Question

b) Calculate the standard deviation of the ages for the First Six U.S. Presidents by hand by answering the following questions and filling in the table. We will want our final answer to be correct to 3 decimal places. So, to make sure we don't get any rounding error, we will do all calculations to 6 decimal places until the final answer. (1point each) Round each answer to 6 decimal places. (X) of the First Six Presidents? What is the mean Round vour answer to 6 decimal places. Mean HINT: You are strongly encouraged to verify this calculation using your calculator Fill in the following values in the table using the rounded mean you got in the question above. Round each answer to 6 decimal places. (X First Six Presidents Age George Washington 57 John Adams 61 Thomas Jefferson 57 James Madison 57 James Monroe 58 John Quincy Adams 57 SUM What is the standard deviation of the First Six Presidents? (4 points) Roundyour anSwer to 3 decimal places as needed Standard Deviation = | HINT: You are strongly encouraged to verify this calculation using your calculator c) Calculate the standard deviation of the ages for the Last Six U.S. Presidents by hand by answering the following questions and filling in the table. We will want our final answer to be correct to 3 decimal places. So, to make sure we don't get any rounding error, we will do all calculations to 6 decimal places until the final answer. ( point each) Round each answer to 6 decimal places. What is the mean age (X) of the Last Six Presidents? Round your answer to 6 decimal places. Mean = HINT: You are strongly encouraged to verify this calculation using your calculator Fill in the following values in the table using the rounded mean you got in the question above Round each an5wer to 6 decimal places. (х — X)? Last Six Presidents Age Jimmy Carter 52 Ronald Reagan 69 George H.W. Bush 64 Bill Clinton 46 George W. Bush 54 Barack Obama 47 SUM the Last Six Presidents? (4 points) What is the standard deviation Round your answer to 3 decimal places needed Standard Deviation HINT: You are strongly encouraged to verify this calculation using your calculator 4) A botanist opened a sample of 50 bean pods and counted the number of beans in each pod. The results obtained were as follows: 4 0 4 5 4 4 4 4 4 4 2 4 1 4 4 0 4 6 2. C 4 a) Fill in the frequency table for these data. (2 points each) Number of Beans in Pod Number of Bean Pods 1 4 4 6 b) Determine the mode of the data. (5 points) Mode = Round your answer to 2 decimal places as needed. .. c) Determine the median of the data. (5 points) Median =| Round your answer to 2 decimal places as needed. d) Calculate the mean (X) of the data. (5 points) Mean Round your answer to decimal places as needed. e) Calculate the standard deviation (S) using your graphing calculator. (5 points) Hint: Also verify that the mean you calculated in part e matches the mean from the calculator. Standard deviation = Round your answer to 2 decimal places as needed. f) Determine the range of variation: (2 points each) (X - S, X S) = ( | Round your answers to 2 decimal places as needed. g) culate what percent of Hint: Create a histogram on paper and shade the included region(s) on your histogram to help visualize the shaded area and help with calculations. data valu are withi tion tl mean one sta Total area of shaded region = Round your answer to 2 decimal places as needed. (4 points) % (3 points) Percent of area within one standard deviation = Round your answer to 2 decimal places as needed. 4) The mean salary of 5 employees is $33700. The median is $34900. The mode is $35700. If the median paid employee gets a $3400 raise, then ... Hint: It will help to write down what salaries you know of the five and think about how you normally calculate mean, median, and mode. a) What is the new mean? (3 point) New Mean S b) What is the new median? (3 points) New Median S c) What is the new mode? (2 point) New Mode $ Question 4. Points possible: 8 This is attempt 1 of 1. 5) The mean salary of 5 employees is S40000. The median is S38200. The lowest paid employee's salary is S31500. If the lowest paid employee gets a $3800 raise, then ... Hint: It will help to write down what salaries you know of the five and think about how you normally calculate mean and median. a) What is the new mean? (3 points) New Mean S b) What is the new median? (3 points) New Median = $ 6) The mean salary of 5 employees is $41100. The employee salaries have 2 modes: $31500 and $49500. If the median salary gets a $2900 raise, then ... Hint: It will help to write down what salaries you know of the five and think about how you normally calculate mean and median.. a) What is the new mean? (3 point) New Mean $ b) What is the new median? (3 points) New Median S

Answer 1

(6) Mean (57 61 57 57 58 57)/6 =57.83333 First Six Presidents Age George Washington John Adams (X X)2 57 (57 57.83333)2 0.694439 (61 57.83333)2 10.0278 57 (57 57.83333)2 0.694439 57 (57 57.83333)2 0.694439 58 (58 57.83333)2 0.027779 57 (57 -57.83333)2 0.694439 61 Thomas Jeffer son James Madison James Monroe John Quincy Adams SUM 12.83333 6 Xi- X)2 1.462 Standard deviation i-1

(c) Mean (52 69 64 46 54 47)/6 55.33333 First Six Presidents Age (X X2 52 (52 55.33333)2 11.11109 69 (69 55.33333)2 186.7779 64 (64 55.33333)2 75.11117 46 (46 55.33333)2 87.11105 54 (54 55.33333)2 1.777769 47 (47 55.33333)2 69.44439 Jimmy Carter Ronald Reagan George H. W. Bush Bill Clinton George W. Bush Barack Obama SUM 431.3334 6 Xi- X)28.479 Standard deviation i-1

4(a)

No. of Beans in Pod	No. of Bean Pods
0	11
1	5
2	4
3	3
4	15
5	9
6	3

4) (b) Mode 4 (since the highest frequency occurred at x = (c) Median cumulative frequency at (d) Mean X 2.9 |(e) S 2.02 f) (X S, X + S) (0.88, 4.92) g. Total are Percent of 4> N/2 > 4 (since N/2 25, cumulative frequency at x = 3) _ 4315 22 one standard deviation of shaded region area within 44% (22/50) 100