Math Multiple Choice

Which of the following statements is true? a. The sum of the deviations from the mean is always zero. b. The sum of the squared deviations from the mean is always zero. c. The standard deviation is always smaller than the variance. d. The distance between the first and third quartiles is twice the distance between the first and second quartiles. e. None of these is true.

A

If a data set has 15 values that have been sorted in ascending order, which value in the data set will be the 25th percentile? a. the fourth value b. the third value c. the second value d. the first value e. There is not enough information to answer this question.

A

In a histogram, the proportion of the total area which must be to the left of the median is: a. exactly 0.50 b. less than 0.50 if the distribution is skewed to the left c. more than 0.50 if the distribution is skewed to the right d. between 0.25 and 0.75 if the distribution is symmetric e. all of these

A

Which of the following best describes measures of center? a. They are numbers around which observations tend to cluster and that describe the location of what in some sense might be called the center of a data set. b. They are numbers that indicate the spread or scatter of observations and show the extent to which individual values in a data set differ from one another and, hence, differ from their central location. c. They are numbers that indicate the degree of asymmetry in a frequency distribution. d. None of these. e. All of these.

A

Which of the following statements is true for the following data values: 17, 15, 16, 14, 17, 18, and 22? a. The mean, median and mode are all equal. b. Only the mean and median are equal. c. Only the mean and mode are equal. d. Only the median and mode are equal. e. The mean, median and mode are all different.

A

A sample of students who have taken a calculus test has a mean score of 78.2, a mode of 67, and a median score of 67. Based on this information, the distribution of test scores is: a. symmetric b. right skewed c. left skewed d. bimodal e. none of these

B

The best-fitting regression line can be used to: a. find the actual value of y for a given value of x b. estimate or predict the value of y for a given value of x c. calculate the correlation coefficient d. all of these e. none of these

B

The stem-and-leaf plot is used to display the distribution of: a. qualitative data b. quantitative data c. two quantitative variables on the same chart d. all of these

B

Which of the following best describes a relative class frequency? a. It is the number of observations that falls into a given class in a frequency distribution. b. It is the proportion of all observations that falls into a given class in a frequency distribution. c. It is the difference between the numerical lower and upper limit of a class of quantitative data. d. It is the number of observations that falls into the smallest class in a frequency distribution. e. None of these.

B

A bar chart is used to display a: a. time series data b. continuous variable c. qualitative variable d. quantitative variable e. discrete variable

C

Data about qualitative variables can be summarized by: a. measures of center b. measures of variability c. proportions d. measures of relative standing e. all of these

C

Generally speaking, if two variables are unrelated (as one increases, the other shows no pattern), the covariance will be: a. a large positive number b. a large negative number c. a positive or negative number close to zero d. a positive or negative number close to 100 e. none of these

C

The sum of the frequencies for all classes will always equal: a. the number of classes b. the class width c. the total number of observations in the data set d. one e. the average

C

Which of the following is not a measure of variability? a. the variance b. the standard deviation c. the mean d. the range e. all are measures of variability

C

Which of the following represents a disadvantage of using the sample range to measure spread or dispersion? a. It produces spreads that are too large. b. The sample range is not measured in the same units as the data. c. The largest or smallest observation (or both) may be an outlier. d. None of these is correct. e. All of these are correct.

C

Which one of the values below represents a lower quartile for the data set 23, 24, 21, and 20? a. 22.0 b. 22.5 c. 20.25 d. 23.5 e. none of these

C

A college placement office conducted a survey of 100 engineers who had graduated from Stanford University. For these engineers, the mean salary was computed to be $72,000 with a standard deviation of $8,000. The percentage of these engineers who earn more than $96,000 or less than $48,000 is: a. approximately 0% b. at least 5.6% (1/18 of the engineers) c. at most 5.6% (1/18 of the engineers) d. at most 11.1% (1/9 of the engineers) e. at least 11.1% (1/9 of the engineers)

D

A sample of 25 observations has a standard deviation of 4. The sum of the squared deviations from the sample mean is: a. 21 b. 25 c. 100 d. 384 e. 400

D

A sample of 600 values produced the following summary statistics: Based on this information, upper fence on a box and whisker plot is: a. 26.80 b. -4.60 c. 75.80 d. 102.60 e. 62.4

D

According to Tchebysheff's Theorem, provided only , regardless of the shape of a population's frequency distribution. The proportion of observations falling within k standard deviations of the mean is: a. at most 1 - b. at least 1 - c. at most 1 - d. at least 1 - e. exactly 1 -

D

One of the differences between a histogram and bar chart is: a. that the bar chart does have gaps between the bars and the histogram does not b. that the histogram is used to display the distribution of quantitative data and the bar chart is used to display qualitative data c. that the width of the bars is the same in both the histogram and the bar chart d. all of these e. none of these

D

The following summary statistics were computed from a sample of size 250: . Based on this information, which of the following statements is correct? a. The distribution of the data is slightly right-skewed. b. The distribution of the data is symmetric. c. A data value of 20 is an outlier. d. None of these. e. All of these.

D

Which of the following are measures of the linear relationship between two variables? a. the covariance b. the correlation coefficient c. the variance d. both the covariance and the correlation coefficient e. both the correlation coefficient and the variance

D

Which of the following randomly selected measurements, x, might be considered a potential outlier (i.e., an unusual measurement) if it was selected from the given population? a. x = 0 from a population with = 0 and = 2 b. x = -5 from a population with = 1 and = 4 c. x = 7 from a population with = 3 and = 2 d. x = 4 from a population with = 0 and = 1 e. x = 1 from a population with = 0 and = 2

D

A graphical portrayal of a relative frequency distribution of continuous quantitative data in such a way that lower and upper limits of data classes are identified by tick marks on a horizontal axis, while the corresponding relative class frequencies are represented by the areas of vertical rectangles connected to each other and stand on top of each of these class intervals, is called: a. a bar chart b. a frequency polygon c. a pictogram d. a time series plot e. none of these

E

If a regression line has a y-intercept of 6.75 and a slope of 1.25, then when x = 2 the actual value of y is: a. 9.25 b. 8.75 c. 2.25 d. 1.45 e. unknown

E