Good research questions Review Good research questions

Create a good research question Age Income Health Education Using two of the concepts from above create a good research question. Explain the criteria as it pertains to your question. What is the average income of high school graduates? Population: High School graduate Variable: Income Numerical Characteristic: Average income

Review Mean as a balance point

Mean as a balance point

Mean as a balance point

Mean as a balance point

Mean as a balance point

Which is your favorite season? Fall Spring ✿ Summer R Winter T

Which is your favorite season? Fall Spring ✿ Summer R Winter T

Brainology Do you think the description matches the way you think and feel about school work? Which parts are true? Which parts are not?

Which is your favorite main subject? Science Language Arts Social Studies Math

Which is your favorite main subject? Science Language Arts Social Studies Math

Module 7 What where the big ideas from Module 7 (dot plots and histograms). Discuss with your group and write one idea of the board.

What continent would you most like to visit?

Africa

Europe

Asia

Australia

What continent would you most like to visit? Africa Asia Europe Australia

Module 8 Discuss module 8 with your group. What questions do you still have. Write them on the board.

Mean What are three other words for mean? What does it mean as mean at the balance point? Practice: Find the mean of the following data. Then find the find the sum of the distance from the mean. 5, 10 16, 6, 55, 22

Which would be hardest to live without? cell phone TV ipod video games

Which would be hardest to live without? cell phone TV ipod video games

What’s the age? This is your group you will work with for the next activity. Find a seat

Interquartile Range and Boxplots Module 9 Math 075 Summer 2015

Variability Depends on how we measure variability: One way is to find the range: Maximum Value – minimum Value But what if the data sets have the same range? Lets look at the distribution of the data.

Variability about the median Quartiles: Divides the data into four equal parts. (25% of the data will be in each quartile) Some quartiles have more variability than others. We find the Interquartile range: Q3 – Q1

The 5 Number Summary The five number summary consist of : The median ( 2nd quartile) The 1st quartile The 3rd quartile The maximum value in a data set The minimum value in a data set

The 5 Number Summary Step 1 - take the set of numbers given… 34, 18, 100, 27, 54, 52, 93, 59, 61, 87, 68, 85, 78, 82, 91 Place the numbers in order from least to greatest: 18, 27, 34, 52, 54, 59, 61, 68, 78, 82, 85, 87, 91, 93, 100

68 is the median of this data set. The 5 Number Summary Step 2 - Find the median. Remember, the median is the middle value in a data set. 18, 27, 34, 52, 54, 59, 61, 68, 78, 82, 85, 87, 91, 93, 100 68 is the median of this data set.

The 5 Number Summary Step 3 – Find the lower quartile. The lower quartile is the median of the data set to the left of 68. (18, 27, 34, 52, 54, 59, 61,) 68, 78, 82, 85, 87, 91, 93, 100 52 is the lower quartile

The 5 Number Summary Step 4 – Find the upper quartile. The upper quartile is the median of the data set to the right of 68. 18, 27, 34, 52, 54, 59, 61, 68, (78, 82, 85, 87, 91, 93, 100) 87 is the upper quartile

18 is the minimum and 100 is the maximum. The 5 Number Summary Step 5 – Find the maximum and minimum values in the set. The maximum is the greatest value in the data set. The minimum is the least value in the data set. 18, 27, 34, 52, 54, 59, 61, 68, 78, 82, 85, 87, 91, 93, 100 18 is the minimum and 100 is the maximum.

The 5 Number Summary Step 5 – Find the inter-quartile range (IQR). The inter-quartile (IQR) range is the difference between the upper and lower quartiles. Upper Quartile = 87 Lower Quartile = 52 87 – 52 = 35 35 = IQR Looking at the middle 50% of the data

The 5 Number Summary Organize the 5 number summary Median – 68 Lower Quartile – 52 Upper Quartile – 87 Max – 100 Min – 18

What about outliers? Boxplots are the only graphical representation where we specifically define an outlier Potential outliers are values that are more than 1.5 IQRs from Q1 or Q3 IQR x 1.5; add that product to Q3; any value(s) beyond that point is an outlier to the right Q1; any value(s) beyond that point is an outlier to the left

Siblings data... Using Stat Crunch, calculate descriptive statistics Let’s calculate (by hand) to see if we have any outliers Q3 – Q1 = IQR IQR x 1.5; add this product to Q3; are there any values in our data set beyond this point to the right? IQR x 1.5; subtract product from Q1; are there any values in our data set beyond this point to the left? Now use Stat Crunch to create a boxplot; are our calculations confirmed with our boxplot?

Box and Whisker Diagrams. Anatomy of a Box and Whisker Diagram. Lower Quartile Upper Quartile Lowest Value Median Highest Value Box Whisker 4 5 6 7 8 9 10 11 12 Box Plots

Graphing The Data Notice, the Box includes the lower quartile, median, and upper quartile. The Whiskers extend from the Box to the max and min.

Do you know your geography? Look at the slip of paper I gave you. With out talking to anyone answer the questions to the best of your ability. Now find your group according to the first question on your paper. Line up in order of your population estimate Find the 5-number summary Determine if there is any outliers Draw one boxplot for each group on the board In your groups find one observation about the two box plots Have students do the 5 number summary.

Do you know your geography? The actual population is 13646 How close was your estimate? Which group did a better job? How can you tell? Why do you think one group did better than the other? Have students do the 5 number summary.

Interpreting the Box Plot: Study your Box and Whisker Plot to determine what it is telling you. Make a statement about what it is saying, then support the statement with facts from your graph.

You should include the following in your interpretation: Range or spread of the data and what it means to your graph Quartiles—compare them. What are they telling you about the data? Median- this is an important part of the graph, and should be an important part of the interpretation. Percentages should be used to interpret the data, where relevant.

Analyzing The Graph The data values found inside the box represent the middle half ( 50%) of the data. The line segment inside the box represents the median

Your turn... In pairs, choose a set of data from the Math 075 spreadsheet that is skewed (to left or right); you probably won’t know if the data is skewed until you copy and paste into Stat Crunch and create a graph Create a box plot; print out; put your names on it Label (on the graph) the 5-number summary (with arrows pointing to each value on the graph) Analyze through SOCS (which measure of central tendency should you use? Which measure of spread should you use?); be sure you show your work to justify that a point/points are outliers Now, using the same data, create a histogram. What characteristics of the data does the histogram show that the box plot does not?

Project #2 You now have time to work on this project. You will need to present this project on Thursday

Homework Read OLI 41-44 Check point for Module 8 Journal #3 Brainology