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Session 1, Part B:
Data Measurement and Variation (65 minutes)

In This Part: Asking Questions and Collecting Data | How Long Is a Minute? | Variables

Let's start our exploration of statistics by focusing on the first two steps of the process: "Ask a question" and "Collect the appropriate data." The other steps will be explored in later sessions. We'll start with a simple statistical question. Note 2

Problem B1

Solution  

Let's say you'd like to find out the length of the room you're in.

Ask a question
How long is the room?

collect data
Measure the length of the room in inches, using two different measurement devices: (1) a one-foot ruler and (2) a yardstick.

Measure the room length five times with each device, and fill in the tables below. Record your measurements to the nearest inch.

Measurement Instrument

Room Length (in Inches)

Ruler

Yardstick

a. 

Are the five measurements you obtained with the ruler exactly the same? Can you explain why there may be differences?

b. 

Are the five measurements you obtained with the yardstick exactly the same? Can you explain why there may be differences?

c. 

Did you get similar answers using the different measuring tools? Why or why not? Did you get identical answers using the different measuring tools? Why or why not?

d. 

Which measuring tool do you think gave you more accurate results, the ruler or the yardstick? Why?

e. 

Do you think a tape measure would be more or less accurate than a ruler or a yardstick? Why? If you have a tape measure available, use it to measure the same room five times and see how the results compare with your previous measurements.



video thumbnail
 

Video Segment
In this video segment, participants discuss the results of the Room-Measurement Activity. Professor Kader then introduces the concept of variation in data. Watch the segment after you have completed Problem B1 and compare the variation in your measurements with those of the onscreen participants.

Which method(s) used by the participants produced the most variation? Which method(s) produced the least variation? How do your results compare with those of the onscreen participants?

If you're using a VCR, you can find this segment on the session video approximately 11 minutes and 46 seconds after the Annenberg Media logo.

 

 
 

Variation, or differences in measured data, occurs for a number of reasons. Examining variation is a crucial part of data analysis and interpretation. In fact, explaining the variation in your data is as important as measuring the data itself.


 

Problem B2

Solution  

Let's study two more statistical questions. For example, suppose you were curious about the relative heights and arm spans of men and women.

Ask a question
Are men typically taller than women?
Do men typically have longer arm spans than women?

collect data
Using a meter stick, measure the heights (without shoes) and arm spans (fingertip to fingertip) of three men and three women. Record your measurements to the nearest centimeter.

a. 

Did you get the same height for all six people? Did you get the same arm span for all six people? Why or why not?

b. 

If you measured all six heights and arm spans again, would the results be identical? Why or why not?


 

Problem B3

Solution  

Let's look at heights and arm spans again, this time measuring 24 people. Here are their data [heights (without shoes) and arm spans were measured to the nearest centimeter, using a meter stick]:

Gender

Height

Arm Span

Male

185

173

Female

160

161

Male

173

177

Female

170

170

Female

188

188

Male

184

196

Female

162

156

Female

170

162

Male

176

177

Female

166

165

Male

193

194

Male

178

178

 

Gender

Height

Arm Span

Male

180

184

Female

162

159

Male

187

188

Male

186

200

Male

182

188

Female

160

157

Male

181

188

Male

192

188

Female

167

170

Female

176

173

Female

155

160

Female

162

161


a. 

Examine the 24 measurements for height and arm span. You'll notice that they are not all the same. What is the source of this variation? Can you explain why there are differences?

b. 

Suppose your goal was to prove that men are typically taller than women. Does this data prove that conclusion? Why or why not?


 

Problem B4

Solution  

Ask a question
How much does a penny weigh?

collect data
We used a metric scale to weigh 32 pennies to the nearest centigram (1/100 of a gram). Here are the resulting weights:

Weight of a Penny (in grams)

3.08

2.50

2.46

3.05

2.45

3.12

3.05

3.14

2.48

3.10

3.02

2.47

3.10

3.03

3.11

2.52

3.00

3.09

3.15

3.06

3.18

2.42

2.43

2.50

3.07

3.09

3.00

3.09

2.47

3.05

2.52

3.07



a. 

The 32 measurements are not all the same. What is the source of this variation?

b. 

What do you think would happen if you weighed the same penny 32 times? How would you expect that data to compare to the weights of the 32 different pennies?


Take it Further

Problem B5

Solution

Based on the data in Problem B4, how much would you expect the 33rd penny to weigh? Could you be sure of its weight before weighing it? If you can't name an exact weight, could you be confident about a range of weights that it falls between? Why?


 

Next > Part B (Continued): How Long Is a Minute?

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