# SOCR Courses 2012 2013 Stat13 1 Lab1

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## Contents |

## Stats 13.1 - Laboratory Activity 1

### Histogram Activity

This is an exploratory data analysis SOCR activity that illustrates the generation and interpretation of the histogram of quantitative data. In a nutshell, a histogram of a dataset is a graphical visualization of tabulated frequencies or counts of data within equispaced partition of the range of the data. A histogram shows what proportion of measurements fall into each of the categories defined by the partition of the data range space.

Go to the SOCR Charts (use the Charts tab at the top of the page). Once the page comes up, go to the left side of the page and drag the gray bar to the right.

#### 1. Histogram from Categories and Frequencies

- In the area on the left, click the arrow next to Bar Charts then XYPlots. Then click on HistogramChartDemo3.
- Click on the SNAPSHOT button and save a copy of this original histogram.
- Click on the DATA tab to view the default data. Notice that the chart requires the user to enter the counts/frequencies of observations within each of the range categories (in this default data case, year).
- Using the SHOW ALL tab you can see all three (graph, data and mapping) in the same view.
- Try revising some of the numbers in the second (frequency) column and click the UPDATE CHART button to see the effect of these changes on the histogram. Change the frequency for at least 6 years.
- Click on the GRAPH button to return to view just the histogram. Take a SNAPSHOT and

print off your new histogram.

#### 2. Simple Histogram from Raw Data

- Click on HistogramChartDemo1 and take a SNAPSHOT of the original histogram.
- Scroll down to find the Bin Size adjustment bar
- Make the size of the bins both smaller and larger. Take a SNAPSHOT of each.

#### 3. Histogram from Simulated Data

- Let's first get some data: Go to the Modeler tab at the top of the page (It's best if you open a new page for this).
- Click on the Data Generation button in the center of the screen. From the drop down bar choose the Normal Distribution and change the number of samples to 20 and the standard deviation to 100. Make sure the Raw Data box on the left is checked.
- Hit Sample then click on the Data tab to see the data you generated.
- Copy these data by highlighting them with the mouse and then using the Copy button at the top.
- Go back to the your histogram plots window and click on the DATA section. Wipe out the old data by pressing on the CLEAR button and then click on the first cell under the column C1. Click on the PASTE button on the left to paste your new data into the window. Double click on 'C1' and relabel your column of data as 'Data' then hit the RETURN key on your keyboard.
- Click UPDATE CHART. Go back to your histogram and take SNAPSHOT of your new histogram.
- Change the bin size of your histogram and take SNAPSHOTs of it with both a smaller and larger bin size.
- Redo the previous steps again but this time generate 150 samples.
- Remember to take a SNAPSHOT of your new histogram with the original bin size, with a smaller bin size and with a larger bin size.

#### 4. Exercise Questions

**Directions**: Answer each question by using complete sentences and appropriate terminology. Remember to word your solutions in such a way so that the reader will understand the question you're being asked to solve. You should include appropriately sized snapshots to help explain your answers.

- From the Histogram from Categories and Frequencies section:
- How many data points are included in the original histogram (before you made your changes).
- Describe the distribution (Where is it centered? How is it shaped? How much spread is there?). Would using the mean or median be more appropriate for describing the center of the distribution? Why?
- How does the snapshot of the original distribution compare to the snapshot of the one you changed (in terms of the center, shape and spread of the distributions)?

- From the Simple Histogram from Raw Data section:
- Describe the original distribution (with bin size = 0.1).
- Compare the original distribution with the other two snapshots with smaller and larger bin sizes. How does the Y-axis change when bins are smaller or larger? Why does this occur?
- As the bin size gets smaller or larger, how is the shape of the distribution afected?

- From the Histogram from Simulated Data section:
- Describe the distributions of the histograms using both 20 and 150 samples (and the original bin size). How do they compare?
- What happens to the shape of the histogram as we take larger samples?
- Look at your snapshots of the histograms with 150 samples. What happens as the size of the bins get smaller and larger? Of the three snapshots you took, which bin size do you think best describes the data?
- Under what circumstances would you use smaller or larger bin sizes?

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