Objective: TSW Calculate the Mean, Median, Mode, and Range of a Given Data Set and Solve

Lesson 11 - Measures of Central Tendency

Objective: Calculate the measures of central tendency for a given data set. Warmup Define Mean – ______

Median – ______

Mode – ______

There may be more than one mode or no mode at all.

Range – ______

Maximum - ______

Minimum - ______

Process/Steps:

Mean Step 1 – Add up all of the numbers given. Step 2 – Divide the sum by the total number of numbers added. Median Step 1 – Put numbers in order from least to greatest. Step 2 – Locate the middle number Step 2a – If there is an exact middle number, that is the median. Step 2b – If there are two numbers in the middle, add them together and divide by 2. (Find their mean) Mode Step 1 – Locate the number that occurs most often Step 1a – If more than one number occurs most often, the mode is those numbers. Step 1b – If no number occurs most often, the mode is NONE, not 0. ( If 0 is written, that means 0 occurred most often. ) Range Step 1 – Locate largest and smallest number Step 2 – Subtract smaller number from larger number (biggest number minus smallest number.) Maximum and Minimum

Example 1: Seven students in the seventh grade took a quiz. They scored the following: 30, 30, 24, 24, 27, 37, 24.

1. To find the mean, add all of the numbers, then divide by number of addends. (number of numbers added)

24 + 24 + 24 + 27 + 30 + 30 + 37 = 196 196 ÷ 7 = 28 The mean is 28 points.

2 To find the median, arrange that data in order from least to greatest, then find the middle number.

24, 24, 24, 27, 30, 30, 37 The median is 27.

3. To find the mode, find the number that occurs most often. The mode is 24. 4. To find the range, subtract the greatest number and the least number. This will show the spread of the data.

37 – 24 = 13 The range is 13 points. Find the mean, median, and mode(s) of the data.

Example 2: 8, 12, 15, 17, 18, 26 Mean: _____ Median: _____ Mode(s): _____

Example 3: 186,144, 201, 164, 182, 164 Mean: _____ Median: _____ Mode(s): _____

Example 4: The monthly charge for seven dial-up internet service providers are listed. What is the mean price? $10, $22, $17, $11, $16, $23, $25 ______

Find the mean, median, mode, range, maximum, and minimum of each set. 1. {1, 2, 2, 3, 4, 5, 11} 2. {7, 6, 1, 7, 4} 3. {7, 10, 3, 2, 5, 12} Mean Mean Mean Median Median Median Mode Mode Mode Range Range Range Maximum Maximum Maximum Minimum Minimum Minimum

Assignment

1.) Money earned from a penny drive at Vista Grande High School. Find the range, mode, median, and mean.

Mean: Grade Amount 9 $165 Median: 10 $125 11 $117 Mode: 12 $140 Staff $153 Range:

2) 5, 10, 15, 1, 2, 3, 7, 8 Mean:

Median

Range:

3) Given the following salary information. If you were going to attract people to this company, would you use the mean, median, or mode salary? Explain. Amount Frequency $25,000 4 $30,000 2 $45,000 2 $50,000 1

4) Mindi surveyed her friends about their current grades. Their responses were: 72, 88, 78, 82, 92, 88, 95, 85, 92, 88, 75, 85, 77, 83, 80, 90 Place the information into a stem-and-leaf plot. Find the: Mean: Median: 6 ______Mode: Range: 7 ______Maximum: 8 ______Minimum: 9 ______

5. The following stem-and-leaf displays the number of times students eat out within a year. Find the: 9 9 Median: Mode: 2 2 3 4 5 6 7 7 8 Range: 1 3 4 4 4 4 Maximum: Minimum: 0 0 0 1 2 2 2 2 2 8

0 4 5 6

6. The frequency chart to the right displays the number of siblings for Ms. Dolezal’s students. # Siblings Frequency 0 5 1 4 2 2 3 7 4 4 5 2 6 2

Find the: Median: _____ Mode: _____ Range: _____ Maximum: _____ Minimum: _____

7. What value of n in the following data set will result in a range of 40? 10, 25, 38, 72, 15, 5, 14, 13, 20, 15, 17, 37, 42, n

8. Consider the ages of everyone in this room, including all students and the teacher. What measure(s) of central tendency would not represent the class best? Why?

9. You scored 70, 95, 75, 75, and 85 on recent quizzes. Which two measures of central tendency would be the same value?

10. The weights of 11 students are listed. What is the upper quartile of this data set? 98, 121, 110, 210, 175, 180, 150, 161, 175, 130, 140