1. The data below gives the eye colors of 20 students in a Statistics class. Make a frequency table for the data.

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1 1. The data below gives the eye colors of 20 students in a Statistics class. Make a frequency table for the data. Green Blue Brown Blue Blue Brown Blue Blue Blue Green Blue Brown Blue Brown Brown Blue Brown Blue Blue Blue Answer Color Green Brown Blue Frequency The data in the figure below represents the annual salaries of 200 professional musicians. The kind of graph shown above is called: Answer: Histogram Histogram A graph used when a numeric variable is continuous and its possible values can vary by small increments Box plot Consists of a rectangular box that sits above a scale and extends from the first Quartile Q1 to the third Quartile Q3 on that scale Bar Graph a chart with rectangular bars with lengths proportional to the values that they represent. The bars can be plotted vertically or horizontally

2 3. The table below shows Joe's golf scores from Saturday. Joe's average golf score on Saturday was (2*5) + (3*8) + (4*11) + (5*5) + (6*3) + (7*1) + (8*2) + (9*1) /36= 4.25 Joe's median golf score on Saturday was Median is the 50 th percentile where half of the data is above the median and half is below the median Apply the definition of percentile When N is odd, the median is at position d (N + 1)/2 When N is even, the median is the average of the values at position d (n/2) and d ([n/2]+1) So since 36 is even, we are looking at position 18 and 19, thus 4 and 4, giving us (4+4)/2=4 Answer: 4

3 4. Use the data set {-2, -3, 1, 8} to answer the following question(s). The mean of the data set is: 1. Mean means average, so = 4/4 = 1 The median of the data set is -.05 To find the mean reorder the list Since the list is even, we take the values at position d (n/2) and d ([n/2]+1) Position D(2) and d(3) = = -1 = -1/2 = Use the data set {,,,..., } consisting of 255 numbers to answer the following question(s). After sorting the data set (in increasing order from left to right), the median is Recall : When N is odd, the median is at position d (N + 1)/2 When N is even, the median is the average of the values at position d (n/2) and d ([n/2]+1) So, 255+1= /2 = 128 the number in the 128th position.

4 6. The data in the figure below represents the annual salaries of 200 professional musicians. The median salary of this group of musicians is approximately: Recall: the median is the 50 th percentile; therefore we are looking at the middle of the data set. Counting the percentages, we look at the salary at 50% inward from either side to get $40, 000

5 7. The table below shows Joe's golf scores from Saturday. The median of golf scores is: Recall : When N is odd, the median is at position d (N + 1)/2 When N is even, the median is the average of the values at position d (n/2) and d ([n/2]+1) So N=36, and therefore the median is at position, 18 and 19. D18 and d19 are each 4, so the median is (4+4)/2=4 The first quartile of golf scores is: Recall the formula for the locator L=(25/100)*36=9, so the value is the average of d9 and d10, thus (3+3)/2 = 3 The third quartile of golf scores is: L=(75/100)*36=27, so the value is the average of d27 and d28, thus (5+5)/2 = 5 The 95th percentile of golf scores is: L=(95/100)*36=34.2, so we round up to 35, thus the value of d35 is 8 The locator for the 20th percentile is: L=(20/100)*36=7.2

6 8. Use the data set {,,,..., } consisting of 251 numbers to answer the following question(s). After sorting the data set (in increasing order from left to right) the first quartile is Recall the formula for the locator L=(25/100)*251=62.75, so since it s not a whole number, we round up and consider the value at position Find the five-number summary for the data set {5, -2, 8, 4, 7, 1, 7, -2, -5}. Recall the values in the five number summary: Min, Q1, M, Q3, Max First order the values in increasing order {-5, -2, -2, 1, 4, 5, 7, 7, 8} From here we get the following: Min: -5 Max:8 When N is odd, the median is at position d (N + 1)/2 When N is even, the median is the average of the values at position d (n/2) and d ([n/2]+1) So N=9, thus d(10/2) = 5, giving the value for median of 4 Recall the formula for the locator L=(25/100)*9=2.5, so since it s not a whole number, we round up and consider the value at position 3, thus a -2 is the value for Q1 L=(75/100)*9=6.75, so since it s not a whole number, we round up and consider the value at position 7, thus a 7 is the value for Q3 Min = -5, Q1= -2, M = 4, Q3= 7, Max = 8

7 10. Draw a box plot for the data set {5, -2, 8, 4, 7, 1, 7, -2, -5}. 11. The box plots represent a comparison of the annual salaries of a group of opera and a group of country western singers respectively. What are the five number summary for the salaries of the opera singers? Min = $40,000, = $45,000, = $55,000, = $65,000, Max = $80,000

8 12 The table below shows Joe's golf scores from Saturday. The range of golf scores was Range= Max-Min or 9-2 thus 7 Use the data set {-2, -3, 1, 8} to find the standard deviation -2, -3, 1, 8 L=(50/100)*4=2, so since it is a whole number, take the average of d2 and d3, thus giving a -1 x x-1 (x-1) =

9 13 Use the frequency table below to answer the following question(s). The standard deviation of this data set is -2, -3, 1, 8 L=(50/100)*65=32.5, so since it is not a whole number we round to 33 and take the value of d33, thus giving a 5 X F (X-5) (X-5) =