Statistics homework help
Statistics (Math 141)
Homework: B2
Instructions
Please complete all problems. Unless otherwise noted, each problem is worth 5 points. To obtain full credit, you must use the methods specified in the course text. Please, format your work as explained in chapter 2 of the Frequently Asked Questions (FAQ) document. When doing calculations, such as the variance or standard deviation, use technology wherever possible. There is no need to do calculations by hand unless I direct you to do so. Round all calculations to three decimal places.
Assignment Problems
Section 2.3
- True or false? The median is the only measure of central tendency that can be used to describe data at the nominal level of measurement.
- True or false? If a vertical line is drawn through the middle of a distribution and both halves are approximately mirror images, the distribution may still be classified as symmetric.
- State whether the shape of the distribution represented by the histogram in Figure 1 is symmetric, uniform, skewed left, skewed right, or none of these.
- Which graph shown in figure 2 best represents the frequency distribution of the weights of students in two classes at a local high school. Assume the weight is in pounds? (Pick one letter from the following.)
- Using Table 1, Find the mean, median, and mode of the data, if possible. If any of these measures cannot be found, explain why.
Cholesterol levels | |||||||||
---|---|---|---|---|---|---|---|---|---|
162 | 210 | 180 | 175 | 170 | 199 | 215 | 167 | 275 | 178 |
- Using Table 2, Find the mean, median, and mode of the data, if possible. If any of these measures cannot be found, explain why.
Number of aircraft | |||||||
---|---|---|---|---|---|---|---|
84 | 135 | 44 | 587 | 298 | 722 | 60 | 27 |
155 | 14 | 487 | 44 | 359 | 422 | 26 |
- Using Table 3, Find the mean, median, and mode of the data, if possible. If any of these measures cannot be found, explain why.
What Surprised Them | Frequency |
---|---|
Amount of first salary: | 89 |
Number of decisions: | 183 |
Paying bills: | 326 |
Trying to find a job: | 138 |
Money needed: | 300 |
Trying to save: | 240 |
Difficulty in breaking away from parents: | 90 |
- Find the weighted mean of the data For the month of July, a checking account has a balance of $275.29 for 14 days, $758.48 for 6 days, $723.84 for 8 days, and $279.40 for 3 days. What is the account’s mean daily balance for July?
Section 2.4
Problems 9-12. Use the data set representing a sample in Table 4 to answer the questions. Note: Review the 1-Var Stats function on the TI83/84 calculator.
Sample Data | ||||
---|---|---|---|---|
38 | 35 | 30 | 32 | 16 |
28 | 15 | 56 | 42 | 24 |
39 | 44 | 46 | 22 | 39 |
29 | 55 | 25 | 64 | 25 |
- What is the range?
- What is the mean?
- What is the variance?
- What is the standard deviation?
Problems 13-15. Use Tables 5a and 5a to answer the questions.
Data Set A: | 100 | 120 | 101 | 119 | 102 | 118 | 118 | 102 | 119 | 101 |
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Data Set B: | 100 | 120 | 114 | 106 | 113 | 107 | 113 | 107 | 112 | 108 |
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- Select the letter of the appropriate data set. Without calculating the standard deviation, which data set has the greatest standard deviation?
- Select the letter of the appropriate data set. Without calculating the standard deviation, which data set has the least standard deviation?
- Explain the reason for your decisions in questions 13 and 14.
- Tree Heights. You study the heights of trees on two wood lots. Lot A has trees with μ=22 feet and σ=2 feet and Lot B has trees with heights, such that μ=22 feet and σ=6 feet. Which lot is most likely to have trees greater than 28 feet high?
- Use the empirical rule to solve the problem. The mean annual income at a small company is $39,400, with a standard deviation of $3,325.00. Between what two values do about 95% of the salaries lie?
Problem 18. Use the following information to answer the question.
Coefficient of Variation. The coefficient of variation (CV) is an alternate way to measure variation. The CV expresses the standard deviation as a percent of the mean. Because it has no unit of measure, you can use the coefficient of variation to compare the variability of data with different units of measure. Note: Either the sample standard deviation, s, or the population standard deviation, σ, may be used for calculating the CV. Use the appropriate value of the standard deviation depending on whether the data pertain to a population or a sample.CV=standard deviationMean×100%
- Find the coefficient of variation for the data set given in Table 4.
Section 2.5
- True or False? If a data set has Q1=60, Q2=85 and Q3=98, then a data value of 145 would be considered an outlier.
- True or False? 50% of the data in a data set with quantitative data is between Q1 and Q3.
Problems 21-25. Use the data in Table 6 to answer the questions.
Data Set | ||||||||
---|---|---|---|---|---|---|---|---|
187 | 238 | 235 | 218 | 248 | 230 | 245 | 209 | 216 |
233 | 228 | 214 | 236 | 250 | 222 | 266 | 231 | 219 |
207 | 219 | 246 | 229 | 226 | 234 | 239 |
- What is Q1?
- What is Q2?
- What is Q3?
- Draw a box-and-whisker plot that represents the data set in Table 6. (Note: When drawing the box-and-whisker plot, please label the 5-number summary values. If you are doing a hand sketch, use an appropriate scale and use graph paper.)
- What is the IQR?