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MATH225 Week 3 assignment: Central Tendency
(Q & A)
Given the following box-and-whisker plot, decide if the data is skewed or symmetrical. Select the correct answer below: The data are skewed to the left. The data are skewed to the right. The data are symmetric. Which of the following frequency tables show a skewed data set? Select all answers that apply. Select all that apply: Select all that apply: Value Frequency 5 2 6 5 7 9 8 15 9 18 10 24 11 19 12 15 13 10 14 4 Value Frequency 13 2 14 5 15 14
16 13 17 23 18 26 19 15 20 2 Value Frequency 5 1 6 1 7 9 8 20 9 24 10 20 11 9 12 4 13 1 14 1 15 1 Value Frequency 0 4 1 12 2 23 3 28 4 17 5 7 6 6 7 3 Which of the following frequency tables show a skewed data set? Select all answers that apply. Select all that apply: Value Frequency 0 2 1 11 2 30
13 11 14 0 15 1 16 0 17 1 Which of the following frequency tables shows a skewed data set? Select all answers that apply. Select all that apply: Value Frequency 7 4 8 8 9 12 10 16 11 15 12 13 13 10 14 5 Value Frequency 5 3 6 3 7 8 8 12 9 15 10 19 11 19 12 10 13 4 14 3 15 3 16 1 Value Frequency 12 1 13 2 14 3
15 13 16 10 17 26 18 25 19 15 20 5 Value Frequency 0 9 1 21 2 23 3 18 4 15 5 9 6 3 7 2 For the following dataset, you are interested to determine the "spread" of the data. Would you employ calculations for the sample standard deviation, or population standard deviation for this dataset: Ages of all students in a Statistics course with an enrollment of 30 students. Select the correct answer below: Use calculations for sample standard deviation Use calculations for population standard deviation Which of the following lists of data has the smallest standard deviation? Select the correct answer below: 11 , 17 , 9 , 4 , 4 , 6 , 6 , 9 , 8 , 18 29 , 21 , 21 , 28 , 28 , 26 , 24 , 24 , 17 , 23 6 , 8 , 10 , 6 , 8 , 8 , 10 , 7 , 10 , 10 23 , 19 , 12 , 19 , 17 , 18 , 16 , 10 , 12 , 21 17 , 12 , 6 , 6 , 15 , 16 , 20 , 20 , 5 , 17
Provide your answer below: 6. The following data values represent the daily amount spent by a family during a 7 day summer vacation. Find the sample standard deviation of this dataset: $96, $125, $80, $110, $75, $100, $ Round the final answer to one decimal place.
Answer 19.
Which of the following lists of data has the smallest standard deviation? Select the correct answer below: 30 , 21 , 19 , 17 , 16 , 32 , 26 , 25 , 19 , 16 5 , 11 , 15 , 7 , 5 , 9 , 8 , 16 , 14 , 11 25 , 24 , 28 , 18 , 32 , 34 , 34 , 22 , 28 , 19 17 , 19 , 17 , 18 , 17 , 16 , 16 , 16 , 17 , 20 9 , 16 , 14 , 22 , 20 , 9 , 19 , 16 , 21 , 8 Which of the following lists of data has the smallest standard deviation? Select the correct answer below: 13 , 12 , 12 , 13 , 11 , 12 , 12 , 14 , 13 , 11 25 , 26 , 23 , 17 , 21 , 28 , 28 , 23 , 25 , 16 5 , 21 , 13 , 12 , 19 , 10 , 16 , 19 , 8 , 7 17 , 16 , 9 , 10 , 14 , 6 , 8 , 16 , 16 , 2 33 , 33 , 30 , 32 , 31 , 24 , 28 , 23 , 24 , 23 Find the median of the following set of miles per gallon for randomly selected sports cars. 36,22,24,30,44,13,21,34, Provide your answer below: 24 (arrange smallest to largest and find middle) Find the mode of the following number of times each machine in a car factory needed to be fixed within the last year. 2,5,6,12,14,12,6,2,5,3,14,
Provide your answer below: 5 (# that occurs most often in the set) Laura runs at the park after school and wants to know the mean number of miles she runs. The numbers for the miles run each day so far are listed below. 8,9,7,13,3,9, Find the mean number of miles she runs daily. Provide your answer below: 9 (average of all numbers) An art collector bought 20 paintings at an art fair, and wants to know the average price of her new paintings. She adds the prices of all the paintings and divides this number by 20 to find an average price of $350. Is this price a sample mean or a population mean, and which symbol would be used to denote it? Select the correct answer below: Population Mean μ Sample Mean x¯¯¯ Given the following list of the number of pens randomly selected students purchased in the last semester, find the median. 13,7,8,37,32,19,17,32,12, Provide your answer below: 18 (because the list has length 10 , which is even, we know the median number will be the average of the middle two numbers, 17 and 19. So the median number of pens randomly selected students purchased in the last semester is 18 .) Find the mode of the following amounts of exercise (in hours) randomly selected runners completed during a weekend. 2,14,14,4,2,4,1,14,4,4, Provide your answer below: 4 (Note that 4 occurs 4 times, which is the greatest frequency) Find the mode of the following list of points earned on a 16 point quiz given during a finance class. 7,7,3,2,7,16,12,16, Provide your answer below: 7 Find the median of the following set of data. 35,43,18,35,29,27,19,
