ME430 Test 1 Ch3

(T/F) A data set with more than one mode is said to be bimodal.

False

(T/F) For a negatively skewed distribution, the longer tail is to the right of the mean for the distribution.

False

(T/F) For a negatively skewed distribution, the mean is greater than the median.

False

(T/F) The mean is not necessarily equal to the median in a symmetrical distribution

False

(T/F) The mean of a set of data always divides the data set in such a way that 50 percent of the values lie above the mean and 50 percent lie below the mean.

False

(T/F) The median of a set of data values is that the value that occurs with the highest frequency.

False

(T/F) The mode is a measure of variablitiy

False

The skewness of any symmetrical distribution will always be a) positive b) negative c) equal to zero d) approximately zero

c) equal to zero

Which of the following is not a measure of dispersion? a) interquartile range b) range c) median d) coefficient of variation

c) median

(T/F) For a positively skewed distribution, the mode is less than the median and the median is less than the mean for the distribution.

True

(T/F) If the number of ovservations in a data set is even, the median cannot be found accurately.

True

(T/F) Of the mean, the median, and the mode of any numerical data set, the mean is the most influenced by an outlying value in the data set.

True

(T/F) The mean of a numerical data set could divide the data set such that at most 50 percent of the values lie above the mean and at most 50 percent lie below the mean.

True

(T/F) The sum of the deviations from the mean for any numerical data set is always zero.

True

32 32 23 25 33 34 25 30 31 38 32 35 39 42 40 The coefficient of skewness using person's estimate is a) +0.3929 b) -0.3929 c) +0.1310 d) -0.1310

a) +0.3929

Example of the following data set: 12 32 45 14 24 31 The total deviation from the mean for the data values is a) 0 b) 26.3333 c) 29.5 d) 12

a) 0

The number of minutes spent in the computer lab by 20 students working on a project are given below: Number of minutes 30| 0 2 5 5 6 6 6 8 40| 0 2 2 5 7 9 50| 0 1 3 5 60| 1 3 The standard deviation for this data set is a) 101.6 b) 403.8 c) 306.0 d) 500.5

a) 101.6

12 15 8 9 14 8 17 14 8 15 The absolute deviation for the number of hours spent studying in this sample is a) 3.0 b) 1.41 c) 1.33 d) 2.5

a) 3.0

For the give sample data set 8, 12, 15, 20, 11, 5, 21, 0, what is the value of the coefficient of variation? a) 62.52 percent b) 11.5 percent c) 7.19 percent d) 159.9 percent

a) 62.52 percent

Which of the following is a measure of variation? a) standard deviation b) midrange c) mode d) median

a) standard deviation

The empirical rule usually can be applied to a) any distribution b) only discrete distribution c) only continuous distribution d) any bell shaped distribution

d) any bell shaped distribution

15.60 1.20 0.40 0.15 0.10 1.50 3.20 3.50 6.36 8.90 12.59 3.35 0.09 10.15 13.99 7.00 17.25 14.55 9.00 16.00 The coefficient of skewness using Pearson's estimate is a) -0.2780 b) +0.2780 c) -0.0927 d) +0.0927

b) +0.2780

The price increases on $7, $1, $8, $4, and $5. The standard deviation for these price increases is a) 2.3 b) 2.7 c) 3.2 d) 4.1

b) 2.7

The following are given for a set of values: I. The values range from 40 to 95 II. The median value is 79 III. Twenty-five percent of the values are less than or equal to a value of 62 IV. seventy-five percent of the values are less than or equal to 90 What is the interquartile range? a) 55 b) 28 c) 50 d) 33

b) 28

The number of minutes spent in the computer lab by 20 students working on a project are given below: Number of minutes 30| 0 2 5 5 6 6 6 8 40| 0 2 2 5 7 9 50| 0 1 3 5 60| 1 3 The range for this data set is a) 300 b) 303 c) 603 d) 600

b) 303

Given that a sample is approximately bell shaped with a mean of 60 and a standard deviation of 3, the approximate percentage of data values that is expected to fall between 54 and 66 is a)75 percent b) 95 percent c) 68 percent d) 99.7 percent

b) 95 percent

Which of the following is not a property of the standard deviation? a) it is affected by extreme values in a data set. b) it is the most widely used measure of spread c) it uses all the values in the data set in its computation d) it is always a positive number

