1. Measures of Central Tendency and Range Choosing Measures of Central Tendency or Range to Describe a Set of Data and Justifying the Choice for a Particular Situation (TEKS 7.12A and B)

2. What do Measures of Central Tendency show us? Numbers or pieces of data that can represent the whole set of data

3. What are Measures of Central Tendency? Mean The arithmetic average of the set of data. The most common measure of central tendency. Median The median is the middle score in a set of data. Half the data will be above the median, and half below when data is ordered. Mode The mode is the most frequently occurring value or most popular choice

4. Consider the following math student: John Doe has gotten the following grades on homework: 9694901008691 8810009696 Without calculating – what type of student do you think John Doe is? (A student, B student, etc.) It appears that John is an A student

5. Grades: 9694901008691 8810009696 Find the mean, median, and mode of the grades Mean: about 85 Median: 94 Mode: 96 What caused John’s mean (average) to be an 85 instead of the A that we expected?

6. Pros and Cons Pros Mean Most familiar measure Uses all the data Median Not affected by extreme values Easy to compute Always exists Mode Easiest to find Not affected by extreme values Good for categorical data Doesn’t always exist Cons Mean Affected by extreme values (very high or very low) Median Doesn’t use all data values Data must be properly ordered Mode Doesn’t use all data values Not always descriptive of entire data set Not necessarily unique

7. Strategies to Choose the Appropriate Measure of Central Tendency Order the data first to make it easier to find the median and mode. Look for outliers (numbers that are a lot higher or lower than the rest of the set – an extreme value) – they affect the mean the most! Is the data numerical or categorical (words)? Start with the easiest – mode, then median, then mean. You may find you don’t need to work out all of them.

8. Using Measures of Central Tendency and Range to find Missing Data Identify which measure of central tendency you are given or if the range is given. Mode – Check to see if the mode of the data in the table and the mode given are the same. Median – Put the median given in the middle and order the data around it. Range – Are you missing the highest or the lowest piece of data? Mean – work backwards.

9. Answer the following using the strategies you have developed.

10. Super BowlChampion TeamDefeated Team XLIII (2009)Pittsburg, 27Arizona, 23 XLII (2008)New York, 17New England, 14 XLI (2007)Indianapolis, 29Chicago, 17 XL (2006)Pittsburg, 21Seattle, ___ XXXIX (2005)New England, 24Philadelphia, 21 XXXVIII (2004)New England, 32Carolina, 29 XXXVII (2003)Tampa Bay, ___Oakland, 21 XXXVI (2002)New England, 20St. Louis, 17 The table below is a list of past Super Bowl games, the champion teams, and the defeated teams. Tampa Bay was the highest scoring team in the years listed. The range of the scores of the champion teams is 31. What was Tampa Bay’s score? Seattle was the lowest scoring team in the years listed. The range of the scores of the defeated teams is 19. What was Seattle’s score?

17. Patrice records the number of calories she burns while exercising each day, as shown below. Day 1: 250 calories Day 2: 350 calories Day 3: 400 calories Day 4: 250 calories Day 5: 300 calories How many calories must Patrice burn on the sixth day to have a mean of 300 calories burned for the 6 days? F 0 calories G 150 calories H 250 calories J 310 calories

18. Randy and his 5 friends played a card game in which the person with the lowest final score wins. The table below shows the final scores for all the players except Erica. If Erica won the game and the range of the scores was 17, what was Erica’s score? F 104 G 106 H 140 J 124 PlayerScore Randy121 Erica Jon119 Sam107 Dawn123 Maya112