 # Mathematics-Statistics: 11 Questions And Their Solutions

## Question

1. USA Today (December 13, 1998) reported on a study of the automobiles purchased by women in 1998. The data in the study consisted of a description of the top five automobiles purchased: Ford Escort (FE), Honda Accord (HA), Chevrolet Cavalier (CC), Ford Taurus (FT), and Hyundai Excel (HE). The actual study summarized the purchases of several thousand women. Let us assume that the data shown below represent a sample of 50 women who purchased one of these five cars.
Summarize these data with ALL appropriate statistical methods (by hand or any statistical software) and provide verbal statements/discussions of the summaries about the model of the cars.

HA   FE   FT   FT   CC HA
HA   FE   FT   HA   HE HE
FT    HE CC   FT   FE   FE
HA   CC CC   FE FE   CC
HA   HA   HE   FT   CC CC
HA   HE   HE   HA   FE FE
FE   HA   HE CC CC FT
HE   FE   FE   CC   HA   FT FT FE

2. A mathematics achievement test consisting of 100 questions was given to 50 sixth grade students at maple Elementary School. The following data show the number of questions answered correct by each student.
75 48 46 65 71 49 61 51 57 49 84 85 79 85 83 55 69
88 89 55 61 72 64 67 61 77 51 61 68 54 63 94 54 53
71 84 79 75 65 50 45 65 77 71 63 67 57 63 71 77
a. Using the following classes as given below, complete the table
Class    frequency    relative freq.    Cumulative freq.    Cumul. Relat. Freq.
40 - 49
50 - 59
60 - 69
70 - 79
80 - 89
90 - 99
________________________________________________________________
b) Draw a relative frequency histogram and discuss the shape of the distribution.
c) How many classes are there?
d) What percent of the data values are at least 70?
e) Calculate the 37th percentile and interpret it.
f) Calculate the 80th percentile and interpret it.
g) Calculate the interquartile range (IQR) and interpret it.
h) Anita scored 68 in the achievement test. What is the percentile value corresponding to her score?
3. The following data set represents the test scores of the freshmen on the first exam in a statistics course at a local university.
62 67 74 48 100 93 49 57 77 63 82 10 78 88 99 44 51 80 71 39 58 76
89 94 70 41 66   82 18 73
a. Calculate the z-score for the observation 63 and interpret it.
b. Find the median of the data set.
4. Christian D’Angelo has scores of 68, 65, 75, and 78 on his statistics tests. Find the scores he can make on his final exam to receive a C in the course .The final exam counts as two test scores and C is received if the final course grade is from 70 to 79.
5. If the z-score for an observation is -1.22, the mean of the data set is 83, and the variance is 84, what is the value of the observation?
6. Todd Booth, an avid jogger, kept detailed records of the number of miles he ran per week during the past year. The frequency distribution in figure below summarizes his records. Find the mean, median, and mode of the number of miles per week that Todd ran.
Miles Run per Week   Number of Weeks
0                                              4
1                                              5
2                                             10
3                                              9
4                                             10
5                                              7
6                                              4
7                                              3

a. Mean number of miles =
b. Median number of miles =
c. Mode number of miles =
7. The mean score of 10 employees in a certain company is \$42,000 and the median is \$38,000. If the highest paid employee got a raise of \$7,500 because of excellent job performance. Answer the following questions.
a. Calculate the new mean salary
b. Calculate the new median salary.
8. The mean age of a class of 25 students is 23.4 years. How old will a 26th student have to be in order for the mean age of the class to be 24 years?
9. For the numbers, 1, 5, 10, 12, and 16:
Find the value (ν ) for which ∑ − 2 (X - v)² is minimized.
Find the value (ν ) for which ∑| x − ν | is minimized

10. Students Who Care is a student volunteer program which college students donate work time in community centers for homeless people. Professor Gill is the faculty sponsor for this student volunteer program. For several years, Dr. Gill has kept a careful record of the total number of hours volunteered by a student in the program each semester. For students in the program, the mean numbers of hours was 29.1 hours each semester, with a standard deviation of 1.7 hours, each semester. Find an interval A to B for the number of hours volunteered in which at least 75% of the students in this program would fit.
11. Given the following frequency distribution, calculate the mean and the standard deviation of the data that generated the distribution.
Classes    frequency
1 - 8                14
9 - 16             21
17 - 24             11
25 - 32             6
33 - 40             4
41 - 48             4
a. mean
b. Standard deviation

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