Chapter 3 Notes & Quiz
Standard Deviation
The square root of the variance
Mode
The value of the observation that appears most frequently
A value that is typical or representative of the data is referred to as a measure of central location. T / F
True
Three persons earn $8 an hour, six earn $9 an hour, and one earns $12 an hour. The weighted mean hourly wage is $9. T / F
True
Which one of the following is referred to as the population mean?
µ
A sample of the monthly amounts spent for food by families of four receiving food stamps approximates a symmetrical distribution. The sample mean is $150 and the standard deviation is $20. Using the Empirical Rule, about 95 percent of the monthly food expenditures are between what two amounts?
$110 and $190
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 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 distribution of a sample of the outside diameters of PVC gas pipes approximates a symmetrical, bell-shaped distribution. The arithmetic mean is 14.0 inches, and the standard deviation is 0.1 inches. About 68 percent of the outside diameters lie between what two amounts?
13.9 and 14.1 inches
The weights of a sample of crates ready for shipment to Moscow, Russia are (in kilograms): 103, 97, 101, 106 and 103. What is the mean deviation?
2.4 kg
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 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 for the semester grades?
2.76
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
Each person who applies for an assembly job at Robert's Electronics is given a mechanical aptitude test. One part of the test involves assembling a plug-in unit based on numbered instructions. A sample of the length of time it took 42 persons to assemble the unit was organized into the following frequency distribution.
3.89
The weights (in kilograms) of a group of crates being shipped to Panama are 95, 103, 110, 104, 105, 112 and 92. What is the mean deviation?
5.43 kg
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%
A population consists of all the weights of all defensive tackles on Sociable 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
Which of the following measures of dispersion are based on deviations from the mean?
All of the above
3 Measures of location
Arithmetic mean, Median, Mode
A set of ordinal, interval or ratio level data may only have one mode. T / F
False
Extremely high or low scores affect the value of the median. T / F
False
For any data set, which measures of central location have only one value?
Mean & Median
Parameter
Measurable characteristic of a population
Statistic
Measurable characteristic of a sample
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
Arithmetic Mean
Most widely used, requires the interval scale. Characteristics: all values are used, it's unique, sum of deviations from mean is 0, is calculated by summing the values and dividing by number of values.
Population mean
Sum of all population values divided by total number of population values
Median
The MIDPOINT of the values after they have been ordered from the minimum to the maximum values
Variance
The arithmetic mean of the squared deviations from the mean
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
Sometimes, data has two values that have the highest and equal frequencies. In this case, the distribution of the data can best be summarized as
bimodal (having two modes)
A disadvantage of using an arithmetic mean to summarize a set of data is that the arithmetic mean
can be biased by one or two extremely small or large values
