A researcher is interested in studying the relationship between commute time (defined as the number of minutes it takes a person to get to work in the morning) and job satisfaction (defined on a scale from 1=very dissatisfied to 5=very satisfied). The researcher believes that a person with a longer commute time will have lower job satisfaction. The researcher surveys 20 Valley commuters and finds the following data. Respond to questions 1 and 2 based on these data. Commuter Length of Commute (minutes) Job Satisfaction (1=very dissatisfied; 5=very satisfied) Commuter 1 10 4 Commuter 2 65 1 Commuter 3 30 4 Commuter 4 40 2 Commuter 5 15 5 Commuter 6 20 5 Commuter 7 60 2 Commuter 8 50 1 Commuter 9 45 3 Commuter 10 20 3 Commuter 11 30 4 Commuter 12 35 4 Commuter 13 20 5 Commuter 14 30 4 Commuter 15 40 2 Commuter 16 10 5 Commuter 17 20 5 Commuter 18 55 1 Commuter 19 40 3 Commuter 20 50 2 We have learned that the appropriate measure of central tendency is determined by the level of measurement of the data. Calculate all appropriate measures of central tendency for each variable (length of commute and job satisfaction). Calculate the standard deviation if it is applicable to the variable. If any of the measures of central tendency or the standard deviation for a variable is not applicable, briefly explain why it is not applicable. 2. In a short paragraph, explain what the mean, median, mode, and/or standard deviation tell you about each variable in question 1.

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter12: Probability

Section12.3: Conditional Probability; Independent Events; Bayes' Theorem

Problem 81E

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Question

A researcher is interested in studying the relationship between commute time (defined as the number of minutes it takes a person to get to work in the morning) and job satisfaction (defined on a scale from 1=very dissatisfied to 5=very satisfied). The researcher believes that a person with a longer commute time will have lower job satisfaction. The researcher surveys 20 Valley commuters and finds the following data. Respond to questions 1 and 2 based on these data.

Commuter	Length of Commute (minutes)	Job Satisfaction (1=very dissatisfied; 5=very satisfied)
Commuter 1	10	4
Commuter 2	65	1
Commuter 3	30	4
Commuter 4	40	2
Commuter 5	15	5
Commuter 6	20	5
Commuter 7	60	2
Commuter 8	50	1
Commuter 9	45	3
Commuter 10	20	3
Commuter 11	30	4
Commuter 12	35	4
Commuter 13	20	5
Commuter 14	30	4
Commuter 15	40	2
Commuter 16	10	5
Commuter 17	20	5
Commuter 18	55	1
Commuter 19	40	3
Commuter 20	50	2

We have learned that the appropriate measure of central tendency is determined by the level of measurement of the data. Calculate all appropriate measures of central tendency for each variable (length of commute and job satisfaction). Calculate the standard deviation if it is applicable to the variable. If any of the measures of central tendency or the standard deviation for a variable is not applicable, briefly explain why it is not applicable.

2. In a short paragraph, explain what the mean, median, mode, and/or standard deviation tell you about each variable in question 1.

Definition Definition Measure of central tendency that is the value that occurs most frequently in a data set. A data set may have more than one mode if multiple categories repeat an equal number of times. For example, in a data set with five item—3, 5, 5, 29, 473—the mode is 5 because it occurs twice and no other value occurs more than once. On a histogram or bar chart, the element with the highest bar represents the mode. Therefore, the mode is sometimes considered the most popular option. The mode is useful for nominal or categorical data (e.g., the most common color car that users purchase), but it is problematic for continuous data because it is more likely not to have any value that is more frequent than the other.

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