Warm Up 1)Are the following categorical or quantitative? a) Typing speed b) Receiving Pass or Fail as a grade c) The number of questions correct on a test 2) Amy got test grades of 80, 97, 88 and 94. What grade would she have to get on her 5 th test to have a 91 average?

Homework Check 2.1

Unit 2, Day 2 Measures of Center

Measures of Center What is the typical value?

Finding the Median 1) 2) 3, 13, 7, 5, 21, 23, 39, 23, 40, 23, 14 4, 2, 11, 6, 2, 9

Measures of Center: Median Most parents don’t worry about the number of letters in their children’s names. Sometimes, though, it does matter. For example, only a limited number of letters will fit the “name” part of a bubble sheet. A manufacturer of bubble sheets for standardized tests needs to know how many spaces to leave for the name so that most test takers names will fit in the name area.

Think About the Situation Discuss the following with your partner or group. Write your answers on your own paper. Be prepared to share your answers with the class. What do you think is the typical number of letters in the full names (first and last) of your classmates? What data do you need to collect and how would you collect it? How would you organize and represent your data? If a new student joined your class today, how might you use your results to predict the length of that student’s name?

Investigation 1 We can use the median of a set of data to describe what is typical about the distribution. Let’s use this measure of center to describe the distribution of names in a class. Below are twelve names. Count the number of letters in each name and write that number in the column labeled “Number of Letters”. Do not count spaces.

1) What is the median? 2) Remove two names from the original data set so that: a) the median stays the same. What names did you remove? b) the median increases. What names did you remove? c) the median decreases. What names did you remove?

3)How does the median of the original data set change if you add a) a name with 16 letters? b) a name with 4 letters? c) the name William Arthur Philip Louis Mountbatten-Windsor (a.k.a. Prince William) to the list?

Thinking About the Situation

The Formula Don’t worry about memorizing this!

Investigation 2: Mean vs. Median The heights of Washington High School’s basketball players are: 5 ft 9in, 5 ft 4in, 5 ft 7 in, 5ft 6 in, 5 ft 5 in, 5 ft 3 in, and 5 ft 7 in. A student transfers to Washington High and joins the basketball team. Her height is 6 ft 10in. 1)What is the mean height of the team before the new player transfers in? median height? 2)What is the mean height after the new player transfers? median height? 3)What effect does her height have on the team’s measures of center? 4)How many players are taller than the new mean team height? How many players are taller than the new median team height? 5)Which measure of center more accurately describes the team’s typical height?

How do I know which measure of central tendency to use? MEAN – useful when the data set does not have an outlier MEDIAN – useful when the data set does have an outlier

Investigation 3: Using the Mean

1)Find the following: a)the total number of students b)the total number of movies watched c)the mean number of movies watched 2)A new value is added for Carlos, who was home last month with a broken leg. He watched 31 movies. a)How does the new value change the distribution on the histogram? b)Is this new value an outlier? Explain. c)What is the mean of the data now? d)Compare the mean from question 1 to the new mean. What do you notice? Explain. e)Does this mean accurately describe the data? Explain.

3)Data for eight more students is added. a)Add these values to the list in your calculator. How do these values change the distribution on the histogram? b)Are any of these new values outliers? c)What is the mean of the data now?

Coming up… Possible quiz?? HW 2.2 Unit 2 TEST – Friday!! Unit 2 Project  due Friday, September 27 th Mrs. Wolf’s extra help Tuesday & Thursday!