Data Analysis Instructional Unit

Jessica Palmer

Standard Covered: M7D1. Students will pose questions, collect data, represent and analyze the data, and interpret results.

a. Formulate questions and collect data from a census of at least 30 objects and

from samples of varying sizes.

b. Construct frequency distributions.

c. Analyze data using measures of central tendency (mean, median, and mode),

including recognition of outliers.

d. Analyze data with respect to measures of variation (range, quartiles,

interquartile range).

Day One

The data analysis project will be introduced at the beginning of class. This is the culminating project for our 6 week data analysis unit. Each student will be required to select a research question that can be asked to a sample of at least 30 students. I will model each step of the data collection and analysis project using the question “How many hours of sleep did you get last night?” using the class as the sample. Each answer must be rounded to the nearest hour.

None of my six students are familiar enough with Microsoft Word to do more than type a paper, so we will be spending a considerable amount of time learning how to create tables.
I will use my computer hooked up to the TV as the class helps me create a table appropriate for the sample question listed above. This will involve a lot of trial and error as the class sees how user friendly (or not user friendly) their suggestions are. Hopefully, our finished product will look like this:

Person Number / # of hours of sleep last night
1
2
3
4
5
6

I’ll write this table on my whiteboard and have each student come up and write in how many hours of sleep they got last night

Day Two

We will start class by briefly reviewing how to construct a frequency table and histogram and how the two displays are related. I’ll have the class copy the completed data table from yesterday onto a sheet of notebook paper and they’ll work in pairs to create a frequency table. Hopefully, it’ll look like this:

# of hours of sleep last night / Tally
6 / II
7 / IIII
8 / II

After each pair has a frequency table in hand that I’ve approved, we’ll go to the computer lab to use Excel to make the histograms. They will each open up a new workbook and type in the label for the y axis under column A- “Number of Hours of Sleep Last Night.” In column B they will write “Frequency” and fill in the appropriate numbers using their frequency table.

Number of Hours of Sleep Last Night / Tally
6 / 2
7 / 4
8 / 2

Then, the class will follow these steps which will be typed and next to their desks:

Select the text and click Insert -> Column -> 2D Column. We will stop here and talk about the characteristics of a histogram and why this is NOT a histogram.

Right click the graph and click “Select Data”
Select the words “Number of Hours of Sleep Last Night” and click “Edit” located in the Horizontal (Category) Axis Labels section.
Once the box pops up, use your mouse to select the data “6,7,8” on your Excel workbook and hit OK.
Click on Upper Limit of Interval to highlight the selection and then click the Remove button.

Note: these instructions were taken from

Day Three

My rationale for allowing Excel to calculate measures of central tendency is twofold: we have already spent 6 weeks learning how to do this and each student is able to perform these calculations and all of my students are allowed to use calculators based on their IEP accommodations.

To complete today’s activities, each student will need to refer back to the original data set that was copied down on Day One.

Person Number / # of hours of sleep last night
1 / 6
2 / 8
3 / 7
4 / 7
5 / 7
6 / 6
7 / 8
8 / 7

First, I will have my students number each participant under column A in Excel. For the purposes of the illustration, I chose to show a much smaller sample size than is required of my students. Column B is where the number of hours will go.

To calculate mean, I will show the class how to highlight the selection

Once the selection is highlighted, I’ll click Formulas, then AutoSum, then Average. The mean will show up below the data set as 7.

Then, we’ll calculate median by writing the numbers in order from least to greatest and finding the middle number (7). The mode will be found by looking at which number occurs most (7). Since we have the data ordered from least to greatest, we’ll also review how to construct a box-and-whisker plot by finding the upper and lower quartiles. The rest of day three will be spent reviewing how to calculate measures of central tendency and quartiles given several data sets. (See Appendix A). We will also calculate interquartile range.

Day Four

This is the first day that my students will begin work on their individual projects. They will get in pairs to talk about research questions that they would be interested in answering. For the purposes of this project, the questions must be answered with numerical data as opposed to categorical data.

After the students have spent about ten minutes in pairs discussing questions, I will give them an index card to write their question on. Each student will share their question and take advice from the class as to how their data table should be designed. The end product of this class will be a research question and the beginning of a data table. Most of the work will be done in pairs or groups so that the students can bounce ideas off each other instead of always asking me what I think. Towards the end of class I’ll allow five or ten minutes to answer questions.

Day Five

Today will be spent in the computer lab designing the data collection tables. I will be available to assist as needed, although this is a culminating project and I expect the students to be able to function largely on their own. At the end of the period, each student should have a hard and soft copy of their data table to be used.

Day Six

Today will be used to collect the data. My students will visit other math classes and make short pitches, one at a time, to the class. They will collect their data and quietly wait for the rest of the class. I expect to be able to visit all three math classes with my six students in one class period.

Day Seven

Today the class will make a frequency table and histogram with their data set in the computer lab using the steps already given. They will be required to print out their final graphs.

Day Eight

Today will be used to analyze the data using measures of central tendency in the computer lab. I will require each student to calculate the measures without technology and then as demonstrated above the data will be entered into Excel to find the mean.

Day Nine

Today is the last day to work on projects- they’ll be creating their box and whisker plot as their last graph and preparing the poster. It must be colorful and interesting and display every element of the standard M7D1.

Appendix A

-3, 14, 0, 3, 6, 8, 0, 4, -3, 13, 1.5, 2, 8, -4, -6, 1, .5, 6, 7

Mean-Mean-

Median- Median-

Mode-Mode-

Range- Range-

Outliers? Outliers?

Upper Quartile-Upper Quartile-

Lower Quartile-Lower Quartile

Upper Extreme-Upper Extreme-

Lower Extreme-Lower Extreme-

IQR-IQR-

0, 1, 2, 6, 15 14, 4, -2, 1, 8, -6, -3, -4