11 1 12 2 13 12 14 6 15 7 16 2 17 0 18 0 19 0 20 0 21 0 22 0 23 1 Select the correct answer below: 11 14 12 13 23 (Note that most of the values are between 11 and 16 , whereas 23 is far above the rest of the values. Therefore, 23 is the potential outlier.) Given the following frequency table of data, what is the potential outlier? Value Frequency 15 1 16 0 17 3 18 4 19 6 20 10 21 3 22 2 23 1 24 0 25 0 26 0 27 0 28 0 29 0
Select the correct answer below: 30 18 23 19 17
A data set lists the number of extra credit points awarded on midterm scores of 15 students taking a statistics
course. For this data set, the minimum is 3 , the median is 15 , the third quartile is 16 , the interquartile range is 4 ,
and the maximum is 19. Construct a box-and-whisker plot that shows the extra credit points awarded.
Provide your answer below: Remember that the interquartile range is the third quartile minus the first quartile. Since we know the
third quartile is 16 , and the interquartile range is 4 , we find that the first quartile must be 16 − 4 = 12.
Find the Five-Number Summary of a Data Set
Question
Given the following list of data, what is the five-number summary?
Select the correct answer below: Min Q1^ Median^ Q3^ Max 10 12 15 18 19 Min Q1^ Median^ Q3^ Max 10 13 15 17 19 Min Q1^ Median^ Q3^ Max 10 15 17 18 19 Min Q1^ Median^ Q3^ Max 10 14 16 17 19 Min Q1^ Median^ Q3^ Max 10 14 15 18 19 The following frequency table summarizes a set of data. What is the five-number summary? "Value " " Frequency "
Min Q1 Median Q3 Max 8 10 11 12 16 Min Q1 Median Q3 Max 8 10 11 13 16 Min Q1 Median Q3 Max 8 10 11 15 16 The following frequency table summarizes a set of data. What is the five-number summary? "Value " " Frequency " "5 " " 3 " "6 " " 5 " "7 " " 2 " "8 " " 2 " "9 " " 3 " "12 " " 1 " "14 " " 3 " Min Q1 Median Q3 Max 5 6 7 9 14 Min Q1 Median Q3 Max 5 8 11 12 14 Min Q1 Median Q3 Max 5 7 9 10 14 Min Q1 Median Q3 Max 5 8 9 11 14 Given the following frequency table of data, what is the potential outlier? Value Frequency 7 1 8 0 9 0 10 0 11 0 12 0 13 0 14 2
15 7 16 4 17 5 18 6 19 5 20 1 7 (7 is the correct answer) 14 15 16 19 The five number summary for a set of data is given below. Min Q1 Median Q3 Max 68 70 74 80 88 What is the interquartile range of the set of data? Enter just the number as your answer. For example, if you found that the interquartile range was 25 , you would enter 25. Provide your answer below: 10 (Remember that the interquartile range is the third quartile minus the first quartile. So we find that the interquartile range is 80−70=10) The five number summary for a set of data is given below. Min Q1 Median Q3 Max 76 84 89 98 99 Using the interquartile range, which of the following are outliers? Select all correct answers. Select all that apply: 6 42 97
The five number summary for a set of data is given below. Min Q1 Median Q3 Max 54 56 80 86 87 Using the interquartile range, which of the following are outliers? Select all correct answers. 1 43 86 92 108 Remember that outliers are numbers that are less than 1.5 IQR⋅ below the first quartile or more than 1.5 IQR⋅ above the third quartile, where IQR stands for the interquartile range. The interquartile range is the third quartile minus the first quartile. So we find IQR=86−56= So a value is an outlier if it is less than Q1−1.5 IQR=56−(1.5)(30)=11⋅ or greater than Q3+1.5 IQR=86+(1.5)(30)=131⋅ So we see that 1 is an outlier. A data set lists the number of hours each student, from a finance class, studied for a midterm. For this data set, the minimum is 3 , the median is 6 , the third quartile is 9 , the interquartile range is 5 , and the maximum is 17. Construct a box-and-whisker plot that shows the number of hours studied. Begin by first placing the middle dot on the median. Then work on placing the rest of the points starting with the ones closest to the median. Remember that the interquartile range is the third quartile minus the first quartile. Since we know the third quartile is 9 , and the interquartile range is 5 , we find that the first quartile must be 9 − 5 = 4. A data set lists the number of hours waiters worked at a restaurant every Friday during the last year. For this data set, the minimum is 1 , the median is 5 , the third quartile is 8 , the interquartile range is 4 , and the maximum is 17. Construct a box-and-whisker plot that shows the number of hours worked on a Friday.
