1. Warm Up #4
Describe in context (using complete sentences) the data represented in the Histogram!

2. Common Core Math I Unit 1: One-Variable Statistics Measures of Center and Spread

3. 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?
This is the warm up for day 4. It is also printed in the handouts for today. Discuss answers with whole class.
Possible answers/additional questions:
What data do you need to collect and how would you collect it?
Ask each group to share their ideas. There is no one right answer here.
Need a list of students names. Get it from the teacher. Poll the class. Ask everyone to write their first and last names on the board. Ask everyone to write the number of letters in their first and last names on the board.
How would you organize and represent your data?
Look for multiple answers to cover what has been covered so far: make a frequency distribution table, dot plot, histogram. Ask: What intervals would you use?
If a new student joined your class today, how might you use your results to predict the length of that student’s name?
Again, expect multiple ideas here, but focus on the center. The center of the distribution describes the typical value, so that is what we can use to predict the length of the new student’s name.

4. Describing Data Numerically
Measures of Center – mean, median
Measures of Spread – range, interquartile range, standard deviation
Again, just to remind students where they are in the study of one-variable stats. So today’s focus is on the median.
REPEATED SLIDE FROM DAY ONE!!!!
S-ID.2  Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets.

5. What is the typical value?
Measures of Center
What is the typical value?
These definitions are a little more student friendly than the ones in C-MAPP and are OK to use. The ones in C-MAPP are more precise.
REPEATED SLIDE FROM DAY ONE!!!!

6. Investigation 1: Dotplots vs. Histograms
Have students complete Investigation 1 from handout. Be sure to discuss as a class.
Possible answers/additional questions:
Describe the distribution of the data in context (shape, center, spread, outliers).
The distribution of name lengths of students in Ms. Jackson’s class is fairly symmetrical (or some may say slightly skewed left) with center around 13 letters. The length of the names varies from 9 letters to 17 letters. There are no apparent outliers. (Some students may say that 9 and/or 17 are outliers because of the gap between the main cluster and these values. This is OK, as long as they justify why they think they are outliers. If there is disagreement on this, that is a good thing because it will lead to the need for a process to identify outliers, which will come later in the unit. If no student mentions outliers, ask “Isn’t 17 an outlier?”)
How are the two graphs alike? How are they different?
In this case, their shapes look exactly alike because the histogram is using interval length of 1. How would this change if we used intervals of 2 or 5? The height of the stacks/bars shows the frequency of each name length.
The dot plot is using a dot to represent each data value but the histogram uses bars. The count is given by the height of the bar. There is a y-axis that shows the frequency.
How can you use each graph to determine the total number of letters in all the names?
Some students might misunderstand this question and give the total number of students, not letters. For example: I could count up all of the dots in the dot plot. In the histogram, I could find the frequency of each bar and add up the frequencies. If this misconception doesn’t come up, bring it up and have students explain why this is an incorrect interpretation.
To find the total number of letters, we need to multiply each value for the number of letters times the frequency of for that value and then add them up. In symbol form,  xf , where x represents a data value and f represents the frequency. This leads into the formula for weighted mean, which is x-bar = ( xf )/,  f . It is not necessary to formalize this with students, but may be helpful to make the connection when you talk later about finding the mean when given a frequency distribution (and not a list of data values). Some students may “un-do” the graph and make a list of values and then add them up. This is not wrong, just inefficient. You could have a discussion on which of the students methods is most efficient, but be careful not to force one method over another!
Cassandra Smithson said, “My name has the most letters, but the bar that shows my name length is one of the shortest on the graph. Why?” How would you answer this question?
The bar heights represent how many students have that name length, not the length of the name itself. So 17 has a bar height of one because only one student has that name length – Cassandra.

7. Complete Investigation 1
Describe the distribution of the data in context (shape, center, spread, outliers).
Shape: Symmetrical, Center: 13-15, Spread= 17-9=8, Outliers = none
How are the two graphs alike? How are they different?
Give the same description one has dots, one has columns
How can you use each graph to determine the total number of letters in all the names?
9*3 + 11*2 + 12*3 + 13*5 + 14*3 + 15*6 + 17*1
Cassandra Smithson said, “My name has the most letters, but the bar that shows my name length is one of the shortest on the graph. Why?” How would you answer this question?
The height of the bar is the frequency, not the length.

8. Investigation 2: Experimenting With the Median
Name
Number of Letters
Peter Thomas
Shaquana Smith
Stewart Hughes
Huang Mi
Richard Lewis
Virginia Bates
Ryan Mendoza
Mary Wall
Danielle Duncan
Will Jones
Ana Romero
Janay Turner
Peter Thomas 11
letters
Have students complete Investigation 3: Experimenting with the Median on the handout.
Possible answers/additional questions:
1. Remove two names from the original data set so that:
the median stays the same. What names did you remove? The median is Students can take any two names as long as the length of one is above letters and one is below 11.5 letters.
the median increases. What names did you remove? Any two names with length below 11.5 letters.
the median decreases. What names did you remove? Any two names with length above 11.5 letters.
2. Now, add two names from the original data set so that:
the median stays the same. What names did you add? The median is Students should add one above and one below Students may give you name lengths instead of actual names. That is OK.
the median increases. What names did you add? Add two names with length greater than 11.5.
the median decreases. What names did you add? Add two names with length less than 11.5
3. How does the median of the original data set change if you add
a name with 16 letters? There are now 11 names and the median name length would be 12 letters.
a name with 4 letters? There are now 11 names and the median name length would be 11 letters. Note that the median now in both cases is an actual data value, as is the case with all data sets that have an odd number of values. What happens with data sets that are an even number of values? (It depends, for example, if the two middle values are the same, then the median is an actual data value, but more often, the median is the midpoint between the two middle values and not an actual value of the data set.)
the name William Arthur Philip Louis Mountbatten-Windsor to the list? The first and last names have 24 letters. The median would change to 12. Note that even though we added a really long name to the list, the median didn’t change that much!

9. Wrapping it all up… How can we… - keep the median the same?
Add the same number of data values below the median and above the median
Add data values exactly the same as the median
- increase the median?
Add data values that are greater than the median
- decrease the median?
Add data values that are less than the median