# SOCR Courses 2007 2008 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 www.socr.ucla.edu and click on the Charts tab at the top of the page. Once the page comes up, go to the left side of he page and drag the grey 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 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 UPDATE button to see the effect of these changes on the histogram. Do this several times. Take a SNAPSHOT and print off one new histogram.

#### 2. Simple Histogram from Raw Data

- Click on HistogramChartDemo
- Scroll down to find the Bin Size adjustment bar
- Change the bin size

#### 3. Histogram from Simulated Data

- Lets first get some data: Go to the Modeler tab at the top of the page. It is 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 using the Copy button at the top. (select all using Apple+a)
- Go back to the data section of the histogram chart and replace the current data with the data you just copied. Make sure to use the PASTE button on the left.
- Click UPDATE CHART
- Change the bin size smaller and larger and observe how the graph changes
- Repeat but change the number of samples to 100
- Take a SNAPSHOT and print off one new histogram

#### 4. Questions

Answer each question fully using appropriate terminology and references to snapshots if appropriate.

1) What is the effect of the width/size of the histogram bin on the shape of the resulting histogram? Would the shape of the histogram change significantly if we alter the bin-size?

2) How do the sample size and bin size interact?

3) Would you expect the shape of the sample histogram to look like the shape of the population distribution the data sample came from?

- SOCR Home page: http://www.socr.ucla.edu

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