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Activity 4

Activity 4—MATH 250

Elements of Statistics—Fall 2015

DUE DATE: 10/06/2015

NAME:

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 often using the filename "yournameActivity4". Once complete, submit your answers to this activity by attaching your Excel file through the completion link in the Unit 2 Activity 4 assignment description in Blackboard. Use the area to the near right in this Excel worksheet when calculating any statistics/parameters from data.

MATH 250- Elements of Statistics

Class Data, Fall 2015---CLEANED Student Data

Overview:

This activity has 3 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 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 Unit 1a Activity. The sample data set collected from the students of this course orignally had a size of n = 148. However to make the set a bit more managable for beginning statistics, a random collection of 76 values were selected. You may recognize your own data within this set if you were one of the randomly selected indivdiuals. This data is complied in the attached worksheet titled Original Data Set for Analysis...see the tab at the bottom of this document window.

Individual#

Gender

Foot Length

Height

Armspan

Age

Number in Family

Hair Color

The first step with analyzing data is to make sure the all data values were entered correctly and seem to be reasonable/proper measurements—this is called cleaning the data. 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 (see this worksheet below as "Orignial Data Set for Analysis"). Using the 1.5IQR rule discussed in the first unit, find the one outlier within the Armspan variable. You must show use of the 1.5IQR rule! Once you demonstrate that an outlier exists, give the individual's number and data as your answer below to this question #1. FINALLY, copy the entire data set to the designated region at the right (several columns over) on THIS worksheet and then delete that one row of data from the copy so this indivdiual's data will NOTbe used in any other calculations performed in answering questions in #2 and #3 below. You should be left with 75 rows of data in the region to the right when finished with this problem.

For this problem, focus only on the the Family Size variable in the data set—you are using the table in which you deleted the entire row chosen in answering #1, correct? Defining the random variable X to be family size, complete the following:

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

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.

Determine the expected value (mean) of the random variable X using your probability distribution table created in part b. directly above. (Hint: the requirment is to use only the information in the table you produced in part b., not to use the raw data---see how to produce the mean from a probability distribution table via the Excel Guides for Unit 2 or through the equivalent text's method explained in Section 5-2.)

MEAN µ:

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--same hint applies as given in part c.)

St. Deviation σ:

Applying the Range Rule of Thumb, decide if any of the included values of the random variable X are unusual (recall that "unusual" and "outlier" are not the same thing.) Give a concluding statement below in regard to your decision.

Create a probability statement which is supported by the values in the probability distribution table. (For example, “The probability that a randomly selected member of this group comes from a family of size 2 or less is ??%”).

Now consider your cleaned data in reference to the height variable of the students. Notice that this data category is quantitative, continuous, ratio level in type. (This portion of the activity is Based on Workshop Statistics, Rossman, p. 66)

In the area to the right, copy the height values (again take the cleaned data set of 75 values) and then sort them in order from least to greatest. From this column of height values, create an appropriate frequency table with exactly 6 classes--remember, we did such frequency charts back in Unit 1. For the next part, you may choose to produce the histogram graph at the same time. Finally extend your frequency table to include a relative frequency column.

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

Compute the mean and standard deviation of the height values…not from the frequency table as done in the discrete case above but as done in the first unit assuming this is sample data.

Mean, xbar:

Standard deviation, s:

Determine the proportion of the students in this sample whose height is less than 163 cm.

Suppose that the heights in the population of all college students taking elementary statistics do in fact follow a normal distribution (though our data did not) with the population mean μ of 169 cm and population standard deviation σ of 9.55 cm. Under this assumption, determine the proportion of all students who have a height measure less than 167 cm. (HINT: this calculation is related to the concepts covered in text section 6-2 and 6-3!)

