Question

Data Set II Identity Theft Complaints (page 767)

The data values show the number of complaints of identity theft for 50 selected cities.

2609    1202    2730    483    655

626 393    1268 279 663

817 1165    551 2654    592

128    189    424    585 78

1836    154 248 239 5888

574    75    226 28 205

176    372 84    229 15

148    117 22    211    31

77 41    200    35    30

88 20    84    465 136

2. Problem

Instructions:

Use the list of raw data given in Data Set II on page 797 regarding Identity Theft Complaints. Note: this is a sample of data values. Show all work for each problem.

1) Using the 50 Identity Theft Complaints, find the mean, median, mode, midrange, range, variance, and standard deviation. Be sure to use the Rounding Rules given in the text.

Rounding Rule: Mean

The mean should be rounded to one more decimal place than occurs in the raw data.

The mean, in most cases, is not an actual data value.

Rounding Rule for the Mean, Variance, and Standard Deviation for a Probability Distribution: The rounding rule for the mean, variance, and standard deviation for variables of a probability distribution is this: The mean, variance, and standard deviation should be rounded to one more decimal place than the outcome X. When fractions are used, they should be reduced to lowest terms.

2) Use Chebyshev's Rule to find the range for which 75% of the 50 data values will fall. (Give the minimum and maximum values of the range.)

3) Using the list of 50 complaints, find the percent of all 50 data values that fall between the minimum and maximum of the range that you found on #2.

4) Find the z-score for the data value 585.

5) Find the percentile rank for the data value 585.

Turn in:

1) Sheet with your name on each page and all answers for #1-5. Include all work or an explanation for every answer (both work and answer will be graded). If you are using the STAT CALC on the TI-84 to find your calculations (directions on page 162), then write all steps that you did on the TI-84 to get the answers and write all results that you see on the calculator window screen. For #1, label your answers so I know which one is the mean, mode, etc.

Answer 1

First, we sort the 50 values in the ascending order ...

	x (Sorted)	(x - mean)^2
	15	345626.41
	20	339772.41
	22	337444.81
	28	330510.01
	30	328214.41
	31	327069.61
	35	322510.41
	41	315731.61
	75	278678.41
	77	276570.81
	78	275520.01
	84	269257.21
	84	269257.21
	88	265122.01
	117	236098.81
	128	225530.01
	136	217995.61
	148	206934.01
	154	201511.21
	176	182243.61
	189	171313.21
	200	162328.41
	205	158324.41
	211	153585.61
	226	142053.61
	229	139801.21
	239	132423.21
	248	125954.01
	279	104911.21
	372	53314.81
	393	44058.01
	424	32005.21
	465	19016.41
	483	14376.01
	551	2693.61
	574	835.21
	585	320.41
	592	118.81
	626	533.61
	655	2714.41
	663	3612.01
	817	45838.81
	1165	315956.41
	1202	358920.81
	1268	442358.01
	1836	1520535.61
	2609	4024437.21
	2654	4207011.21
	2730	4524554.41
	5888	27932282.01
Sums =	30145	50387786.5

(1) Mean = sum of data/number of data = 30145/50 = 602.9

Median = middle value = (25th value + 26th value)/2 = (226 + 229)/2 = 227.5

Mode = most frequent value = 84    

Range = max value - minimum value = 5888 - 15 = 5873

Midrange = (maximum value + minimum value)/2 = (15 + 5888)/2 = 2951.5

Variance = ∑ (x - mean)^2/(n - 1) = 50387786.5/(50 - 1) = 1028322

Standard deviation = √variance = 1014.06    

(2) 75% = 0.75      

0.75 = 1 - (1/k)^2      

k = ±2       

Lower limit = mean - 2 * std dev = 602.9 - 2 * 1014.06 = -1425.22 = 0

Upper limit = mean + 2 * std dev = 602.9 - 2 * 1014.06 = 2631.02

(3) Number of values between [0, 2631.02] = 47 (47/50 * 100 = 94%)

(4) z = (x - μ)/σ = (585 - 602.9)/1014.06 = -0.018   

(5) Percentile rank = area to the left of z = -0.018, which is 0.4928 (49.28)