b) it is the most widely used measure of spread

Which is the most common type of distribution observed? a) Negatively skewed distributions b) positively skewed distributions c) symmetrical distributions d) all of the above have an equal chance of being observed

b) positively skewed distributions

Which of the following is not affected by and extreme value in a data set? a) the mean absolute deviation b) the median c) the range d) the standard deciation

b) the median

The mean number of days it rained in january for a 10 year period on a college campus was 9 with with a standard deviation of 3. The average amount of rainfall during the same 10 year period on the same campus was 8 inches with a standard deviation of 3 inches which variable has the higher relative variation? a) neither b) number of days it rained c) the amount of rainfall d) number of days it rained but not the amount of rainfall

c) the amount of rainfall

The standard deviation always will be larger than the absolute mean deviation because a) the absolute values are not computed for the standard deviation b) the standard deviation is the square root of the variance c) the larger values in the data set receive stronger emphasis when squared d) none of the above

c) the larger values in the data set receive stronger emphasis when squared

A statement is made that the average distance from the mean in a set of data values is 10. which measure is being used here? a) the range b) the interquartile range c) the mean absolute distribution d) the standard deviation

c) the mean absolute distribution

The interquartile range in an ordered data set is the difference between a) the median for the entire data set and the median for the lower 50 percent of the data set b) the median for the upper 50 percent of the data set and the median for the entire data set c) the median for the upper 50 percent and the median for the lower 50 percent of the data set d) the maximum value and the minimum value

c) the median for the upper 50 percent and the median for the lower 50 percent of the data set

Which of the following is not a measure of central tendancy? a) mean b) median c) the third quartile Q3 d) mode

c) the third quartile Q3

For which of the following is the coefficient of variation the smallest? a) x_bar = 10 and s = 2 b) x_bar = 14 and s = 3 c) x_bar = 30 and s = 5 d) x_bar = 39 and s = 8

c) x_bar = 30 and s = 5

Given the following sample values, what is the sample variance? 15 20 40 25 35 a) 9.27 b) 86.0 c) 10.37 d) 107.5

d) 107.5

18 21 25 21 28 23 21 19 24 26 21 24 18 27 23 The standard deviation for this data set is a) 9 b) 9.6857 c) 21 d) 3.1122

d) 3.1122

7 4 4 7 2 9 10 6 7 3 8 5 The inter quartile range for this set is a) 7.5 b) 6.5 c) 8 d) 3.5

d) 3.5

values frequency 20 2 29 4 30 4 39 3 44 2 The variance of the distribution is a)32.07 b) 30 c) 7.44 d) 55.35

d) 55.35

Given a sample is approximately bell shaped with a mean of 25 and a standard deviation of 2, the approximate percentage of data values that is expected to fall between 19 and 31 is a) 75 percent b) 95 percent c) 68 percent d) 99.7 percent

d) 99.7 percent

Which of the following statements is correct? a) two sets of numbers with completely different means and standard deviations may have the same coefficient of variation b) the most frequently used measure of variation is the standard deviation c) the range is a crude measure of dispersion because it only involves the smallest and the largest values in a data set d) all of the above statements are correct

d) all of the above statements are correct

If a distribution has zero variance, which of the following is true? a) all of the values are positive b) all of the values are negative c) the number of positive values and the number of negative values are equal d) all the values are equal to each other

d) all the values are equal to each other

A sample of 10 students was asked by the instructor to record the number of hours each spend studying for a given exam from the time the exam was announced in class. The following data values were the recorded number of hours: 12 15 8 9 14 8 17 14 8 15 The variance for the number of hours spent studying for this sample is a) 10.000 b) 9.0000 c) 3.4641 d) aproximately 12

d) aproximately 12

If we would like to compare to the relative variation among three variables, the most appropriate statistics to use would be the a) variances of the three variables b) range of the three variables c) interquartile range of the three variables d) coefficient of variation of the three variables

d) coefficient of variation of the three variables

In order to compute the Pearson's measurement of skewness of any distribution, we can compute it by knowing a) only the mean and standard deviation b) only the median and standard deviation c) only the mean and the median d) only the mean, median and standard deviation

d) only the mean, median and standard deviation

A single numerical value to describe a characteristic of a sample data set , such as the sample median, is referred to as a a) sample parameter b) sample median c) population parameter d) sample statistic

d) sample statistic

Which of the following is the crudest measure of dispersion? a) the mean avsolute deviation b) the variance c) the mode d) the range

d) the range