Download Fathom Project Pacing a Normal Distance Word Doc

Fathom Project: Pacing a Normal Distance
Due: Friday, October 11
Worth: 30 points
Over the past several years, students in Mr. Bross’ physics classes have measured the distance
between buildings on campus by pacing the distance between the buildings. You will be using
Fathom to analyze this data. Your answers to the questions below, along with supporting
graphs, will be in a Word Document. Be sure to name your file with your name and your
partner’s name. When finished, upload the file to dropitto.me/nataro (password: nataro).
1) Find the Fathom file on the student common drive in the Nataro folder. It is called “Pacing a
Normal Distance”.
2) With the collection selected, drag a table to the desktop. There are three distances given –
Heath to Snyder, Snyder to Walter and Heath to Walter. How many observations are in each
of the three lists? What do you think Mr. Bross has listed at the bottom of each list?
3) Remove the values in rows 525 and 526. Do this by clicking on the row. Then right click and
choose Delete Case. (Row 525 is an empty row.)
4) Create a histogram for each set of data. Does the distribution appear to be approximately
normal based on the histogram? If not, what is the shape?
5) There are two obvious outliers. List their values. What do you think happened to this
person when they did their data collection?
6) Create a five number summary for each data set. Also, find the mean and standard
deviation. Which set of data has the most variation? Explain why this makes sense.
7) If a distribution is symmetric, the mean and median are approximately equal. How close are
the mean and median for each of the three distributions?
8) Does the Walter to Heath distribution follow the 68-95-99.7 rule? Place the lines for mean +
std. dev. and mean – std. dev. on the histogram. Do this by right clicking (or Control clicking) on
the histogram and choosing Plot Value. Enter the values of mean + standard deviation and
mean – standard deviation to create two vertical lines.
9) To count how many values fall within one standard deviation of the mean, right click (or
Control Click) on the column WalterHeath and choose Add Filter. Type the following:
(WalterHeath < mean + standard deviation) and (Walter Heath > mean – standard deviation)
and then click on Apply and OK. NOTE: You should be typing the numerical value for mean +
standard deviation and mean – standard deviation and not the words. This should have filtered
out all the values that are within one standard deviation of the mean. What percent of the
data are within one standard deviation of the mean?
10) Modify the filter to filter out mean + 2 standard deviations and mean + 3 standard
deviations. What percent of the data are within two standard deviations of the mean? What
percent of the data are within three standard deviations of the mean? Based on the 68-9599.7 rule, is the distribution approximately normal?
11) Create a normal probability plot for the Walter to Heath Distribution. In Fathom, it is called
a Normal Quantile Plot. Based on the plot, do you think the Walter to Heath distribution is
approximately normal? Explain how the plot justifies your answer.
Note to teachers: Students had about 5 minutes to practice pacing beside a
meter stick to calibrate themselves to 1 pace = 1 meter. Students were
then sent out in waves to count the number of paces between the buildings.
This helped to make sure students were collecting their own data and kept
interruptions to pace counting at a minimum. Also, it is best to have three
different distances for students to compare distributions. The distribution of
paces between the closest buildings should show the least variation and
the distribution of paces between the farthest buildings should show the
most variation. Although the data set used here had over 500
observations, 100 pieces of data might begin to show a distribution that is
approximately normal. With enough students, a new data set could be
created each year. Or data could accumulate over several years.
Frank M.
Andrew N
Fathom Project: Pacing a Normal Distance
2. 524 observations in each list. Mr. Bross listed the actual distance between the buildings at the bottom
of each list.
4. All of the distributions appear approximately normal.
5. SnyderWalter: 201 and WalterHeath: 120. The person might have been confused on how far a meter
is for every step they took and they also might have written down the distance for the wrong buildings.
6.WalterHeath has the most variation because it is the longest distance and the longer the distance the
more inaccurate the data will be.
7. All have less than a 1 meter difference between the median and mean.
9. 72.3%
10. Two standard deviations: 96.3%
Three standard deviations: 99. 4%
The distribution is approximately normal. 68 to 72.3, 96.3 to 95, 99.4 to 99.7.
11. Yes, because the line is nearly straight.