PROBLEM 2: Average wait in minutes for the train QM3; n=12 15 4 5 9 6 12 17 10 8 13 8 16 example: of how it should be answer: PROBLEM: #colds / year n=18 subjects 10; 8; 5; 2; 3; 3; 3; 6; 4; 2; 4; 5; 4; 4; 1; 0; 3; 5; For computations done by hand, data must be ordered. 0 1 2 2 3 3 3 3 4 Median 4 4 4 5 5 5 6 8 10 Q1 Q3 Sample mean = =72/18 = 4 colds Sample median = 4 colds (midpoint of data) Sample mode = 3 and 4 (the value that occurs most often; this is a bimodal data set) First Quartile (approximation) = 0.25 * N = 0.25 * 18 = 4.5; If the value is not an integer, we can round it up to the nearest integer 5 à value is 3 Third Quartile (approximation) = 0.75 * N = 0.75 * 18 = 13.5 à 14 à value is 5 Range = max – min =10 – 0 = 10 IQR = Q3 – Q1 = 5 – 3 = 2 Variance = s2 = = 96/17 = 5.64 colds squared Standard deviation = s = = 2.37 colds Coefficient of variation = CV = x 100% =2.37/4 *100% = 59.25% To convert to a Z-score: Zi = (Xi - mean)/s The 0 becomes (0 – 4) / 2.37 = -1.68; the 1 becomes (1 – 4) /2.37 = -1.27; the 2 becomes (2- 4)/2.37 = .84; and the 4 becomes a 0; etc. All values below the mean have negative Z scores and all values above the mean have positive Z scores. This is the output from MS Excel using the descriptive tool. For your homework solution an output as the one below (for the excel solution) will be sufficient. Column1 Mean 4 Standard Error 0.560112 Median 4 Mode 3 Standard Deviation 2.376354 Sample Variance 5.647059 Kurtosis 1.497461 Skewness 0.887652 Range 10 Minimum 0 Maximum 10 Sum 72 Count 18 Quartiles are approximations. A more refined definition is the following: For Lower Quartile (25%): Sort all observations in ascending order Compute the position L1 = 0.25 * N, where N is the total number of observations. If L1 is already a whole number (integer), the lower quartile is midway (average) between the L1-th value and the next one. If L1 is not a whole number, change it by rounding up to the nearest integer. The value at that position is the lower quartile. For Upper Quartile(75%): Sort all observations in ascending order Compute the position L3 = 0.75 * N, where N is the total number of observations. If L3 is a whole number, the upper quartile is midway (average) between the L3-th value and the next one. If L3 is not a whole number, change it by rounding up to the nearest integer. The value at that position is the upper quartile. Please follow the above definitions in calculating the quartiles. There are two distinct situations: set size equal to a power of 4 (L is already a whole number – integer), set size not a power of 4.

PROBLEM 2: Average wait in minutes for the train QM3; n=12 15 4 5 9 6 12 17 10 8 13 8 16 example: of how it should be answer: PROBLEM: #colds / year n=18 subjects 10; 8; 5; 2; 3; 3; 3; 6; 4; 2; 4; 5; 4; 4; 1; 0; 3; 5; For computations done by hand, data must be ordered. 0 1 2 2 3 3 3 3 4 Median 4 4 4 5 5 5 6 8 10 Q1 Q3 Sample mean = =72/18 = 4 colds Sample median = 4 colds (midpoint of data) Sample mode = 3 and 4 (the value that occurs most often; this is a bimodal data set) First Quartile (approximation) = 0.25 * N = 0.25 * 18 = 4.5; If the value is not an integer, we can round it up to the nearest integer 5 à value is 3 Third Quartile (approximation) = 0.75 * N = 0.75 * 18 = 13.5 à 14 à value is 5 Range = max – min =10 – 0 = 10 IQR = Q3 – Q1 = 5 – 3 = 2 Variance = s2 = = 96/17 = 5.64 colds squared Standard deviation = s = = 2.37 colds Coefficient of variation = CV = x 100% =2.37/4 100% = 59.25% To convert to a Z-score: Zi = (Xi - mean)/s The 0 becomes (0 – 4) / 2.37 = -1.68; the 1 becomes (1 – 4) /2.37 = -1.27; the 2 becomes (2- 4)/2.37 = .84; and the 4 becomes a 0; etc. All values below the mean have negative Z scores and all values above the mean have positive Z scores. This is the output from MS Excel using the descriptive tool. For your homework solution an output as the one below (for the excel solution) will be sufficient. Column1 Mean 4 Standard Error 0.560112 Median 4 Mode 3 Standard Deviation 2.376354 Sample Variance 5.647059 Kurtosis 1.497461 Skewness 0.887652 Range 10 Minimum 0 Maximum 10 Sum 72 Count 18 Quartiles are approximations. A more refined definition is the following: For Lower Quartile (25%): Sort all observations in ascending order Compute the position L1 = 0.25 N, where N is the total number of observations. If L1 is already a whole number (integer), the lower quartile is midway (average) between the L1-th value and the next one. If L1 is not a whole number, change it by rounding up to the nearest integer. The value at that position is the lower quartile. For Upper Quartile(75%): Sort all observations in ascending order Compute the position L3 = 0.75 * N, where N is the total number of observations. If L3 is a whole number, the upper quartile is midway (average) between the L3-th value and the next one. If L3 is not a whole number, change it by rounding up to the nearest integer. The value at that position is the upper quartile. Please follow the above definitions in calculating the quartiles. There are two distinct situations: set size equal to a power of 4 (L is already a whole number – integer), set size not a power of 4.

Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)

6th Edition

ISBN:9781337111348

Author:Bruce Crauder, Benny Evans, Alan Noell

Publisher:Bruce Crauder, Benny Evans, Alan Noell

Chapter5: A Survey Of Other Common Functions

Section5.3: Modeling Data With Power Functions

Problem 6E: Urban Travel Times Population of cities and driving times are related, as shown in the accompanying...

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PROBLEM 2: Average wait in minutes for the train QM3; n=12

15 4 5 9 6 12 17 10 8 13 8 16

example: of how it should be answer:

PROBLEM: #colds / year n=18 subjects

10; 8; 5; 2; 3; 3; 3; 6; 4; 2; 4; 5; 4; 4; 1; 0; 3; 5;

For computations done by hand, data must be ordered.

0 1 2 2 3 3 3 3 4 Median 4 4 4 5 5 5 6 8 10

Q1 Q3

Sample mean = =72/18 = 4 colds

Sample median = 4 colds (midpoint of data)

Sample mode = 3 and 4 (the value that occurs most often; this is a bimodal data set)

First Quartile (approximation) =

0.25 * N = 0.25 * 18 = 4.5; If the value is not an integer, we can round it up to the nearest integer 5 à value is 3

Third Quartile (approximation) = 0.75 * N = 0.75 * 18 = 13.5 à 14 à value is 5

Range = max – min =10 – 0 = 10

IQR = Q3 – Q1 = 5 – 3 = 2

Variance = s² = = 96/17 = 5.64 colds squared

Standard deviation = s = = 2.37 colds

Coefficient of variation = CV = x 100% =2.37/4 *100% = 59.25%

To convert to a Z-score: Z_i = (X_i - mean)/s

The 0 becomes (0 – 4) / 2.37 = -1.68;

the 1 becomes (1 – 4) /2.37 = -1.27;

the 2 becomes (2- 4)/2.37 = .84;

and the 4 becomes a 0; etc.

All values below the mean have negative Z scores and all values above the mean have positive Z scores.

This is the output from MS Excel using the descriptive tool. For your homework solution an output as the one below (for the excel solution) will be sufficient.

Column1

Mean	4
Standard Error	0.560112
Median	4
Mode	3
Standard Deviation	2.376354
Sample Variance	5.647059
Kurtosis	1.497461
Skewness	0.887652
Range	10
Minimum	0
Maximum	10
Sum	72
Count	18

Quartiles are approximations. A more refined definition is the following:

For Lower Quartile (25%):

	Sort all observations in ascending order
	Compute the position L₁ = 0.25 * N, where N is the total number of observations.
	If L₁ is already a whole number (integer), the lower quartile is midway (average) between the L₁-th value and the next one.
	If L₁ is not a whole number, change it by rounding up to the nearest integer. The value at that position is the lower quartile.

For Upper Quartile(75%):

	Sort all observations in ascending order
	Compute the position L₃ = 0.75 * N, where N is the total number of observations.
	If L₃ is a whole number, the upper quartile is midway (average) between the L₃-th value and the next one.
	If L₃ is not a whole number, change it by rounding up to the nearest integer. The value at that position is the upper quartile.

Please follow the above definitions in calculating the quartiles. There are two distinct situations: set size equal to a power of 4 (L is already a whole number – integer), set size not a power of 4.

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