Provide your answer below: Remember that the interquartile range is the third quartile minus the first quartile. Since we know the third quartile is 8 , and the interquartile range is 4 , we find that the first quartile must be 8−4=4. To construct the box-and-whisker plot, remember that the minimum value of the data (1) is at the end of the left whisker, the first quartile (4) is the left edge of the box, the median value (5) is the vertical line in the box, the third quartile (8) is the right edge of the box, and the maximum value (17) is the end of the right whisker. The following dataset represents the favorite color reported by young children at a birthday party: Blue, Green, Red, Blue, Blue, Yellow, Pink, Yellow, Red, Red, Blue, Blue, Blue, Green, Blue. Which of the following would be best to describe a typical value in the dataset? Select the correct answer below: the mean the median the mode All of the above can appropriately be used to describe a typical value in the dataset. The following histogram shows the monthly rents reported in a survey of university students. Which of the following would be a reasonable measure of central tendency for this dataset? Select all that apply. Select all that apply: the mean the median
the mode, 100 the mean, 80 the median, 95 the median, 90 The mean is 80 , but there are 13 data values above the mean compared to 6 data values below the mean, so it is not a good measure of central tendency. The mean is generally not a good measure of central tendency when there are outliers or the dataset is skewed, as is the case here. The following is a dataset of salaries for a company (in thousands). Find the mean and median and determine if the mean or median is the better measure of central tendency. 11,87,85,95,92,93, Select the correct answer below: Mean =80, Median = The mean is the better measure of central tendency. Mean =80, Median = The median is the better measure of central tendency. Mean =92, Median = The mean is the better measure of central tendency. Mean =92, Median = The median is the better measure of central tendency. The following dataset represents the math test scores for a class of 20 students. 90 , 85 , 95 , 100 , 100 , 90 , 100 , 65 , 100 , 85 , 80 , 95 , 80 , 100 , 85 , 75 , 100 , 90 , 90 , 75 Would the mode be a good measure of central tendency for this dataset? Select the correct answer below: Yes, since this dataset has a well-defined, unique mode. Yes, since this dataset contains no outliers. No, since there are many more data values below the mode than above. No, since there are many more data values above the mode than below. No, since this dataset does not have a well-defined, unique mode. No, since this dataset contains no outliers. No, since there are many more data values below the mode than above. The mode is the data value that appears most often. In this case, the mode is 100. Since 100 appears six times in the dataset and all other values appear fewer than six times. There are 14 data values below the mode and 0 data values above the mode. Since there are many more data values below the mode than above, the mode would not be a good measure of central tendency.
The following histogram shows menu prices of entrees at a local restaurant. Identify the best measure of central tendency for this dataset. Select the correct answer below: the mean the median the mode none of the above The following dataset represents the math test scores for a class of 20 students. 90 , 85 , 95 , 100 , 100 , 90 , 100 , 70 , 100 , 85 , 80 , 95 , 80 , 100 , 85 , 75 , 100 , 90 , 90 , 75 How many outliers are in this dataset? Provide your answer below: 0 (An outlier is a data value that is significantly different from other data values in the dataset. The lowest value in the dataset, 70 , is not significantly far from the other values (two values in the dataset are 75 ). The greatest value in the dataset, 100 , is not significantly far from the other values (the data value 100 appears six times in the dataset). Since no data value is significantly different from other data values in the dataset, there are no outliers). A trainer would like to find the mean number of sports drinks the people in her class had in the last week. She collects data from 26 participants in her aerobics class. The graph shows the frequency for the number of sports drinks. Find the mean number of sports drinks consumed by the 26 participants, and round your answer to the nearest tenth. Record your answer by dragging the purple point to the mean.
