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Summary statistics

2. (no explanation required) suppose we have a set of sample data. For each quantity listed below, could the quantity be negative? (For each quantity, answer Yes or No.)

Quantity Possibly Negative? (Yes or No)
Arithmetic Mean
Standard Deviation
Frequency
Median
Mode
Range
First Quartile
Interquartile Range

3. The stopping distance on a wet surface was determined for 17 cars each traveling at 30 miles an hour. The stopping distances (in feet) are:
63 69 85 65 90 66 71 75 84
104 87 72 85 85 71 73 91

(a) Find the median. Show work/explanation.
(b) Find the mode.
(c) Find the first quartile. Show work/explanation.
(d) Find the third quartile. Show work/explanation.
(e) Find the range.
(f) Find the interquartile range.
(g) Find the 90th percentile. Show work/explanation.

4. For each of six days, the outdoor temperature was recorded at noon, and the following temperatures were recorded (and listed in ascending order):

8 39 41 45 49 52

(a) Find the median temperature.
(b) Find the mean temperature.
(c) What is the shape of the distribution of temperatures? (skewed left, symmetric, or skewed right?)
(d) Compute the sample variance and sample standard deviation, completing the table below.

8
39
41
45
49
52

Sample variance: ___________

Sample standard deviation: ___________

(e) Compute the coefficient of variation (CV).
(f) Suppose we discover that there has been an error in recording the temperatures. Suppose that instead of 8, it should have been 38, so that the data are actually

38 39 41 45 49 52

If we redo our calculations, indicate what we should expect, by answering the following:

(i) Will the newly calculated mean be lower, the same, or higher than before? _________

(ii) Will the newly calculated median be lower, the same, or higher than before? ________

(iii) Will the newly calculated sample standard deviation be lower, the same, or higher than before? _______

5. The (fictional) university Central University has two professional graduate programs, the Business School and the Law School. The following tables show data about 700 male applicants and about 500 female applicants.

Table M: MALE Applicants
Admitted Not admitted Total
Business School 480 120
Law School 10 90
Total
Table F: FEMALE Applicants
Admitted Not admitted Total
Business School 180 20
Law School 100 200
Total

(a) Fill in the totals in Table M and in Table F.

(b) For Table M, construct a table of row percentages. For Table F, construct a table of row percentages.

MALE Applicants
Admitted Not admitted Total
Business School
Law School
Total
FEMALE Applicants
Admitted Not admitted Total
Business School
Law School
Total

(b) Looking at the Business School, who is admitted at a higher rate, men or women?

(c) Looking at the Law School, who is admitted at a higher rate, men or women?

(d) Looking at the last row, the totals for both business and law schools combined, who is admitted at a higher rate, men or women?

(e) Why is the answer for (d) so different than for (b) and (c)? Can you see what is causing this effect? Discuss briefly.
HINT: Try constructing tables for the total percentages and see if that provides additional insight.
MALE Applicants
Admitted Not admitted Total
Business School
Law School
Total
FEMALE Applicants
Admitted Not admitted Total
Business School
Law School
Total

6. Dinner check amounts at a particular restaurant have the frequency distribution shown below.

Dinner Frequency
Check
$25 - under $35 3
$35 - under $45 9
$45 - under $55 13
$55 - under $65 20
$65 - under $75 15
Total 60

Compute the estimated mean dinner check amount for these grouped data. Show work.
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Solution Summary

Answers questions on summary statistics-mean, median, mode, first quartile, third quartile, range, interquartile range, 90th percentile, shape of the distribution, skewness, sample variance and sample standard deviation, coefficient of variation, grouped data

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