Exam 3: Describing Data: Numerical Measures

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(i. The mode is 21. (ii. The arithmetic mean is 20.4. (iii) The median is 21.

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(i. If a distribution is highly skewed, the mean (measure of central tendency) should be avoided. (ii. A characteristic of the population is called a statistic. (iii) A sample revealed that the ages of musicians playing in small local combos are 36, 29, 37, 32, 36 and 75. The median is the most appropriate measure of central tendency to represent the ages Of the musicians.

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(i. The mode is 21. (ii. The arithmetic mean is 20.4. (iii) The median is 23.

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B

The ages of newly hired, unskilled employees were grouped into the following distribution: The ages of newly hired, unskilled employees were grouped into the following distribution:   What is the median age? What is the median age?

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(i. The mean is the measure of central tendency that uses all of the observations in its calculation. (ii. The mode is the class with the largest number of observations. (iii) If a set of observations contains an extreme value and none of the observations repeat Themselves, the mean is the most representative measure of central tendency.

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(i. The range for laminate flooring is 0 or none. (ii. The range for polyester carpet is $0.04 or 4 cents. (iii) The mean deviation for laminate flooring is 0.

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i. The standard deviation is the positive square root of the variance. ii. For a symmetrical distribution, the variance is equal to the standard deviation. iii. If the standard deviation of the ages of a female group of employees is six years and the Standard deviation of the ages of a male group in the same plant is ten years, it indicates that there Is more spread in the ages of the female employees.

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Fifteen accounting majors had an average grade of 90 on a finance exam. Seven marketing majors Averaged 85, while ten finance majors averaged 93 on the same exam. What is the weighted mean For the 32 students taking the exam?

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Listed below is the box plot of average earnings ratio for full-year, full-time male workers from 1999 To 2008: Listed below is the box plot of average earnings ratio for full-year, full-time male workers from 1999 To 2008:   From this we can interpret that the range of average earnings for men for the years 1999-2008 was Approximately: From this we can interpret that the range of average earnings for men for the years 1999-2008 was Approximately:

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(i. The arithmetic mean (measure of central tendency) cannot be determined if the distribution has An open-ended class. (ii. The measure of central tendency used to determine the average annual percent increase in Sales from one time period to another is the arithmetic mean. (iii) The smallest measure of central tendency in a positively skewed distribution is the mode

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Using the information gathered for real estate prices in Regina and surrounding areas in the early 2000's, determine the mean of the selling prices at that time. Using the information gathered for real estate prices in Regina and surrounding areas in the early 2000's, determine the mean of the selling prices at that time.

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If a major sports star were to move into your neighbourhood, what would you expect to happen to The neighbourhood's "average" income?

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(i. The research director of a large oil company conducted a study of the buying habits of Consumers with respect to the amount of gasoline purchased at full-service pumps. The arithmetic Mean amount is 11.5 gallons and the median amount is 11.95 litres. The standard deviation of the Sample is 4.5 litres. The Pearson's coefficient of skewness can be calculated to be -0.30. (ii. Rainbow Trout, Inc., feeds fingerling trout in special ponds and markets them when they attain a Certain weight. A group of 9 trout (considered the population) were isolated in a pond and fed a Special food mixture called Grow Em Fast. At the end of the experimental period, the weights of the Trout were (in grams): 124, 125, 123, 120, 124, 127, 125, 126 and 121. Another special mixture, Fatso 1B, Was used in another pond. The mean of the population was computed to be 126.9 grams and the Standard deviation was 1.20 grams. When these data are analysed, we discover that the food Resulting in a more uniform weight is Fatso 1B. (iii) A study has been made of the number of hours a light bulb will operate before it burns out. If the Standard deviation of this distribution were computed, it would be measured in hours squared

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(i. A small manufacturing company with 52 employees has annual salaries distributed such that the Mean is $25,459, the median is $24,798 and the mode is $24,000. An additional foreman is hired at An annual salary of $50,700. The measure of central tendency that is most affected by the addition Of this salary is the arithmetic mean. (ii. In the relationship between the mean and median in a negatively skewed distribution the mean is Less than the median. (iii) In the relationship between the median and the mode in a positively skewed distribution, the Median is greater than the mode.

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What is a disadvantage of the range as a measure of dispersion?

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(i. The range for laminate flooring is 0 or none. (ii. The standard deviation for nylon carpet is 4.64 cents (iii) The range for nylon carpet is $0.12 or 12 cents.

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What is a disadvantage of the range as a measure of dispersion?

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Which one of the following is referred to as the population mean?

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The annual incomes of the five vice presidents of Elly's Industries are: $41,000, $38,000, $32,000, $33,000 and $50,000. The annual incomes of Unique, another firm similar to Elly's Industries, were Also studied and found to have a mean of $38,900 and a standard deviation of $6,612. Which firm Has the greater coefficient of variation?

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Mr. and Mrs. Jones live in a neighbourhood where the mean family income is $45,000 with a Standard deviation of $9,000. Mr. and Mrs. Smith live in a neighbourhood where the mean is $100,000 and the standard deviation is $30,000. What are the relative dispersions of the family Incomes in the two neighbourhoods?

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