## Central Tendencies and Normal Distribution Curve

### Dan SchmidtSanta Rosa District Schools

#### Description

Students will be given data (class test scores) to determine central tendencies, and will find information needed to construct a normal distribution curve.

#### Objectives

Adds, subtracts, multiplies, and divides real numbers, including square roots and exponents using appropriate methods of computing (mental mathematics, paper-and-pencil, calculator).

Determines the impacts when changing parameters of given functions.

Interprets data that has been collected, organized, and displayed in charts, tables, plots.

Calculates measures of central tendency (mean, median, mode)and dispersion (range, standard deviation, and varience) for complex sets of data and determines the most meaningful measure to describe the data.

-Calculator
-Worksheet

#### Preparations

1. Duplicate worksheets (see associated file).
2. Obtain a calculator for each student.

#### Procedures

Pre-requisite: This lesson will show students that data can be presented in many different forms. Before beginning this lesson talk to students about the different ways data or information can be presented.

1. Students write down given data (see the associated file) and then organize the data in increasing order.

2. Help students find the mode: the number used most often in the data. Note: You can have more than one mode, or no mode at all.

3. Find the median: This will be the middle number in the data that is organized in increasing order. If there are two middle numbers add them and divide by two.

4. Find the mean (average): Sum the numbers in the data and divide by the number of pieces of data.

5. Find the Range: Take the difference between the largest number in the data and the smallest number in the data.

6. Find the deviation: This will be the difference between each number in the data and the mean. Number in data - Mean = Deviation. Do this for each number in the data.

7 Find the variance: - square each deviation
- sum
- divide by (number of pieces of data minus 1)

8. Find the standard deviation: Take the square root of the variance.

9. Use the standard deviation to construct a normal distribution curve (normal curve).
- Find the following standard deviations: (see example if there are any questions)
+1 standard deviation: Mean + standard deviation
+2 standard deviation: Mean + 2(standard deviation)
+3 standard deviation: Mean + 3(standard deviation)
-1 standard deviation: Mean - standard deviation
-2 standard deviation: Mean - 2(standard deviation)
-3 standard deviation: Mean - 3(standard deviation)

10. Students then determine how many pieces of the data fall within + 1 standard deviation. Then students will find the percentage of numbers that fell in this area. It should be around 68%.

#### Assessments

Assess student work using the rubric in the associated file.

#### Extensions

This lesson can be applied to any data given to or found by students