Question

MAT143-HOMEWORK 1 FOR CHAPTER2 Must show the all work, draw a neat table and histogram (with the axes labeled clearly in order to get full credit. Following are the published weights (in lbs) of all the team members of the San Francisco 49ers from a previous year. 177:205,210 210:232:205:185;185,178210:206:212184;174;185:242188:212:215,247 241 223 220:260:245:259.278:270:280,295:275,285:290 272273 280 285,286,200215:185,230250 241; 190:260;250:302;265:290;276:228:265 1. a) Construct a stem and leaf plot to sort the data from the lowest to the highest weight b) Use the data to construct a frequency distribution table starting with the lower class limit of 174 lbs and calculated class width. Use the class width formula as discussed in class. Construct frequency table. It must contain 5 classes, class boundaries and frequency. c) Construct a histogram (a bar graph of class boundaries vs frequency) d) Discuss shape of the histogram e) What is the average weight of a team member as seen by your organized table.

Answer 1

1)

a) Steam and leaf for the given data will be

b) lower class limit =174

upper class limit =302

number of classes =5

So the class width =(302-174)/5=25.6=26

So the frequency distribution table will be

so the frequency distribution table will be

c) the histogram for this frequency distribution will be

Untitled Chart 15 13 12.5 10 10 10 10 10 7.5 2.5 174-200 200-226 226-252 252-278 278-304 Frequency distribution histrogram Highcharts.com

d) Here we can see the frequency distribution is same for the maximum classes so we can say that it is a uniformly distributed histogram hence the shape of the histogram is uniform.

e)we are having table for frequency distribution as

So we have the mean weight

$\bar{X}=\frac{\sum f.m}{n}$

where

f=frequency in each class

m=mid of each class

n=Total number of samples

So the mean weight

$\bar{X}=\frac{\sum f.m}{n}=\frac{(10*187)+(13*213)+(10*239)+(10*265)+(10*291)}{53}=237.52$

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