ME-430 CH 4

A z score always indicates the number of standard deviations a data value is above the mean score.

False

The midrange is the average of the first and third quartiles.

False

For a symmetrical distribution, exactly 50 percent of the values are below the second quartile, and exactly 50 percent of the values are above the second quartile.

True

A box plot for a data set can be constructed if one knows the minimum value, the first quartile, the second quartile, the third quartile, and the maximum value of the data set.

True

A large outlying value in a data set may affect the value of the 99th percentile.

True

An outlier does not affect the value of the median in a data set.

True

An instructor recorded the following quiz scores (out of a possible 10 points) for the 12 students present. The scores were 7, 4, 4, 7, 2, 9, 10, 6, 7, 3, 8, and 5. The 25th percentile for this set of scores is: (a) 4. (b) 6. (c) 6.5. (d) 7.5.

(a)

When it is necessary to determine whether an observation from a set of data falls in the upper 25 percent or lower 75 percent of the ordered data set, which measure should be used? (a) Third quartile (b) Mean (c) First quartile (d) Seventieth percentile

(a)

The number of students entering a university cafeteria during a random selected hour was observed. Following are the numbers for 20 different randomly selected hours during a week of final examinations when the cafeteria was open for business. 141, 100, 94, 88, 79, 74, 72, 71, 55, 54, 52, 41, 35, 34, 33, 31, 29, 28, 28, 23 What is the value of the interquartile range for this set of values? (a) 53.00 (b) 31.50 (c) 77.75 (d) 46.25

(d)

An instructor recorded the following quiz scores (out of a possible 10 points) for the 12 students present. The scores were 7, 4, 4, 7, 2, 9, 10, 6, 7, 3, 8, and 5. The sixth decile for this set of scores is: (a) 9. (b) 7.5. (c) 6.5. (d) 7.

(d)

Examine the following data set: 12, 32, 45, 14, 24, 31 The value of the interquartile range is: (a) 14. (b) 32. (c) 27.5. (d) 18.

(d)

For the data set 8, 12, 15, 20, 11, 5, 21, 0, what is the value of the seventh decile? (a) 6.5 (b) 11.5 (c) 17.5 (d) 15

(d)

Given that a sample is approximately bell-shaped with a mean of 60 and a standard deviation of 3, the approximate value for the 16th percentile for this distribution is: (a) 54. (b) 66. (c) 63. (d) 57.

(d)

If a sample has a mean of 100 and a standard deviation of 6, what is the value in the data set that corresponds to a z score of 2? (a) 88 (b) 94 (c) 92 (d) 112

(d)

The 75th percentile of a data set is equivalent to (a) the seventh decile of the data set. (b) the first quartile of the data set. (c) the second quartile of the data set. (d) the third quartile of the data set.

(d)

The number of deciles in a data set is (a) 10. (b) 12. (c) 99. (d) 9.

(d)

If the 75th percentile for scores on a 100-point exam is 75, and the percentile position number c had to be rounded up to a whole number, then a student's score that ranks at the 75th percentile is equal to 75.

True

A cyclist recorded the number of miles perday she cycled for five days. The recordings were as follows: 13, 10, 12 ,10, 11. The 50th percentile for the number of miles she cycled per day is: (a) 12.5. (b) 11. (c) 10. (d) 11.5.

(b)

A student has seven statistics books open in front of him. The page numbers are as follows: 231, 423, 521, 139, 347, 400, 345. The second quartile for this set of numbers is: (a) 231. (b) 347. (c) 330. (d) 423.

(b)

Examine the following frequency distribution: Value: Frequency: 20 2 29 4 30 4 39 3 44 2 The second quartile of the distribution is (a) 29. (b) 30. (c) 39. (d) 29.5.

(b)

Examine the following frequency distribution: Value: Frequency: 20 2 29 4 30 4 39 3 44 2 The 77th percentile of the distribution is: (a) 29. (b) 30. (c) 39. (d) 32.

(c)

If the right whisker is significantly longer than the left whisker on a box plot, then the distribution is skewed to the right.

True

In a box plot, if the median is close to the center of the box, the distribution of the data values will be approximately symmetrical.

True

In a box plot, if the median is to the right of the center of the box, the distribution of the data values will be positively skewed.

False

In finding percentiles, it is not necessary to first order the data values.

False

On a statistics exam, Joe's score was at the 30th percentile, and John's score was at the 60th percentile; thus we can say that John's score was twice that of Joe's score.

False

The 50th percentile of a data set corresponds to the mean value of the data set.

False

The third decile corresponds to the 70th percentile.

False

There are 10 deciles in a data set.

False

There are 100 percentiles in a data set.

False

There are four quartiles in any data set.

False

z scores can be obtained only for sample values.

False

The 50th percentile is the same as the median.

True

The 9th decile is the same as the 90th percentile.

True

If a student's exam score corresponds to a negative z score, then the student has a score that is less than the mean of the set of exam scores.

True

In a box plot, if the median is to the left of the center of the box, then the distribution of the data values will be (a) positively skewed. (b) negatively skewed. (c) symmetrical. (d) bell-shaped.

(a)

In a box plot, if the right whisker is longer than the left whisker, the distribution of the data values will be (a) positively skewed. (b) negatively skewed. (c) symmetrical. (d) uniform.

(a)

The number of students entering a university cafeteria during a random selected hour was observed. Following are the numbers for 20 different randomly selected hours during a week of final examinations when the cafeteria was open for business. 141, 100, 94, 88, 79, 74, 72, 71, 55, 54, 52, 41, 35, 34, 33, 31, 29, 28, 28, 23 What is the value of the second quartile for this set of values? (a) 53.00 (b) 31.50 (c) 77.75 (d) 46.25

(a)

For the data set 38, 42, 45, 50, 41, 35, 51, 29, the value corresponding to the lower hinge (left vertical side) in the horizontal box plot would be equal to: (a) 43.5. (b) 36.5. (c) 41.5. (d) 47.5.

