Business Statistics Exam One
To determine the class interval Answers: Divide the class frequencies in half. Divide the class frequency by the number of observations. Find the difference between consecutive lower class limits. Count the number of observations in the class.
Find the difference between consecutive lower class limits
For a set of data arranged or sorted in numerical order, the value of the observation in the center is called the weighted mean. Answers: True False
False
Ordinal level of measurement is considered the "lowest" level of measurement. Answers: True False
False
The order that runners finish in a race would be an example of continuous data. Answers: True False
False
A study of the scores on an in-plant course in management principles and the years of service of the employees enrolled in the course resulted in these statistics: - Mean test score was 200 with a standard deviation of 40 - Mean number of years of service was 20 years with a standard deviation of 2 years. In comparing the relative dispersion of the two distributions, what are the coefficients of variation? Answers: Test 50%, service 60% Test 100%, service 400% Test 20%, service 10% Test 35%, service 45%
Test 20%, service 10%
A research organization is making a study of the selling price of home computers. There are 45 computers in the study. How many classes would you recommend? Answers: 10 20 6 3
6
In a set of 10 observations the mean is 20 and the median is 15. There are 2 values that are 6, and all other values are different. What is the mode? Answers: 15 20 6 None of the above.
6
The science of statistics includes which of the following: Organizing data Presenting data Interpreting data All the above
All the above
The standard deviation is Answers: Based on squared deviations from the mean. In the same units as the mean. Uses all the observations in its calculation. All of the above.
All the above
In a frequency distribution the categories must Answers: Be mutually exclusive. Have at least 5 observations. Be of the same size. Be of nominal scale.
Be mutually exclusive
In descriptive statistics, our main objective is to:
Describe the data we collected
A relative frequency distribution shows the number of observations in each class. Answers: True False
False
The weighted mean is a special case of the Answers: Mean Median Mode Geometric mean
Mean
Which of the following measures of central location is affected most by extreme values? Answers: Median Mean Mode Geometric mean
Mean
In a frequency table Answers: the classes must be mutually exclusive. the data is quantitative. the should be at least 100 observations in the sample. All of the above are correct.
The classes must be mutually exclusive
A row of a stem-and-leaf chart appears as follows: 3 | 0 1 3 5 7 9. Assume that the data is rounded to the nearest unit. Answers: The frequency of the class is seven. The minimum value in the class is 0. The maximum value in the class is 39. The class interval is 5.
The maximum value is 39
In a positively skewed distribution Answers: The mean, median, and mode are all equal. The mean is larger than the median. The median is larger than the mean. The standard deviation must be larger than the mean or the median.
The mean is larger than the median
In a symmetric distribution Answers: The mean, median, and mode are equal. The mean is the largest measure of location. The median is the largest measure of location. The standard deviation is the largest value.
The mean, median, and mode are equal
A class interval, which is the width of a class, can be determined by subtracting the lower limit of a class from the lower limit of the next higher class. Answers: True False
True
A frequency distribution groups data into classes showing the number of observations in each class. Answers: True False
True
In a line chart the horizontal axis: Answers: Is usually in dollars. Usually involves time, such as months or years. Is usually shown with a dotted line. Is usually reported as a percent.
Usually involves time, such as month or years
The variance is Answers: Found by dividing by N by the mean. In the same units as the original data. Found by squaring the standard deviation. All of the above.
Found by squaring the standard deviation
Which of the following statements is true regarding a sample? Answers: It is a part of population. It must contain at least five observations. It refers to descriptive statistics. All of the above are correct.
It is a part of a population
A qualitative variable Answers: Always refers to a sample. Is not numeric. Has only two possible outcomes. All of the above are correct.
It is not numeric
The coefficient of variation for a set of annual incomes is 18%; the coefficient of variation for the length of service with the company is 29%. What does this indicate? Answers: More dispersion in the distribution of the incomes compared with the dispersion of their length of service More dispersion in the lengths of service compared with incomes Dispersion in the two distributions (income and service) cannot be compared using percents Dispersions are equal
More dispersion in the lengths of service compared with incomes
When a frequency distribution is exhaustive, each individual, object, or measurement from a sample or population must appear in at least one category. Answers: True False
True
Which of the following statements is true regarding the standard deviation? Answers: It cannot assume a negative value. If it is zero, then all the data values are the same. It is in the same units as the mean. All the above are all correct.
All the above
Which of the following is not a measure of dispersion? Answers: Range Variance Standard deviation All of the above are measures of dispersion
All the above are measures of dispersion
A discrete variable is Answers: An example of a qualitative variable. Can assume only whole number values. Can assume only certain clearly separated values. Cannot be negative.