Original Data Set for Analysis

MATH 250- Elements of Statistics
Class Data, Fall 2015---FIRST EXAMINATION of Student Data
	Individual#	Gender	Foot Length	Height	Armspan	Age	Number in Family	Hair Color
	1	Female	25.4	170.18	170.2	43	5	Brown
	2	Female	22	160.02	162.6	39	12	Brown
	3	Female	18.5	139.5	140	29	3	Brown
	4	Female	26	176.5	178	41	9	Blonde
	5	Male	25.5	181	179.5	29	9	Brown
	6	Female	24	162.5	132	21	4	Brown
	7	Male	28	173	160	39	6	Brown
	8	Female	23.5	161	158	32	4	Blonde
	9	Female	23	161	154	25	3	Brown
	10	Female	26	156	152	31	6	Red
	11	Female	26	173	173	18	4	Brown
	12	Female	24	161.5	160	24	7	Blonde
	13	Male	26.5	185	188	24	5	Brown
	14	Female	25	165	172.5	36	4	Blonde
	15	Female	25.5	170	170	33	4	Brown
	16	Female	23	161.5	166.5	20	4	Brown
	17	Female	24	170	164	46	5	Brown
	18	Female	22	135	140	31	4	Brown
	19	Male	28	173	168	29	4	Brown
	20	Female	23	167.5	150	25	3	Brown
	21	Female	23.5	165	157	30	5	Brown
	22	Female	25.5	175	170	37	5	Blonde
	23	Female	22.5	157.5	148.5	28	6	Brown
	24	Male	25	173	176	25	7	Blonde
	25	Male	25	172.5	161	20	4	Black
	26	Female	24.5	162.5	164.5	34	5	Brown
	27	Male	25	178	181	19	5	Brown
	28	Female	23.5	157.5	160	22	2	Brown
	29	Female	20	159	160	22	4	Brown
	30	Female	21.5	163.5	162	26	3	Brown
	31	Female	22	152	150	20	3	Brown
	32	Male	28.5	187.5	185.5	24	4	Blonde
	33	Male	24	174	155	44	1	Brown
	34	Female	24	169	178	27	3	Brown
	35	Female	24.00	171	162	26	5	Brown
	36	Female	20.9	166	169	23	3	Blonde
	37	Female	24.5	165	167.5	29	5	Brown
	38	Female	51	170	167.5	28	3	Brown
	39	Female	25	156	151	55	4	Brown
	40	Female	23.5	157	153	41	3	Blonde
	41	Male	24	174	174	41	1	Red
	42	Female	25.5	162	166.5	30	9	Brown
	43	Female	25.5	171	171	28	2	Blonde
	44	Male	28	183	187.5	37	4	Red
	45	Female	24	173.5	167.5	27	5	Blonde
	46	Female	24	170.5	170	20	5	Brown
	47	Male	33	192	183	26	5	Brown
	48	Female	23.5	159	161.9	44	3	Brown
	49	Female	23	157.5	154.5	30	10	Brown
	50	Female	25.5	170	179	41	4	Brown
	51	Female	26	165	164.5	52	5	Black
	52	Female	24.5	165	162.5	38	11	Blonde
	53	Female	24	173	164	48	1	Blond
	54	Male	24	72.5	68.5	60	5	Blonde
	55	Female	24	162.5	168	50	24	Brown
	56	Male	18.5	180	132	21	3	Black
	57	Male	28	183.5	183	23	5	Brown
	58	Male	28	180	177	30	5	Brown
	59	Female	23	169	127	31	6	Red
	60	Female	24.5	160.5	159	19	9	Brown
	61	Female	19	152.5	152.5	33	5	Black
	62	Female	21.5	161.5	139.5	31	2	Brown
	63	Female	25	170.5	174	25	2	Blonde
	64	Female	24	160	152	24	7	Blonde
	65	Male	29	180	179	25	3	Brown
	66	Female	24	170	178	20	5	Red
	67	Female	24.5	171.5	161	29	3	Brown
	68	Female	27	180.5	173.5	45	4	Brown
	69	Female	23.5	157	153	41	3	Blonde
	70	Female	23	162.5	160	33	4	Brown
	71	Female	25.5	183	173	28	4	Blonde
	72	Female	23.5	174	147.5	39	4	Brown
	73	Female	26	176	177	26	6	Brown
	74	Male	27.9	182.9	188	24	3	Red
	75	Female	24	175.5	170	30	3	Blonde
	76	Male	25.5	185.5	190	24	3	Brown