MATH 250- Elements of Statistics
Class Data, Spring 2025---FIRST EXAMINATION of Student Data
Individual ID#	Gender	Foot Length	Height	Age	Armspan	Number in Family	Hair Color
1	Female	19.0	154.5	8	133.0	5	Brown
2	Male	29.0	189.0	51	198.0	4	Brown
3	Male	30.5	191.0	23	185.0	4	Brown
4	Male	49.0	192.0	64	194.0	3	Grey
5	Female	24.0	162.5	28	161.5	10	Brown
6	Female	25.0	172.0	43	165.0	3	Blonde
7	Female	24.0	169.5	33	163.5	10	Blonde
8	Female	21.5	157.5	23	155.0	3	Blonde
9	Female	19.0	167.5	19	162.5	3	Brown
10	Male	23.5	175.5	24	175.0	8	Blonde
11	Male	27.0	172.5	19	170.0	3	Brown
12	Female	20.0	157.0	20	161.0	3	Brown
13	Male	24.0	172.5	42	172.0	3	Brown
14	Male	28.0	182.0	28	183.0	6	Brown
15	Female	22.0	160.0	21	140.0	7	Brown
16	Male	30.0	188.0	33	185.5	8	Blonde
17	Female	25.5	172.5	21	172.5	1	Blonde
18	Female	24.0	170.0	19	172.0	4	Black
19	Female	26.0	168.0	29	170.0	2	Black
20	Male	23.0	170.0	26	176.0	3	Brown
21	Female	26.0	168.0	29	170.0	2	Black
22	Male	26.5	190.0	20	196.0	11	Black
23	Female	23.5	152.5	34	144.5	3	Brown
24	Female	26.0	155.0	35	156.0	6	Brown
25	Female	24.5	157.5	19	155.0	4	Brown
26	Female	28.0	173.0	19	186.0	3	Brown
27	Male	27.5	180.0	33	177.0	3	Brown
28	Female	26.0	175.5	20	160.0	4	Brown
29	Female	24.0	170.0	31	168.0	4	Brown
30	Male	28.0	183.0	30	180.5	4	Brown
31	Male	27.0	183.0	30	182.5	14	Blonde
32	Female	24.5	174.0	19	165.0	3	Brown
33	Female	24.5	163.5	21	168.5	5	Blonde
34	Female	22.0	170.0	29	170.0	4	Blonde
35	Female	23.0	160.0	19	165.0	2	Black
36	Female	25.0	155.0	28	153.0	5	Red
37	Female	23.0	152.0	46	152.0	7	Blonde
38	Female	24.5	166.0	44	165.0	11	Brown
39	Male	25.5	183.0	26	183.0	10	Brown
40	Male	25.5	183.5	21	179.5	4	Black
41	Female	23.0	160.0	26	167.0	8	Brown
42	Male	25.5	183.0	31	182.0	7	Brown
43	Female	20.0	155.0	20	154.0	5	Black
44	Male	27.5	179.0	29	150.0	3	Brown
45	Female	26.5	144.5	24	146.0	1	Brown
46	Female	23.0	160.0	37	159.0	3	Brown
47	Male	27.5	187.0	38	185.0	2	Brown
48	Female	24.0	168.0	33	164.0	9	Brown
49	Male	27.0	188.0	36	185.0	2	Brown
50	Female	27.0	169.0	31	161.5	4	Brown
51	Female	23.0	160.0	19	157.0	4	Brown
52	Female	24.0	159.0	32	161.5	4	Brown
53	Female	25.0	165.0	18	153.5	4	Brown
54	Female	23.5	165.5	30	166.5	10	Black
55	Male	27.0	190.0	21	189.0	5	Brown
56	Female	23.0	167.0	35	154.0	2	Brown
57	Male	20.5	168.5	44	171.0	6	Brown
58	Female	24.0	167.5	52	162.5	5	Brown
59	Female	26.0	175.5	20	164.5	5	Blonde
60	Female	22.5	162.5	19	162.5	3	Black
61	Male	25.5	183.0	25	184.0	5	Brown

General Instructions: Please place your name above, then complete the following questions. NOTE: Read the entire document below to get a feel for the activity before continuing. Make sure to save this Excel file using the filename "yournameActivity5.xlsx". Once complete, submit your answers to this activity by attaching your Excel file to the Speadsheet Activity 5 - Probability Distributions assignment in Blackboard. Use the area to the near right in this Excel worksheet when calculating all values/statistics/parameters. Methods/work to calculate values must be shown in this spreadsheet tab in order to receive full credit. (Work for part 1. should be shown in the tab labelled "Original Data Set for Analysis")

overview:

This activity has three major purposes. First, it is designed to show the importance of examining the data prior to performing statistical calculations. Second, the activity should help you recognize the difference between a discrete random variable and a continuous random variable. Finally, the activity is designed to help you see how the descriptive statistical analysis differ for both types of data. The data to be used in answering the questions below comes from the data collected in the first spreadsheet activity. The sample data set collected from the students of this course originally had a size of n = 137. However, to make the set a bit more manageable for beginning statistics, a collection of 61 individuals' data was randomly selected. You may recognize your own data within this set if you were one of the randomly selected individuals. This data is supplied in the attached worksheet titled "Original Data Set for Analysis"...see the tab at the bottom of this document window.

