Statistics Chapter 3
On a finance exam, 15 accounting majors had an average grade of 90. On the same exam, 7 marketing majors averaged 85, and 10 finance majors averaged 93. What is the weighted mean for all 32 students taking the exam?
89.84
Based on the Empirical rule, what percent of the observations will lie between plus or minus two standard deviations from the mean?
95%
A population consists of all the weights of all defensive tackles on a university's football team. They are Johnson, 204 pounds; Patrick, 215 pounds; Junior, 207 pounds; Kendron, 212 pounds; Nicko, 214 pounds; and Cochran, 208 pounds. What is the population standard deviation (in pounds)?
About 4
For the most recent seven years, the U.S. Department of Education reported the following number of bachelor's degrees awarded in computer science: 4,033; 5,652; 6,407; 7,201; 8,719; 11,154; 15,121. What is the annual arithmetic mean number of degrees awarded?
About 8,327
A sample of assistant professors on the business faculty at state-supported institutions in Ohio revealed the mean income to be $72,000 for nine months, with a standard deviation of $3,000. Using Chebyshev's theorem, what proportion of the faculty earns more than $66,000, but less than $78,000?
At least 75%
What is the relationship among the mean, median, and mode in a symmetric distribution?
They are all equal
The sum of the deviations from the mean for the set of numbers 4, 9, and 5 will equal zero.
True
Variation describes the degree of dispersion in the data.
True
Which one of the following is referred to as the population mean?
µ
A value that is typical or representative of the data is referred to as a measure of central location.
True
According to the Empirical rule, about 95% of the observations lie within plus and minus 2.00 standard deviations.
True
For any data set, Chebyshev's theorem estimates the proportion of observations that occurs within k standard deviations of the mean, where k is greater than 1.0.
True
In a sample of 10 people, 3 persons earn $8 an hour, 6 earn $9 an hour, and 1 earns $12 an hour. The weighted mean hourly wage is $9.
True
The arithmetic mean is the sum of the quantitative observations divided by the total number of observations.
True
The geometric mean is the nth root of n observations.
True
The mode is the value of the observation that appears most frequently.
True
The standard deviation is the positive square root of the variance.
True
For the past week, a company's common stock closed with the following prices: $61.5, $62, $61.25, $60.875, and $61.5. What was the price range?
$1.125
The monthly amounts spent for food by families of four receiving food stamps approximates a symmetrical, normal distribution. The sample mean is $150 and the standard deviation is $20. Using the Empirical rule, about 95% of the monthly food expenditures are between what two amounts?
$110 and $190
For a sample of similar sized all-electric homes, the March electric bills were (to the nearest dollar): $212, $191, $176, $129, $106, $92, $108, $109, $103, $121, $175, and $194. What is the range?
$120
The following are the weekly amounts of welfare payments made by the federal government to a sample of six families: $139, $136, $130, $136, $147, and $136. What is the range?
$17
The sample variance of hourly wages was 10. What is the sample standard deviation?
$3.16
A stockbroker placed the following order for a customer: • 50 shares of Kaiser Aluminum at $104 a share • 100 shares of GTE at $25.25 a share • 20 shares of Boston Edison at $9.125 a share What is the weighted arithmetic mean price per share?
$46.51
A sample of the paramedical fees charged by clinics revealed these amounts: $55, $49, $50, $45, $52, and $55. What is the median charge?
$51.00
The net incomes (in $millions) of a sample of steel fabricators are $86, $67, $86, and $85. What is the modal net income?
$86
For a data set with an odd number of observations that have been sorted from smallest to largest values, where is the median located?
(n+1)/2
A survey item asked students to indicate their class in college: freshman, sophomore, junior, or senior. Which measure(s) of central location would be appropriate for the data generated by that questionnaire item?
Mode and median
Which measures of central location are not affected by extremely small or extremely large values?
Mode and median
What is the lowest level of measurement to which a median can be computed?
Ordinal
The weekly sales from a sample of 10 computer stores yielded a mean of $25,900, a median of $25,000, and a mode of $24,500. Given this, the shape of the distribution would be _________.
Positively skewed
If the variance of the "number of daily parking tickets issued is 100, the standard deviation is defined as the _____________.
Square root of the variance of the "number of daily parking tickets"
In the calculation of the arithmetic mean for grouped data, which value is used to represent all the values in a particular class?
The class midpoint
A purchasing agent for a trucking company is shopping for replacement tires for their trucks from two suppliers. The suppliers' prices are the same. However, Supplier A's tires have an average life of 60,000 miles with a standard deviation of 10,000 miles. Supplier B's tires have an average life of 60,000 miles with a standard deviation of 2,000 miles. Which of the following statements is true?
The life of Supplier B's tire is more predictable than the life of Supplier A's tires
What is the relationship between the variance and the standard deviation?
