A. Incorrect! This would be the negative of the range. B. Correct! The range is the maximum data value minus the minimum data value.

Transcription

1 AP Statistics - Problem Drill 05: Measures of Variation No. 1 of The range is calculated as. (A) The minimum data value minus the maximum data value. (B) The maximum data value minus the minimum data value. (C) The maximum data value plus the minimum data value. (D) The mean minus the median. (E) The maximum data value times the minimum data value. This would be the negative of the range. B. Correct! The range is the maximum data value minus the minimum data value. The range is the maximum data value minus the minimum data value. The range is the maximum data value minus the minimum data value. The range is the maximum data value minus the minimum data value. The range is the maximum data value minus the minimum data value. (B) The maximum data value minus the minimum data value.

2 No. 2 of Find the range of the data set: 54, 76, 82, 89, 91 (A) 37 (B) 78 (C) 309 (D) 91 (E) 54 A. Correct! The range is is the mean of the data set. 390 is the sum of all of the observations. 91 is the maximum of the data set. 54 is the minimum of the data set. The range is calculated as the maximum minus the minimum. Here, the maximum is 91 and the minimum is 54. Therefore, the range is = 37. (A) 37

3 No. 3 of Which of the following is not a measure of variation? (A) Range (B) Standard Deviation (C) Variance (D) Median (E) None of these are measures of variation The range is a measure of variation. The standard deviation is a measure of variation. The variance is a measure of variation. D. Correct! The median is a measure of central tendency, not a measure of variation. Only one of the answer choices is not a measure of variation. Of the answer choices, only the median is not a measure of variation. The range, standard deviation, and the variance are all measures of variation. (D) Median

4 No. 4 of Calculate the variance of the data set: 12, 95, 34, 55, 29 (A) (B) 45 (C) (D) 34 (E) 83 This is the standard deviation. This is the mean. C. Correct! The variance is This is the median. This is the range. x i 45 n We calculate the mean to be x = =. The sum of the squares of the deviations is then: (12 45) + (95 45) + (34 45) + (55 45) + (29 45) = Now, dividing by n 1 yields s = = (C)

5 No. 5 of Calculate the variance of the data set: 2, 3, 1, 2, 1 (A) (B) 1.8 (C) 2 (D) 0.7 (E) 3 This is the standard deviation. This is the mean. This is the median. D. Correct! The variance is 0.7. This is the maximum data value. x i 1.8 n We calculate the mean to be x = =. The sum of the squares of the deviations is then: (2 1.8) + (3 1.8) + (1 1.8) + (2 1.8) + (1 1.8) = 2.8. Now, dividing by n 1 yields s = = (D) 0.7

6 No. 6 of Calculate the standard deviation of the data set: 12, 95, 34, 55, 29 (A) (B) 45 (C) (D) 34 (E) 83 A. Correct! The standard deviation is This is the mean. This is the variance. This is the median. This is the range. x i 45 n We calculate the mean to be x = =. The sum of the squares of the deviations is then: (12 45) + (95 45) + (34 45) + (55 45) + (29 45) = Now, dividing by n 1 yields s = = This is the variance. We find the standard deviation by taking 4 the square root: s = = (A) 31.88

7 No. 7 of Calculate the standard deviation of the data set: 5, 5, 5, 5, 5. (A) 5 (B) 25 (C) 625 (D) 0 (E) Cannot be determined Think about what variation means. How much variation is there in this data set? Think about what variation means. How much variation is there in this data set? Think about what variation means. How much variation is there in this data set? D. Correct! The standard deviation is 0. Notice that there is no variation in this data set. Think about what variation means. How much variation is there in this data set? Although we could go through all of the calculations to verify that the standard deviation (and the variance) is zero, it is easier to note that because all of the data values are the same, there is no variation. (D) 0

8 No. 8 of Given the following calculator screenshot, determine the value of the standard deviation: (A) 225 (B) (C) (D) (E) 8 This value is actually the sum of all data elements. This value is the sum of the squares of all data elements. C. Correct! This is the correct answer! The value of the standard deviation is This is the value of the mean is This is the number of data elements. The standard deviation is denoted by Sx and equals in this case. (C) 27.75

9 No. 9 of 10 Instruction: (1) Read the problem statement and answer choices carefully (2) Work the problems on paper as 9. Given the following calculator screenshot, determine the value of the variance: (A) 1149 (B) (C) (D) (E) 5 This value is actually the sum of all data elements. B. Correct! This is the correct answer! The value of the variance is This value is the sum of the squares of all data elements. This is the value of the mean. This is the number of data elements. The standard deviation is denoted by Sx and equals in this case. Recall that the variance is the square of the standard deviation. Therefore, the variance is s 2 = ( ) 2 = (B)

10 No. 10 of Suppose that you start with a data set. If a constant is added to each value in that data set, what is the effect on the variance? (A) The variance is increased by that same constant. (B) The variance is multiplied by the square of that constant. (C) There is no effect. (D) The variance is reduced by the constant. (E) The variance is divided by the constant. Recall that the distance between data values does not change. How would this affect the variance? Recall that the distance between data values does not change. How would this affect the variance? C. Correct! This is the correct answer. There is no effect on any of the measures of variation. Recall that the distance between data values does not change. How would this affect the variance? Recall that the distance between data values does not change. How would this affect the variance? Since the distance between data values does not change by adding the same constant to each data value, there is no effect on the variance or on any of the measures of variation. (C) There is no effect.