1. Given the sample 6, 5, 9, 9, 7, 7, 4, 7, 4, 13, find the following. (Round yo
ID: 3180719 • Letter: 1
Question
1. Given the sample 6, 5, 9, 9, 7, 7, 4, 7, 4, 13, find the following. (Round your answers to two decimal places.)
(a) Variance s2 using formula below
s2 =
(b) Variance s2 using formula below
s2 =
(c) Standard deviation, s
s =
2. One aspect of the beauty of scenic landscape is its variability. The elevations (feet above sea level) of 12 randomly selected towns in the Finger Lakes Regions of Upstate New York are recorded here.
(a) Find the mean. (Give your answer correct to the nearest whole number.)
(b) Find the standard deviation. (Give your answer correct to the nearest whole number.)
3. Does studying for an exam pay off? The number of hours studied, x, is compared with the exam grade received, y.
x 1 3 7 3 3
y 60 65 95 75 85
(a) Complete the preliminary calculations: SS(x), SS(y), and SS(xy).
(SS(x))
(SS(y))
(SS(xy))
(b) Find r. (Give your answer correct to three decimal places.)
4. The accompanying data show the number of hours, x, studied for an exam and the grade received, y (y is measured in tens; that is, y = 8 means that the grade, rounded to the nearest 10 points, is 80).
(a) Use the given scatter diagram to estimate r for the sample data on the number of hours studied and the exam grade.
r
(b) Calculate r. (Give your answer correct to two decimal places.)
r =
5. Does it pay to study for an exam? The number of hours studied, x, is compared to the exam grade received, y.
1360 685 1225 955 1495 1360 1036 901 1117 847 955 604 (T-T)2 n-Explanation / Answer
Q2.
Mean = Sum of observations/ Count of observations
Mean = (1360 + 685 + 1225 + 955 + 1495 + 1360 + 1036 + 901 + 1117 + 847 + 955 + 604 / 12) = 1045
Variance
Step 1: Add them up
1360 + 685 + 1225 + 955 + 1495 + 1360 + 1036 + 901 + 1117 + 847 + 955 + 604 = 12540
Step 2: Square your answer
12540*12540 =157251600
…and divide by the number of items. We have 12 items , 157251600/12 = 13104300
Set this number aside for a moment.
Step 3: Take your set of original numbers from Step 1, and square them individually this time
1360^2 + 685^2 + 1225^2 + 955^2 + 1495^2 + 1360^2 + 1036^2 + 901^2 + 1117^2 + 847^2 + 955^2 + 604^2 = 13943136
Step 4: Subtract the amount in Step 2 from the amount in Step 3
13943136 - 13104300 = 838836
Step 5: Subtract 1 from the number of items in your data set, 12 - 1 = 11
Step 6: Divide the number in Step 4 by the number in Step 5. This gives you the variance
838836 / 11 = 76257.8182
Step 7: Take the square root of your answer from Step 6. This gives you the standard deviation
276.1482
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