(b)

Given that a sample is approximately bell-shaped with a mean of 50 and a standard deviation of 5, the value for the 84th percentile for this distribution is (a) 45. (b) 55. (c) 60. (d) 65.

(b)

Given that a sample is approximately bell-shaped with a mean of 60 and a standard deviation of 3, the approximate value for the 98th percentile for this distribution is: (a) 63. (b) 66. (c) 69. (d) 57.

(b)

If the number of values in any data set is even, then (a) the second quartile cannot be found. (b) the second quartile will be the average of two numbers. (c) the interquartile range will be half the length between the minimum value and the median. (d) the second quartile will be twice the first quartile.

(b)

In the 2004 Athens Summer Olympic Games, the following were the top 20 total number of gold medals earned by the different countries: 35, 32, 27, 17, 14, 16, 11, 10, 9, 9, 9, 9, 8, 8, 6, 5, 4, 3, 3, 3 What is the percentile ranking for the value of 10? (a) 20.0 (b) 62.5 (c) 30.0 (d) 35.0

(b)

The following information for a data set is given: minimum value = 130, Q_1 = 140, Q_2 = 145, Q_3 = 160, and maximum value = 195. From this information, the distribution is (a) symmetrical. (b) positively skewed. (c) negatively skewed. (d) bell-shaped.

(b)

The following values are the ages of 15 students in a statistics class: 18, 21, 25, 21, 28, 23, 21, 19, 24, 26, 21, 24, 18, 27, 23 The percentile rank of 25 would be: (a) 20th. (b) approximately 77th. (c) 80th. (d) 75th.

(b)

The number of students entering a university cafeteria during a random selected hour was observed. Following are the numbers for 20 different randomly selected hours during a week of final examinations when the cafeteria was open for business. 141, 100, 94, 88, 79, 74, 72, 71, 55, 54, 52, 41, 35, 34, 33, 31, 29, 28, 28, 23 What is the value of the first quartile for this set of values? (a) 118.0 (b) 31.50 (c) 77.75 (d) 46.25

(b)

The numbers 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 first quartile for this data set is (a) 402. (b) 306. (c) 500. (d) 403.5.

(b)

For a bell-shaped distribution, the most frequently occurring value in a data set will be the (a) third quartile. (b) interquartile range. (c) second quartile. (d) first quartile.

(c)

Given that the the z score for a given value in a data set is zero, then this value must be (a) above the mean. (b) below the mean. (c) same as the mean. (d) equal to zero.

(c)

The 50th percentile is the same as the (a) mode. (b) mean. (c) median. (d) midrange.

(c)

The following information for a data set is given: minimum value = 105, Q_1 = 140, Q_2 = 155, Q_3 = 160, and a maximum value = 165. From this information, the distribution is (a) symmetrical. (b) positively skewed. (c) negatively skewed. (d) bell-shaped.

(c)

The following values are the ages of 15 students in a statistics class: 18, 21, 25, 21, 28, 23, 21, 19, 24, 26, 21, 24, 18, 27, 23. The value of the first quartile for this set of data is: (a) 25. (b) 23. (c) 21. (d) 22.5.

(c)

The interquartile range is the difference between (a) the second quartile and the first quartile. (b) the third quartile and the second quartile. (c) the third quartile and the first quartile. (d) the maximum value and the minimum value.

(c)

The number of students entering a university cafeteria during a random selected hour was observed. Following are the numbers for 20 different randomly selected hours during a week of final examinations when the cafeteria was open for business. 141, 100, 94, 88, 79, 74, 72, 71, 55, 54, 52, 41, 35, 34, 33, 31, 29, 28, 28, 23 What is the value of the third quartile for this set of values? (a) 53.00 (b) 31.50 (c) 76.5 (d) 46.25

(c)

A data value is considered to be an outlier if (a) it lies between -1.5 X IQR and +1.5 X IQR. (b) it lies between Q_1 - 1.5 X IQR and Q_3 + 1.5 X IQR. (c) it lies between Q_1 and Q_3. (d) if it is smaller than Q_1 - 1.5 X IQR or larger than Q_3 + 1.5 X IQR.

(d)

A final statistics exam had a mean of 70 and a variance of 25. If Bruce made an 80 on his exam, what is his z score? (a) -2 (b) 10 (c) 0.4 (d) 2

(d)

The numbers 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 interquartile range for this data set is (a) 306. (b) 402. (c) 500.5. (d) 194.5.

(d)

The vertical sides on a horizontal box plot are located at (a) the minimum value and first quartile of the data set. (b) the minimum value and the maximum value of the data set. (c) the third quartile and the maximum value of the data set. (d) the first quartile and the third quartile of the data set.

(d)

Which of the following is a measure of position? (a) Standard deviation (b) Box plots (c) Mode (d) Quartile

(d)

Which of the following is not a measure of position? (a) First quartile (b) Median (c) Fourth decile (d) Mean

(d)

Which of the following may be affected the most if there is an extremely large value in a data set? (a) The first quartile (b) The second quartile (c) The third quartile (d) The 99th percentile

(d)

At most 50 percent of a set of data values lie between the first and third quartiles of the data set.

True

At the most 50 percent of an ordered set of data values lie below the first quartile and above the third quartile.

True

The following is given: minimum value = 20, Q_1 = 25, Q_2 = 30, Q_3 = 35, and maximum value = 40. From this information we can conclude that the distribution of values from which this information was obtained is symmetrical.

True

The z score associated with a data value represents the number of standard deviations that the value lies above or below the mean of the data set.

True