1. The first step with analyzing data is to make sure that all data values were sbumitted correctly and seem to be reasonable/proper measurementsthis is called cleaning the data. In initial analysis of the student data by instructors, there were several mismeasurments or incorrectly given measurements; much of this was cleaned already. More formally one would also look for possible outliers using a process (like the 1.5IQR rule) and decide whether or not to include these data in further analysis. In general, a valid and well established argument should always be given for removal of any data from a data set; removal of any collected data should NOT be done arbitrarily or to skew the data to some desired viewpoint. Analyze the data given in the ATTACHED worksheet (again, see this worksheet below as "Original Data Set for Analysis"). Using the 1.5IQR rule discussed in the first unit, establish there is exactly one outlier within the foot length variable. For our course, examine only the foot length variable for outliers! Once you demonstrate that an outlier exists, give the individual's ID# and data as your answer below to this question #1. FINALLY, copy the data set, excluding the outlier, to the designated region at the right (several columns over to the right on this worksheet). Do not delete the outlier's data on the "Original Data Set for Analysis" tab. We want to keep a record of all the data, but this individual's (the outlier's) data will NOT be used in any other calculations performed in answering questions #2 and #3 below in this activity. NOTE: You should be left with 60 rows of data in the region to the right when finished with this problem, even though the ID# will start with 1 and end at 61.

2. For this problem, we will first assume the data is population data (only these 60). Now we focus only on the Number in Family variable in the data set you copied to the right...in which you deleted the entire row chosen in answering #1 (again your data table should contain 60 individuals' data.) Define the random variable X to be "Number in Family" and complete the following for these sixty data values:

a.) What makes X a discrete random variable and not a continuous one?

b.) In the area to the right, create a probability distribution table showing the possible values of X, the frequency of each value, and the associated relative frequency values P(X) as determined by the collected data.

c.) Determine the expected value (mean) of the random variable X using your probability distribution table created in part b. directly above. (Hint: the requirement is to use only the information in the table you produced in part b., not to use the raw data---review how to produce the mean from a probability distribution table via the text or the Excel Guides for Unit 2.)

MEAN :__________

d.) Determine the standard deviation of the random variable X, again using only the values within your probability distribution table. (You can check your answers by finding the population s.d. of the data on family size, BUT this problem needs to be answered through use of only the probability distribution table built in part b--again see the text and Excel Guides.)

St. Deviation :___________

e.) Frequently, any data outside of the Two- Sigma Rule interval is considered "unusual." Decide if any of the included values of the random variable X are unusual. Give a concluding statement below in regard to your decision. Show work for 2 Sigma Rule to the right of the problem.

f.) Determine the probability that the random variable X is within one standard deviation of the mean. Show work for calculating the lower and upper bounds of the event in question and the probability to the right of the problem. Express your answer in a complete sentence.

3. Now consider your cleaned data in reference to the Footlength variable/factor of the student data. Notice that this variable is categorized as quantitative, continuous, and ratio level in type. (This portion of the activity is Based on Workshop Statistics, Rossman, p. 66)

a.) In the area to the right, copy the Footlength data values (again take the cleaned data set of 60 values) and then sort them in order from least to greatest. From this column of footlength values, create an appropriate frequency table with exactly six classes--remember, we did such frequency charts back in Unit 1. For the next part, b, you may choose to produce the histogram graph at the same time. Finally extend your frequency table to include a relative frequency (probability) column.

b.) Produce a histogram for your frequency table (if you did not do so as you constructed your table in part a). Describe the distribution. Does the distribution of the footlength data appear to be a roughly normal distribution? Explain your answer briefly.

c.) Compute the mean and standard deviation of the footlength data values...not from the frequency table as done in the discrete case above but as done in the first unit, but this time assuming this is SAMPLE DATA of all stats students.

Sample mean, xbar ( x ):_________

Sample std. deviation, s: __________

d.) Determine the proportion of the students in this sample whose footlength is at least 25.5 cm.

e.) Suppose that the footlengths in the population of all university students taking elementary statistics do in fact follow a perfect normal distribution (though our sample group did not) with the population mean = 24.5 cm and population standard deviation = 2.2 cm . Under this assumption, determine the proportion of all students who have footlength measure greater than 25.5 cm.