Variance is the square of the standard deviation
The sum of the differences between sample observations and the sample mean is equal to _______.
Zero
The U.S. Federal Aviation Administration reported that passenger revenues on international flights increased from $528 million in 1986 to $5,100 million in 2009. What is the geometric mean annual percent increase in international passenger revenues?
10.4
The ages of all the patients in the isolation ward of the hospital are 38, 26, 13, 41, and 22. What is the population variance?
106.8
The distribution of a sample of the outside diameters of PVC pipes approximates a symmetrical, bell-shaped distribution. The arithmetic mean is 14.0 inches, and the standard deviation is 0.1 inches. About 68% of the outside diameters lie between what two amounts?
13.9 and 14.1
A sample of small bottles and their contents has the following weights (in grams): 4, 2, 5, 4, 5, 2, and 6. What is the sample variance of bottle weight?
2.33
Assume a student received the following grades for the semester: History, B; Statistics, A; Spanish, C; and English, C. History and English are 5 credit-hour courses, Statistics a 4 credit-hour course, and Spanish is a 3 credit-hour course. If 4 grade points are assigned for an A, 3 for a B, and 2 for a C, what is the weighted mean grade for the semester?
2.76
The variance of a sample of 121 observations equals 441. The standard deviation of the sample equals
21
What is the median of 26, 30, 24, 32, 32, 31, 27, and 29?
29.5
A sample of single persons receiving Social Security payments revealed these monthly benefits: $826, $699, $1,087, $880, $839, and $965. How many observations are below the median?
3
The Investment Research Institute reported in its Mutual Fund Fact Book that the number of mutual funds increased from 5725 in 1999 to 7977 in 2009. What is the geometric mean annual percent increase in the number of funds?
3.37
According to the Empirical rule, the middle 95% of the wires tested had a tensile strength between approximately what two values?
420 and 580
Production of passenger cars in Japan increased from 3.94 million in 1999 to 6.74 million in 2009. What is the geometric mean annual percent increase?
5.5
The times (in minutes) that several underwriters took to review applications for similar insurance coverage are 50, 230, 52, and 57. What is the median length of time required to review an application?
54.5
According to Chebyshev's theorem, at least what percent of the observations lie within plus and minus 1.75 standard deviations of the mean?
67%
Over the last six months, the following numbers of absences have been reported: 6, 0, 10, 14, 8, and 0. What is the median number of monthly absences?
7
The number of students at a local university increased from 2,500 students to 5,000 students in 10 years. Based on a geometric mean, the university grew at an average percentage rate of
7.1 percent per year
Sometimes, a data set has two values that have the highest and equal frequencies. In this case, the distribution of the data can best be described as __________.
Bimodal (having two modes)
When computing the mean, the smallest value
Can be any value
A set of ordinal-, interval-, or ratio-level data may only have one mode.
False
According to Chebyshev's theorem, 75% of the observations lie within plus and minus 2.00 average mean deviations.
False
Extremely high or low scores affect the value of the median.
False
For a set of data arranged or sorted in numerical order, the value of the observation in the center is called the weighted mean.
False
For any distribution, there are an equal number of values above and below the mean.
False
In a company, the standard deviation of the ages of female employees is 6 years and the standard deviation of the ages of male employees is 10 years. These statistics indicate that the dispersion of age is greater for females than for males.
False
The variance is the mean of the sum of the squared deviations between each observation and the median.
False
Which measure of central location is used to determine an average annual percent increase?
Geometric mean
The same mean:
Is found by adding all data values and dividing them by n
A disadvantage of using an arithmetic mean to summarize a set of data is that __________.
It can be biased by one or two extremely small or large values
What is a disadvantage of the range as a measure of dispersion?
It is based on only two observations
The mean, as a measure of central location, would be inappropriate for which one of the following?
Marital status of college students at a particular university
A statistic computed by summing all of the values of a distribution and dividing by the number of values is called the __________.
Mean
If a distribution is highly skewed, the measure of central location called the ________ should be avoided.
Mean
The measure of central location that uses all of the observations in its calculation is called the ___________.
Mean
The sum of the deviations of each data value from this measure of central location will always be zero.
Mean
For any data set, which measures of central location have only one value?
Mean and median
For a data set, half of the observations are always greater than the ____.
Median
If a set of quantitative observations contains an extreme value, the most representative measure of central location would be the __________.
Median
The measure of central location that requires the data to be ranked before it is possible to determine it is called the _________.
Median
A question in a market survey asks for a respondent's favorite car color. Which measure of central location should be used to summarize this question?
Mode
In a frequency distribution, the class with the largest number of observations is called the ___________.
Mode
The value that occurs most often in a set of data is called the ________.
Mode
