Statistics Questions and Answers

Problem 1: Finding the Median Volume

1)The volume of gasoline dispensed at a commercial gas station for a nominal 10 L volume was measured on five separate trials to be 9.89 L, 10.02 L, 10.3 L, 9.48 L, and 9.91 L. What is the median volume?

2) The volume of gasoline dispensed at a commercial gas station for a nominal 10 L volume was measured on five separate trials to be 9.89 L, 10.02 L, 10.3 L, 9.48 L, and 9.91 L. Based on the median and mean, do you think the distribution of prices is skewed? Explain.

a

Since the mean and median are equal, the distribution is not skewed.

b

Since the mean is higher than the median, the distribution is slightly skewed to the right.

c

Since the median is higher than the mean, the distribution is slightly skewed to the left.

d

More information is needed to determine skewness.

e

None of the above

3) The masses of 8 nominally identical items were determined to be 4.23 g, 4.37 g, 3.98 g, 4.75 g, 4.12 g, 4.45 g, 4.71 g, and 3.35 g. What is the mean weight? (Round answer to three decimal places)

4) The masses of 8 nominally identical items were determined to be 4.23 g, 4.37 g, 3.98 g, 4.75 g, 4.12 g, 4.45 g, 4.71 g, and 3.35 g. What is the variance of these items? (Round to 3 decimal places)

5) The masses of 8 nominally identical items were determined to be 4.23 g, 4.37 g, 3.98 g, 4.75 g, 4.12 g, 4.45 g, 4.71 g, and 3.35 g. What is the standard deviation? (Round your answer to three decimal places)

6) The masses of 8 nominally identical items were determined to be 4.23 g, 4.37 g, 3.98 g, 4.75 g, 4.12 g, 4.45 g, 4.71 g, and 3.35 g. Calculate the range

7) The masses of 8 nominally identical items were determined to be 4.23 g, 4.37 g, 3.98 g, 4.75 g, 4.12 g, 4.45 g, 4.71 g, and 3.35 g. The range is approximately how many standard deviations? (Round your answer to two decimal places

8) The five-number summary for all student scores on an exam is 29, 42, 70, 75, 79. Suppose 200 students took the test. How many students had scores between 42 and 70?

9) Consider the following data set: 7, 7, 0, 3, 7, 7, 3, 5, 7, 5, 2, 1
What is the interquartile range (IQR)?

10) Consider the following data set: 7, 7, 0, 3, 7, 7, 3, 5, 7, 5, 2, 1
What is the z-score for the smallest observation? (Round your answer to two decimal places

11) Consider the following data set: 7, 7, 0, 3, 7, 7, 3, 5, 7, 5, 2, 1
What is the z-score for the largest observation? (Round your answer to two decimal places)

12) Consider the following data set: 7, 7, 0, 3, 7, 7, 3, 5, 7, 5, 2, 1
Considering the z-score, are the smallest and largest observation unusually small or large?

a

Since neither z-score exceeds 2 in absolute value, none of the observations are unusually small or large.

b

Since the z-score for the smaller observation is larger than 2 in absolute value, the smaller value is unusually small.

c

Since the z-score for the larger observation is larger than 2 in absolute value, the larger value is unusually large.

d

Since both z-scores exceed 2 in absolute value, both of the observations are unusual.