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# Descriptive Statistics Frequency..

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Hello, I need help with the problems below.

1. The final exam scores listed below are from one section of MATH 200. How many scores were within one standard deviation of the mean? How many scores were within two standard deviations of the mean?
99 34 86 57 73 85 91 93 46 96 88 79 68 85 89

2. The scores for math test #3 were normally distributed. If 15 students had a mean score of 74.8% and a standard deviation of 7.57, how many students scored above an 85%?

3. If you know the standard deviation, how do you find the variance?

4. To get the best deal on a stereo system, Louis called 8 out of 20 appliance stores in his neighborhood and asked for the cost of a specific model. The prices he was quoted are listed below:
\$216 \$135 \$281 \$189 \$218 \$193 \$299 \$235

Find the standard deviation.
5. A company has 70 employees whose salaries are summarized in the frequency distribution below.
Salary Number of Employees
5,001-10,000 8
10,001-15,000 12
15,001-20,000 20
20,001-25,000 17
25,001-30,000 13
A. Find the standard deviation.
B. Find the variance.

6. Calculate the mean and variance of the sample data set provided below. Show and explain your steps. Round to the nearest tenth.
14, 16, 7, 9, 11, 13, 8, 10

7. Create a frequency distribution table for the number of times a number was rolled on a die. (It may be helpful to print or write out all of the numbers so none are excluded.)
3, 5, 1, 6, 1, 2, 2, 6, 3, 4, 5, 1, 1, 3, 4, 2, 1, 6, 5, 3, 4, 2, 1, 3, 2, 4, 6, 5, 3, 1

8. Answer the following questions using the frequency distribution table you created in No. 7.
a Which number(s) had the highest frequency?
b How many times did a number of 4 or greater get thrown?
c How many times was an odd number thrown?
d How many times did a number greater than or equal to 2 and less than or equal to 5 get thrown?

9. The wait times (in seconds) for fast food service at two burger companies were recorded for quality assurance. Using the data below, find the following for each sample.
a Range
b Standard deviation
c Variance
Lastly, compare the two sets of results.
Company Wait times in seconds
Big Burger Company 105 67 78 120 175 115 120 59
The Cheesy Burger 133 124 200 79 101 147 118 125

10. What does it mean if a graph is normally distributed? What percent of values fall within 1, 2, and 3, standard deviations from the mean?

https://brainmass.com/statistics/random-variables/descriptive-statistics-frequency-616223

#### Solution Preview

FREQUENCY
1. The final exam scores listed below are from one section of MATH 200. How many scores were within one standard deviation of the mean? How many scores were within two standard deviations of the mean?
99 34 86 57 73 85 91 93 46 96 88 79 68 85 89
Scores, X X - X̅ (X - X̅)^2
99 21.06666667 443.8044446
34 -43.93333333 1930.137777
86 8.06666667 65.07111116
57 -20.93333333 438.2044443
73 -4.93333333 24.33777774
85 7.06666667 49.93777782
91 13.06666667 170.7377779
93 15.06666667 227.0044445
46 -31.93333333 1019.737778
96 18.06666667 326.4044446
88 10.06666667 101.3377778
79 1.06666667 1.137777785
68 -9.93333333 98.67111104
85 7.06666667 49.93777782
89 11.06666667 122.4711112
1169 5068.933333
Mean, μ = = 77.93
Standard deviation, σ = = 19.03
μ - σ = 77.93 - 19.03 = 58.9
μ + σ = 77.93 + 19.03 = 96.96
There are 11 scores within one standard deviation of the mean.
μ - 2σ = 77.93 - (2 * 19.03) = 39.87
μ + 2σ = 77.93 + (2 *19.03) = 115.99
There are 14 scores within two standard deviation of the mean.
2. The scores for math test #3 were normally distributed. If 15 students had a mean score of 74.8% and a standard deviation of 7.57, how many students scored above an 85%?
Let X be the scores for math test #3. Given that X is normal with mean µ = 74.8 and standard deviation  = 7.57.
We need P (X > 85). Standardizing the variable X using and from standard normal tables, we have
P (X > 85) = = P (Z > 1.34742) = 0.0889
Hence the students scored above an 85% = 15 * 0.0889 = 1.33 ≈ 1
Details
Normal Probabilities

Common Data
Mean 74.8
Standard Deviation 7.57

Probability for X >
X Value 85
Z Value 1.347424042
P(X>85) 0.0889
3. If you know the standard deviation, how do you find the variance?