Can only assume only certain clearly separated values
Categorizing voters as Democrats, Republicans and Independents is an example of interval level measurement. Answers: True False
False
For salaries of $102,000, $98,000, $45,000, $106,000 and $101,000, the arithmetic mean would be an appropriate average. Answers: True False
False
What does the interquartile range describe? Answers: The lower 50% of the observations The middle 50% of the observations The upper 50% of the observations The lower 25% and the upper 25% of the observations None of the above
The middle 50% of the observations
The class frequency is Answers: The number of observations in each class. The difference between consecutive lower class limits. Always contains at least 5 observations. Usually a multiple of the lower limit of the first class.
The number of observations in each class
A pie chart is used when we wish to emphasize Answers: The number of observations in each category. The percent of observations in each category. The level of measurement of the observations. All of the above.
The percent of observations in each category
What is the possible range of values for the coefficient of variation? Answers: -1 and +1 -3 and +3 0% and 100% Unlimited values
0% and 100%
Which of the following are examples of continuous variables? Answers: Birth weight of babies Distance between tollbooths on the New Jersey Turnpike. Age of the CEOs of the Fortune 500 companies All of the above.
All the above
The mean deviation is Answers: Based on squared deviations from the mean. Also called the variance. Based on absolute values. Always reported in squared units.
Based on absolute values
To convert a frequency distribution to a relative frequency distribution Answers: Find the difference between consecutive lower class limits. Divide the class frequency by the total number of observations. Divide the lower limit of the first class by the class interval. Multiple the class frequency by 100.
Divide the class frequency by the total number of observations
To find the class midpoint Answers: Divide the class interval in half and add the result to the lower limit. Find the difference between consecutive lower limits. Count the number of observations in the class. Divide the class frequency by the number of observations.
Divide the class interval in half and add the result to the lower limit
A set of ordinal, interval or ratio level data may only have one mode. Answers: True False
False
The ratio scale of measurement Answers: Usually involves ranking. Cannot assume negative values. Has a meaningful zero point. Is usually based on counting.
Has a meaningful zero point
Which of the following is not a guideline for a frequency distribution? Answers: Avoid open-ended classes. Have more than 5 but less than 15 classes. Make the lower limit of the first class a multiple of the class interval. Have more than 5 observations in each class.
Have more than 5 observations in each class
The ordinal scale of measurement Answers: Has a meaningful zero point. Is based on ranks Cannot assume negative values. All of the above.
Is based on ranks
Which of the following statements is true regarding a population? Answers: It must be a large number of values. It must refer to people. It is a collection individuals, objects, or measurements. None of the above.
It is a collection of individuals, objects, or measurments
In a set of observations, which measure of central tendency reports the value that occurs most often? Answers: Mean Median Mode Geometric mean
Mode
A difference between calculating the sample mean and the population mean is Answers: Only in the symbols, we use n instead of N. We divide the sum of the observations by n - 1 instead of n. The observations are ranked and select the middle value for the population mean. There are no differences.
Only in the symbols
A disadvantage of the range is Answers: Only two values are used in its calculation. It is in different units than the mean. It does not exist for some data sets. All of the above.
Only two values are used in its calculation
The difference between a histogram and a frequency polygon is Answers: The frequency polygon is reported as a percent. The histogram employs bars whereas the midpoints are connected for a frequency polygon. Bars cannot be adjacent in a histogram. Open-ended classes can be accommodated with a frequency polygon.
The histograms employs bars whereas midpoints are connected for a frequency polygon
A negatively skewed distribution is not symmetrical. The long tail is to the left or in the negative direction. Answers: True False
True
A population is a collection of all individuals, objects, or measurements of interest. Answers: True False
True
A sample is a portion or part of the population of interest. Answers: True False
True
A value that is typical or representative of the data is referred to as a measure of central location. Answers: True False
True
Dispersion is the degree of variation in the data. Answers: True False
True
If a variable is measured at the interval or ratio level, all the values are included when computing the mean. Answers: True False
True
In frequency distributions, classes are mutually exclusive if each individual, object, or measurement is included in only one category. Answers: True False
True
The Empirical Rule states that about 68% of the observation will lie within one standard deviation of the mean; about 95% of the observations will lie within two standard deviations of the mean; and virtually all (99.7%) will lie within three standard deviations of the mean. Answers: True False
True
The mode is the value of the observation that appears most frequently. Answers: True False
True
In a scatter diagram, we describe the relationship between Answers: two variables measured at the ordinal level two variables, one measured as an ordinal variable and the other as a ratio variable two variables measured at the interval or ratio level a variable measure on the interval or ratio level and time.
Two variables measured at the interval or ratio level
A nominal scale variable is Answers: Usually the result of counting something. Has a meaningful zero point. May assume negative values. Cannot have more than two categories.
Usually the result of counting something
In a cumulative frequency polygon Answers: The class frequencies are converted to a percent. There must be at least 5 observations in each class. We add the class frequencies starting with the first class. All of the above.
We add the class frequencies starting with the first class