FINAL EXAM QUESTIONS

*QUESTION 10* The five number summary for a set of data is given below. Min: 40 Q1: 69 Median: 72 Q3: 79 Max: 86 Using the interquartile range, which of the following are outliers? Select all correct answers. 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=79−69=10 So a value is an outlier if it is less than Q1−1.5⋅IQR=69−(1.5)(10)=54 or greater than Q3+1.5⋅IQR=79+(1.5)(10)=94 So we see that 43, 44, and 48 are outliers.

ANSWER: 43, 44, 48

*Question 3:* Given the frequency table below, which of the following is the corresponding relative frequency table? Value: 1, 2, 3, 4, 5 Frequency: 6, 5, 5, 2, 7 By adding the frequencies, we see that there are a total of 25 values in the set of data. Dividing each frequency by this total gives the relative frequency. So, for example, the relative frequency for the value 1 is 6/25=0.24

ANSWER: Value: 1, 2, 3 ,4 5 Relative Frequency: 0.24, 0.2, 0.2, 0.08, 0.28

*QUESTION 9* Given the frequency table below for a list of the number of holes groundhogs dug in randomly selected backyards, find the mean. (Please do not include the units in your answer.) Value: 11, 12, 13, 14, 15, 16, 17, 18 Frequency: 1, 5, 3, 1, 2, 3, 4, 5 Remember that the mean is the sum of all the numbers divided by the total number of values in the data set. The frequency table tells you the number of times that each number appears in the set of data. So to get the sum of all the numbers in the set of data, we take each frequency multiplied by its value and add them all up: Sum=11⋅1+12⋅5+13⋅3+14⋅1+15⋅2+16⋅3+17⋅4+18⋅5=11+60+39+14+30+48+68+90=360 The number of numbers in the list is the sum of the frequencies.Number of numbers=1+5+3+1+2+3+4+5=24So the mean of the number of holes groundhogs dug in randomly selected backyards is Sum Number of numbers=360/24=15

ANSWER: mean= 15

*Question 4:* Given the following list of prices (in thousands of dollars) of randomly selected trucks at a car dealership, find the median. 20, 46, 19, 14, 42, 26, 33 Put the numbers in order. 14,19,20,26,33,42,46 Now, because the list has length 7, which is odd, we know the median number will be the middle number. In other words, we can count to item 4 in the list, which is 26. So the median price (in thousands of dollars) of randomly selected trucks at a car dealership is 26.

ANSWER: median= 26 thousand dollars

*QUESTION 5* Use the dot plot to determine the minimum value for the data set.

ANSWER: 2 dots The leftmost dots are above the number 2. Therefore, the minimum is 2.

*QUESTION 17* The following dataset represents the number of registered students for 60 college courses, sorted and arranged in rows of 5. What is the 50th percentile of the data? Remember that the 50th percentile is also known as the median so we can just locate the value in the middle of the data set. The numbers are already in order least to greatest. We notice there are two values in the middle, 57 and 57. Therefore, the average of these two numbers is also 57. Our median, or 50th percentile, is 57 students.

ANSWER: 57 students

*QUESTION 11* Which of the data sets represented by the following box and whisker plots has the smallest standard deviation? Remember that the standard deviation is a measure of how spread out the data is. If the values are concentrated around the mean, then a data set has a lower standard deviation.A box and whisker plot with short whiskers and a short box has values that are less spread out, and hence has a smaller standard deviation.

ANSWER: C

*QUESTION 13* In order to study the mean blood pressure of people in his town, Richard samples the population by dividing the residents by age and randomly selecting a proportionate number of residents from each age group. Which type of sampling is used? Convenience sampling Cluster sampling Stratified sampling Systematic sampling This scenario demonstrates stratified sampling. Stratified sampling involves dividing the population into groups and randomly selecting a proportionate number of individuals from each group.

ANSWER: Stratified sampling

*QUESTION 15* Timothy wants to estimate the mean number of siblings for each student in his school. He records the number of siblings for each of 75 randomly selected students in the school. What is the statistic? the specific number of siblings for each randomly selected student the 75 randomly selected students the mean number of siblings for the randomly selected students the mean number of siblings for all students in the school all the students in the school A statistic is a numerical characteristic of the sample. In this case, the statistic is the mean number of siblings for the randomly selected students.

ANSWER: the mean number of siblings for the randomly selected students

*QUESTION 7* Jennifer wants to estimate the percentage of parents that use cloth diapers. She asks a randomly selected group of 200 parents whether or not they use cloth diapers. What is the parameter? A parameter is a number that is used to represent a population characteristic. In this case, the parameter is the percentage of all parents that use cloth diapers.

Answer: the percentage of all parents that use cloth diapers

*QUESTION 18* Describe the shape of the given histogram. uniform unimodal and symmetric unimodal and left-skewed unimodal and right-skewed bimodal A histogram that is unimodal and right-skewed has a single peak with a longer tail on the right side.

Answer: unimodal and right-skewed