BSTAT CH. 3

According to the Chebyshev rule, at least what percentage of the observations in any data set are contained within a distance of 2 standard deviations around the mean? a) 67% b) 75% c) 88.89% d) 95% ANSWER: b

b) 75%

Which measure of central tendency can be used for both numerical and categorical variables? a) Arithmetic mean. b) Median. c) Mode. d) Geometric mean. ANSWER: c

c) Mode.

Which of the following statistics is not a measure of central tendency? a) Arithmetic mean. b) Median. c) Mode. d) Q 3. ANSWER: d

d) Q 3.

In right-skewed distributions, which of the following is the correct statement? a) The distance from Q 1 to Q 2 is greater than the distance from Q 2 to Q 3. b) The distance from Q 1 to Q 2 is less than the distance from Q 2 to Q 3. c) The arithmetic mean is less than the median. d) The mode is greater than the arithmetic mean. ANSWER: b

b) The distance from Q 1 to Q 2 is less than the distance from Q 2 to Q 3.

According to the empirical rule, if the data form a "bell-shaped" normal distribution, _______ percent of the observations will be contained within 3 standard deviations around the arithmetic mean. a) 68.26 b) 75.00 c) 95.0 d) 99.7 ANSWER: d

d) 99.7

According to the Chebyshev rule, at least 93.75% of all observations in any data set are contained within a distance of how many standard deviations around the mean? a) 1 b) 2 c) 3 d) 4 ANSWER: d

d) 4

When extreme values are present in a set of data, which of the following descriptive summary measures are most appropriate: a) CV and range. b) arithmetic mean and standard deviation. c) the median equals the arithmetic mean. d) variance and interquartile range. ANSWER: c

C) the median equals the arithmetic mean.

According to the empirical rule, if the data form a "bell-shaped" normal distribution, _______ percent of the observations will be contained within 1 standard deviation around the arithmetic mean. a) 68.26 b) 75.00 c) 88.89 d) 93.75 ANSWER: a

a) 68.26

Which of the following statements about the median is not true? a) It is more affected by extreme values than the arithmetic mean. b) It is a measure of central tendency. c) It is equal to Q 2. d) It is equal to the mode in bell-shaped "normal" distributions. ANSWER: a

a) It is more affected by extreme values than the arithmetic mean

In general, which of the following descriptive summary measures cannot be easily approximated from a box plot? a) The variance. b) The range. c) The interquartile range. d) The median. ANSWER: a

a) The variance.

A manufacturer of flashlight batteries took a sample of 130 batteries from a day's production and used them continuously until they were drained. The number of hours until failure are recorded. Given below is the boxplot of the number of hours it took to drain each of the 130 batteries. The distribution of the number of hours is Boxplot Hours 260 460 660 860 1060 a) right-skewed b) left-skewed c) symmetrical d) none of the above ANSWER: a

a) right-skewed

According to the Chebyshev rule, at least 75% of all observations in any data set are contained within a distance of how many standard deviations around the mean? a) 1 b) 2 c) 3 d) 4 ANSWER: b

b) 2

Which of the arithmetic mean, median, mode, and geometric mean are resistant measures of central tendency? a) The arithmetic mean and median only. b) The median and mode only. c) The mode and geometric mean only. d) The arithmetic mean and mode only. ANSWER: b

b) The median and mode only

In a right-skewed distribution a) the median equals the arithmetic mean. b) the median is less than the arithmetic mean. c) the median is greater than the arithmetic mean. d) none of the above. ANSWER: b

b) the median is less than the arithmetic mean.

Which of the following is sensitive to extreme values? a) The median. b) The interquartile range. c) The arithmetic mean. d) The 1st quartile. ANSWER: c

c) The arithmetic mean.

According to the Chebyshev rule, at least what percentage of the observations in any data set are contained within a distance of 3 standard deviations around the mean? a) 67% b) 75% c) 88.89% d) 99.7% ANSWER: c

c) 88.89%

Data on the change in the cost of tuition, a shared dormitory room, and the most popular meal plan from one academic year to the next academic year for a sample of 100 public universities are collected. Below is the boxplot for the change in cost in dollars. The distribution of the change in cost is Boxplot Change in Cost ($) 300 800 1300 1800 2300 a) right-skewed b) left-skewed c) symmetrical d) none of the above ANSWER: a

a) right-skewed

The smaller the spread of scores around the arithmetic mean, a) the smaller the interquartile range. b) the smaller the standard deviation. c) the smaller the coefficient of variation. d) All the above. ANSWER: d

d) All the above. -the smaller the interquartile range. -the smaller the standard deviation. -the smaller the coefficient of variation

In perfectly symmetrical distributions, which of the following is NOT a correct statement? a) The distance from Q 1 to Q 2 equals to the distance from Q 2 to Q 3. b) The distance from the smallest observation to Q 1 is the same as the distance from Q 3 to the largest observation. c) The distance from the smallest observation to Q 2 to the largest observation. d) The distance from Q 1 is the same as the distance from Q 2 is half of the distance from the smallest to the largest observation. ANSWER: d

d) The distance from Q 1 is the same as the distance from Q 2 is half of the distance from the smallest to the largest observation.

Which of the following is NOT a measure of central tendency? a) The arithmetic mean. b) The geometric mean. c) The mode. d) The interquartile range. ANSWER: d

d) The interquartile range.

Which descriptive summary measures are considered to be resistant statistics? a) The arithmetic mean and standard deviation. b) The interquartile range and range. c) The mode and variance. d) The median and interquartile range. ANSWER: d

d) The median and interquartile range.

Which of the following is NOT sensitive to extreme values? a) The range. b) The standard deviation. c) The interquartile range. d) The coefficient of variation. ANSWER: c

c) The interquartile range.

Which of the following is the easiest to compute? a) The arithmetic mean. b) The median. c) The mode. d) The geometric mean. ANSWER: c

c) The mode.

In left-skewed distributions, which of the following is the correct statement? a) The distance from Q 1 to Q 3 to Q 2 is smaller than the distance from Q 2 to Q 3. b) The distance from the smallest observation to Q 1 to the largest observation. c) The distance from the smallest observation to Q 2 is larger than the distance from Q 3 to the largest observation. d) The distance from Q 1 is less than the distance from Q 2 to Q 3 is twice the distance from the Q 1 to Q 2. ANSWER: b

b) The distance from the smallest observation to Q 1 to the largest observation.

In a perfectly symmetrical distribution a) the range equals the interquartile range. b) the interquartile range equals the arithmetic mean. c) the median equals the arithmetic mean. d) the variance equals the standard deviation. ANSWER: c

c) the median equals the arithmetic mean.

According to the empirical rule, if the data form a "bell-shaped" normal distribution, _______ percent of the observations will be contained within 2 standard deviations around the arithmetic mean. a) 68.26 b) 88.89 c) 93.75 d) 95.44 ANSWER: d

d) 95.44

In a perfectly symmetrical bell-shaped "normal" distribution a) the arithmetic mean equals the median. b) the median equals the mode. c) the arithmetic mean equals the mode. d) All the above. ANSWER: d

d) All the above. -the arithmetic mean equals the median. -the median equals the mode. -the arithmetic mean equals the mode.