QUIZ 6
The numbers of words defined on randomly selected pages from a dictionary are shown below. Find the mean, median, and mode of the listed numbers. 57 49 43 47 32 31 30 40 67 39
-What is the mean? Select the correct choice below and, if necessary, fill in the answer box within your choice. A. The mean is 43.543.5. (Round to one decimal place as needed.) -What is the median? Select the correct choice below and, if necessary, fill in the answer box within your choice. A. The median is 41.541.5. (Round to one decimal place as needed.) -What is(are) the mode(s)? Select the correct choice below and, if necessary, fill in the answer box within your choice. B. There is no mode.
Define and distinguish among mean, median, and mode.
-The mean is the sum of all the values divided by the number of values. It can be strongly affected by outliers. -The median is the middle value in a data set. It is not affected by outliers. -The mode is the most common value in a data set. It is not affected by outliers.
After recording the pizza delivery times for two different pizza shops, you conclude that one pizza shop has a mean delivery time of 44 minutes with a standard deviation of 4 minutes. The other shop has a mean delivery time of 43 minutes with a standard deviation of 22 minutes. Interpret these figures. If you liked the pizzas from both shops equally well, which one would you order from? Why?
-The means are nearly equal, but the variation is significantly greater for the second shop than for the first. -Choose the first shop. The delivery time is more reliable because it has a lower standard deviation.
Briefly describe the use of the range rule of thumb for interpreting the standard deviation. What are its limitations?
-The standard deviation is approximately the range divided by four. The range rule of thumb does not work well when the highest or lowest value is an outlier.
Consider the distribution of exam scores (graded from 0 to 100) for 86 students when 38 students got an A, 28 students got a B, and 20 students got a C. Complete parts (a) through (d) below.
-There would probably be one peak because there are no obvious reasons why the exam scores would form different groups. -A Smallest line -The distribution would probably be left-skewed because many of the students got an A, and very few got a C. -The variation would probably be large because many students got an A, some got a B, and a small number got a C, and so the data are not clustered.
Describe the process of calculating a standard deviation. Give a simple example of its calculation (such as calculating the standard deviation of the numbers 2, 3, 4, 4, and 6). What is the standard deviation if all of the sample values are the same?
-subtracting the mean from -squares -add -total number of data values minus 1. -square root -1.483 -0
What is a normal distribution? Briefly describe the conditions that make a normal distribution.
A normal distribution is a symmetric, bell-shaped distribution with a single peak. Its peak corresponds to the mean, median, and mode of the distribution. Its variation is characterized by the standard deviation of the distribution.
Exam results for 100 students are given below. For the given exam grades, briefly describe the shape and variation of the distribution. median=68, mean=70, low score=65, high score=
Right skewed low
The number of times that people change jobs during their careers.
The median because it is unaffected by outliers.
I examined the data carefully, and the range was greater than the standard deviation.
The statement makes sense because the range is approximately four times the standard deviation.
An acquaintance tells you that his IQ is in the 102nd percentile. What can you conclude from this information?
You can conclude that he doesn't understand percentiles because it is impossible to be in the 102nd percentile.
Consider the following set of three distributions, all of which are drawn to the same scale. Identify the two distributions that are normal. Of the two normal distributions, which one has the larger variation?
a and b b -b has the smallest curve c's curve starts quickly
The highest exam score was in the upper quartile of the distribution.
The statement makes sense because the highest score will be in the highest quartile.
Exam results for 100 students are given below. For the given exam grades, briefly describe the shape and variation of the distribution. median=79, mean=73, low score=6, high score=81
left-skewed high
Suppose a car driven under specific conditions gets a mean gas mileage of 40 miles per gallon with a standard deviation of 3 miles per gallon. On about what percentage of the trips will your gas mileage be above 43 miles per gallon?
About 16%, because 43 miles per gallon is 1 std. deviation above the mean. By the 68-95-99.7 rule, about 68% of the distribution lies within 1 std. deviation of the mean. So 32% lies outside of this range, 16% in each tail.
State, with an explanation, whether you would expect the following data sets to be normally distributed. The last digit of the Social Security number of 1000 randomly selected people.
The data set is not expected to be normally distributed. Of the people randomly selected, there could be more digits greater than 5 or more less than 5, which would skew the distribution.
Find the mean and median for the waiting times at Best Bank given below. Show your work clearly, and verify that both are the same. The following values are measured in minutes. Best Bank (one line): 6.6 6.7 6.7 6.9 7.1 7.2 7.3 7.4 7.7 7.8 7.8
The median is the 6th value in the sorted data set. -7.2 -equal to
Scores on the quantitative section of a certain graduate school entrance exam are normally distributed with a mean of 146 and a standard deviation of 9.1. Scores for a certain group of students range between 132 and 173. What are the percentiles of these scores?
The percentile of the score 132 is 6.206.20%. Part 2 The percentile of the score 173 is 99.8599.85%.
Scores on the quantitative section of a certain graduate school entrance exam are normally distributed with a mean of 155 and a standard deviation of 9.2. Scores for a certain group of students range between 139 and 178. What are the percentiles of these scores?
The percentile of the score 139 is 4.10%. Part 2 The percentile of the score 178 is 99.38%
What is the 68-95-99.7 rule for normal distributions? Explain how it can be used to answer questions about frequencies of data values in a normal distribution.
The rule states that about 68%, 95%, and 99.7% of the data points in a normal distribution lie within 1, 2, and 3 standard deviations of the mean, respectively.
For the 30 students who took the test, the high score was 80, the median was 75, and the low score was 40.
The statement makes sense because it is possible that when sorting the 30 scores from low to high, the first value was 40, the highest value was 80, and 75 was halfway between the 15th and the 16th score.
In a normal distribution, where do about 2/3 of the data values fall?
They fall within 1 standard deviation of the mean. This is because by the 68-95-99.7 rule, approximately 68% or two-thirds of all data points in a normal distribution fall within 1 standard deviation of the mean.
Suppose you read that the average height of a class of 36 eighth-graders is 49 inches with a standard deviation of 39 inches. Is this likely? Explain.
This is not likely because a mean of 49 and a standard deviation of 39 would imply that about 5% of the heights differ from the mean by more than 78, which is impossible
My professor graded the final score on a curve, and she gave a grade of A to anyone who had a standard score of 2 or more.
This makes sense because a standard score of 2 or more corresponds to roughly the 97th percentile. Though this curve is stingy on giving out A's to students, it is still giving the top students the highest grade.
Decide whether the following statement makes sense or does not make sense. Explain your reasoning. Jack is in the 50th percentile for height, so he is of median height.
This makes sense. The 50th percentile height means that 50% of all the heights in the data set are less than or equal to Jack's height. The median is the middle value, which means it splits the distribution in half. These two statements are the same.
Consider the following set of three distributions, all of which are drawn to the same scale. Identify the two distributions that are normal. Of the two normal distributions, which one has the larger variation?
a and c c
Assume that a set of test scores is normally distributed with a mean of 80 and a standard deviation of 5. Use the 68-95-99.7 rule to find the following quantities.
a. The percentage of scores less than 80 is 50.0%. Part 2 b. The percentage of scores greater than 85 is 16.0%. Part 3 c. The percentage of scores between 70 and 85 is 81.5%.