - How would the range change if the number 32 replaced one of the 36 in the set?

#### Math Skill Quizzes

Now it's time to start to see how the mean and median are affected by smaller changes.