Provide an appropriate response.
1) The two most frequently used measures of central tendency are the mean and the median. Compare these two measures for each of the following characteristics:
1. Takes every score into account?
2. Affected by extreme scores?
3. Advantages.
Provide an appropriate response.
2) Responses to a survey question about eye color are coded as 1 (for brown), 2 (for blue), 3 (for green), 4 (for hazel), and 5 (for any other color). Does it make sense to find the mean, median, or mode of the coded eye colors?
3) A city has 4 different area codes for phone numbers. Does it make sense to find the mean of these rea codes?
4) Does the mode of a numerical data set always lie close to the median? Explain your answer and give an example of a data set to illustrate your answer.
5) Dave is a college student contemplating a possible caner option. One factor that will influence his decision is the amount of money he is likely to make. He decides to look up the average salary of graduates in that profession. Which information would be more useful to him, the mean salary or the median salary? Why?
6) The distribution of salaries of professional basketball players is skewed to the right. Which measure of central tendency would be the best measure to determine the location of the center of the distribution?
7)
For the distribution drawn here, identify the mean, median, and mode.
Provide an appropriate response.
8) Explain how two data sets could have equal means and modes but still differ greatly. Give an example with two data sets to illustrate.
9) Suppose a study of houses that have sold recently in your community showed the following frequency distribution for the number of bedrooms:
|
Bedrooms
|
Frequency
|
|
1
|
1
|
|
2
|
18
|
|
3
|
140
|
|
4
|
57
|
|
5
|
11
|
Based on this information, the mode for the data is 140.
Provide an appropriate response.
10) In a sample of 18 students at East High School the following number of days of absences were recorded for the previous semester 4, 3, 1, 0, 4, 2, 3, 0, 1, 2, 3, 0, 4, 1, 1, 5, 1, 1. Compute:
1. The range,
2. Midrange
3. Mean
4. Median
5. Mode
6. Variance
7. Standard deviation
11) Many firms use on-the-job training to teach their employees new software. Suppose you work in the personnel department of a firm that just finished training a group of its employees in new software, and you have been requested to review the performance of one of the trainees on the final test that was given to all trainees. The mean of the test scores is 72. Additional information indicated that the median of the test scores was 76. What type of distribution most likely describes the shape of the test scores? Why?
Solve the problem.
12) The data below consists of the heights (in inches) of 20 randomly selected women. Find the 20% trimmed mean of the data set. The 20% trimmed mean is found by arranging the data in order, deleting the bottom 10% of the values and the top 10% of the values and then calculating the mean of the remaining values.
|
67
|
68
|
64
|
61
|
65
|
64
|
70
|
67
|
62
|
63
|
|
61
|
64
|
75
|
67
|
60
|
59
|
64
|
68
|
65
|
71
|
Find the coefficient of variation for each of the two sets of data, then compare the variation. Round results to one decimal place.
13) Listed below are the systolic blood pressures (in mm Hg) for a sample of men aged 20-29 and for a sample of men aged 60-69.
|
Men aged 20-29: 117
|
122
|
129
|
118
|
131
|
123
|
|
Men aged 60-69: 130
|
153
|
141
|
125
|
164
|
139
|
Solve the problem.
14) A student earned grades of 92, 79, 93, and 74 on her four regular tests. She earned a grade of 79 on the final exam and 88 on her class projects. Her combined homework grade was 87. The four regular tests count for a combined 40% of the final grade, the final exam counts for30%, the project counts for 10%, and homework counts for 20%. What is her weighted mean grade? Round to one decimal place.
Find the range, variance, and standard deviation for each of the two samples, then compare the two sets of results.
15) When investigating times required for drive-through service, the following results (in seconds) were obtained.
|
Restaurant A
|
120
|
67
|
89
|
97
|
124
|
68
|
72
|
96
|
|
Restaurant B
|
115
|
126
|
49
|
56
|
98
|
76
|
78
|
95
|
16) The manager of a bank recorded the amount of time each customer spent waiting in line during peak business hours one Monday. The frequency distribution below summarizes the results. Find the sample mean, sample variance, and sample standard deviation of the waiting time. Round your answer to one decimal place. You can use a graphing calculator to answer this question.
|
Waiting time (minutes)
|
Number of customers
|
|
0 - 3
|
15
|
|
4 - 7
|
9
|
|
8 - 11
|
11
|
|
12 - 15
|
6
|
|
16 - 19
|
5
|
|
20 - 23
|
3
|
|
24 - 27
|
1
|
Provide an appropriate response.
17) The amount of television viewed by today's youth is of primary concern to Parents Against Watching Television (PAWT). 300 parents of elementary school-aged children were asked to estimate the number of hours per week that their child watched television. The mean and the standard deviation for their responses were 16 and 4, respectively. PAWT constructed a stem-and-leaf display for the data that showed that the distribution of times was a bell-shaped(Symmetric) distribution. Give an interval around the mean where you believe most (approximately 95%) of the television viewing times fell in the distribution.
18) A study was designed to investigate the effects of two variables - (1) a student's level of mathematical anxiety and (2) teaching method - on a student's achievement in a mathematics course. Students who had a low level of mathematical anxiety were taught using the traditional expository method. These students obtained a mean score of 460 with a standard deviation of 40 on a standardized test. Assuming a bell-shaped(Symmetric) distribution, where would approximately 68% of the students score?
19) A study was designed to investigate the effects of two variables - (1) a student's level of mathematical anxiety and (2) teaching method - on a student's achievement in a mathematics course. Students who had a low level of mathematical anxiety were taught using the traditional expository method. These students obtained a mean score of 480 with a standard deviation of 20 on a standardized test. Assuming no information concerning the shape of the distribution is known, what percentage of the students scored between 440 and 520?