1. PRE-ALGEBRA

2. Lesson 12-1 Warm-Up

3. PRE-ALGEBRA Mean, Median, and Mode (12-1) measure of central tendency: a measure that tells us where the middle of a bunch of data lies. The three most common measures of central tendency are the mean, the median, and the mode. mean (also called average): a number that describes the center (or middle) of a set of data (numbers). It is the sum of the numbers divided by the numbers of items added. Example: The mean (average) of 7, 8, 7, 9, 10, 6, 9, 8, 2, 7 is: 7 + 8 + 7 +9 + 10 + 6 + 9 + 8 + 2 + 7 = 73 / 10 = 7.3 median” – the “middle” number in a set of data (numbers) arranged from least to greatest or greatest to least (If there are two numbers in the middle, find the mean or average of the two numbers by adding them and dividing by 2) Example: 2, 6, 7, 7, 7, 8, 8, 9, 9, 10, median = 7 + 8 / 2 = 15 / 2 = 7.5 mode: the number that comes up the “most” Example: 2, 6, 7, 7, 7, 8, 8, 9, 9, 10 mode = 7 outlier: the number that doesn’t belong with the rest (much higher or lower than normal) Example: 2, 17, 18, 19, 16, 17, 15, 18, 20, 17 outlier = 2 What are “measures of central tendency”? What is a “mean”? What is a “median”? What is a “mode”? What is an “outlier”?

4. PRE-ALGEBRA Mean, Median, and Mode (12-1) range: the distance between the greatest and least value Example: 2, 6, 7, 7, 7, 8, 8, 9, 9, 10 Range: 10 – 2 = 8 Example: Find the mean, median, mode, and outlier(s) for the Read-a-thon graph. mean: Add the numbers and divide by the number of items added. 50 + 45 + 59 + 40 + 50 + 48 = 292 / 6 = 48.666…. 48.7 median: Put the numbers in order and find the one(s) in the middle. Since there are two numbers in the middle, find the mean (number in the middle) of those two numbers. 40, 45, 48, 50, 50, 59 48+50 = 98/2 = 49 mode: 50 appears most often = 50 range: highest – lowest number = 59 – 40 = 19 outlier: 59 appears to be an outlier, because it is 9 away from the closest value, whereas the rest of the values are within 5 of each other What is the “range”?

5. PRE-ALGEBRA Rita’s quiz scores were 72, 96, 74, 80, 96, and 79. Find the (a) mean, (b) median, (c) mode and (d) range of the data if you leave out Latana’s pages. a. Mean: 72 + 96 + 74 + 80 + 96 + 79 6 = 497 6 = 83.8  Rita’s mean or average test score is about 84. sum of data values number of data values LESSON 12-1 Additional Examples Mean Median and Mode

6. PRE-ALGEBRA (continued) b. Median: 72, 74, 79, 80, 96, 96 Write the data in order. The median is the average of the middle numbers = 79 + 80 / 2 = 79.5. c. Mode: Find the data value that occurs most often. The mode is 96. d. Range: Greatest value – Least value = 96 – 72 = 24. LESSON 12-1 Additional Examples Mean Median and Mode

7. PRE-ALGEBRA a. $1.10 $1.25 $2.00 $2.10 $2.20 $3.50 No values are the same, so there is no mode. b. 1 3 4 6 7 7 8 9 10 12 12 13 How many modes, if any, does each have? Name them. c. tomato, tomato, grape, orange, cherry, cherry, melon, cherry, grape Cherry appears most often. There is one mode. Since they appear the same number of times, there are two modes. LESSON 12-1 Additional Examples Mean Median and Mode Both 7 and 12 appear more than the other data values.

8. PRE-ALGEBRA a. Which data value is an outlier? Use the data: 7%, 4%, 10%, 33%, 11%, 12%. The data value 33% is an outlier. It is an outlier because it is 21% away from the closest data value. b. How does the outlier affect the mean? The outlier raises the mean by about 4 points or 4 / 12.8  31% 12.8 – 8.8 = 4 Find the mean with the outlier. 77 6 12.8 Find the mean without the outlier. 44 5 8.8 LESSON 12-1 Additional Examples Mean Median and Mode

9. PRE-ALGEBRA Mean, Median, and Mode (12-1) How do you choose the best measure of central tendency to describe a set of data? Example Situation: The favorite movie of students in the eight grade. Best Measure  Mode: The mode is the most appropriate measure, since you’re trying to find the one that most people like (“favorite”) and mode describes the most frequent item chosen. Example Situation: The daily high temperature during a week in July.. Best Measure  Mean: The mean describes what the high temperatures are most likely around (There probably won’t be an outlier, so the mean should be pretty accurate.) Exampe Situation: The distance students travel to school. Best Measure  Median: The median is more appropriate, since there is very likely at least one outlier for this set of data (at least one student probably lives much farther from school than the majority), which would influence the mean but not the median (middle value or values)

10. PRE-ALGEBRA a. the monthly amount of rain for a year Which measure of central tendency best describes each situation? Explain. Mean; since the average monthly amount of rain for a year is not likely to have an outlier, mean is the appropriate measure. When the data have no outliers, use the mean. b. most popular color of shirt Mode; since the data are not numerical, the mode is the appropriate measure. When determining the most frequently chosen item, or when the data are not numerical, use the mode. LESSON 12-1 Additional Examples Mean Median and Mode

11. PRE-ALGEBRA c. times school buses arrive at school (continued) Median; since one bus may have to travel much farther than other buses, the median is the appropriate measure. When an outlier may significantly influence the mean, use the median. LESSON 12-1 Additional Examples Mean Median and Mode

12. PRE-ALGEBRA Which measure of central tendency best describes each situation? 1.numbers of legs on the animals in a zoo 2.favorite digits (from 0 to 9) of the students in a class 3.numbers of days-per-student that students are absent from school 4.test scores median mode mean LESSON 12-1 Mean Median and Mode Lesson Quiz