# Measures of Center and Variability Worksheets

When we are analyzing data sets, large or small, it is very helpful to understand the nature and dynamics that might exist within the set itself. One solid method to help you establish the identity of what the information is telling you is to locate the center of of the statistics itself. We would like to establish what is average and what is not. After we identify the middle, it is helpful to understand how spread out that data may be. Variability is the measure of how dispersed from the center, the values that we have collected are. These statistics worksheets will have students use data pools and learn to calculate measures of center and the degree to which the data differs.

### Aligned Standard: Grade 7 Statistics - 7.SP.B.4

- Median and Mean Step-by-step Lesson- Use the bar graph to determine the best answer to each of the questions.
- Guided Lesson - Find out how additional statistics could change your current conditions. Then take a look at Orange Airlines.
- Guided Lesson Explanation - I led 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 what all of these figures mean.
- Matching Worksheet - See if you have any trouble following what I am driving at with this one.

- Answer Keys - These are for all the unlocked materials above.

### 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 figures that you are working with.
- 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 stream of information.
- 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.

- Quiz 1 - Find the mean of first four multiples of 4.
- Quiz 2 - If the mean is 8, which number could be c?
- Quiz 3 - Find the mean (or average) amount of time those surveyed devote to one drawing.

### What are Measures of Center and Variability?

When we have a question about something or are trying to make sense of an outcome, we often reflect on large amounts of data that may be available. When we take our time to understand this information it will not only help understand why something may have happened, but it enables us to make much more well thought out decisions.

Accurately collecting data is very important and essential to come out with a valid explanation or insight. Making sense of this figures is one of the more challenging aspect of data interpretation and it often done by looking at some key metrics that indicate the nature of any data set. When we evaluate these sets, we often center or thoughts on five key areas to better understand what it tells us. Those areas include:

**Central Tendency** - A single value that describes a set of data by identifying the central position in a given set of figures 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 statistics are 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 set of values. 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 a sets of numbers. It also helps in comparing the statistics of your data with other information that you may have available or have collected. 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. This is often not a critical aspect of a form of interpretation but is helpful when preparing to visualize and organize the data to explain to others.

Regardless of the type of statistics you are focused on, these measures will help you instantly begin to piece together any relationships that might exist within the information that is the focus of your evaluation. It is often the first step in any form of data evaluation.