20. Calculate the range, variance, and standard deviation of the following data set:
5, 5, 6, 6, 6, 8, 8, 8, 8, 10, 10, 11, 12, 12, 20
(Points: 5)
Range = 15; Variance = 225; Standard Deviation = 7.5
Range = 3.85; Variance = 14; Standard Deviation = 3.74
Range = 20; Variance = 15; Standard Deviation = 4
Range = 15; Variance = 14.82; Standard Deviation = 3.85
Find the mean first = sum of scores/number of scores
Subtract each of the scores from the mean and square each difference. Find the sum of these squares. Divide that by the number of scores to get variance.
Standard deviation = square root of variance
Range = highest score - lowest
I'll let you do the calculations.
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2y^3(3y+1)
Given the following data sets, determine the range, variance, and standard deviation
Well, well, well! It's time to crunch some numbers, my friend! Let's see what we've got here. We've got the data set: 5, 5, 6, 6, 6, 8, 8, 8, 8, 10, 10, 11, 12, 12, and 20.
To start off, let's find the range. The range is simply the difference between the highest and lowest values in the data set. In this case, the range is 20 - 5 = 15.
Now, hold onto your funny bone because we're about to tackle the variance. The variance measures how spread out the data is from the mean. After some number crunching, the variance for this data set is 14.82.
Finally, let's break out the juggling pins for the standard deviation. The standard deviation is the square root of the variance. Therefore, the standard deviation for this data set is approximately 3.85.
So, to sum it all up: the range is 15, the variance is 14.82, and the standard deviation is 3.85. Ta-da!
To calculate the range of a data set, subtract the minimum value from the maximum value. In this case, the minimum value is 5 and the maximum value is 20.
Range = 20 - 5 = 15
To calculate the variance of a data set, you need to find the mean (average) of the data set, then subtract the mean from each data point, square the result, and finally find the average of the squared differences.
Step 1: Find the mean of the data set.
Mean = (5 + 5 + 6 + 6 + 6 + 8 + 8 + 8 + 8 + 10 + 10 + 11 + 12 + 12 + 20) / 15
Mean = 137 / 15
Mean = 9.13 (rounded to two decimal places)
Step 2: Subtract the mean from each data point and square the result.
(5 - 9.13)^2 = (-4.13)^2 = 17.05
(5 - 9.13)^2 = (-4.13)^2 = 17.05
(6 - 9.13)^2 = (-3.13)^2 = 9.77
(6 - 9.13)^2 = (-3.13)^2 = 9.77
(6 - 9.13)^2 = (-3.13)^2 = 9.77
(8 - 9.13)^2 = (-1.13)^2 = 1.28
(8 - 9.13)^2 = (-1.13)^2 = 1.28
(8 - 9.13)^2 = (-1.13)^2 = 1.28
(8 - 9.13)^2 = (-1.13)^2 = 1.28
(10 - 9.13)^2 = (0.87)^2 = 0.76
(10 - 9.13)^2 = (0.87)^2 = 0.76
(11 - 9.13)^2 = (1.87)^2 = 3.50
(12 - 9.13)^2 = (2.87)^2 = 8.24
(12 - 9.13)^2 = (2.87)^2 = 8.24
(20 - 9.13)^2 = (10.87)^2 = 118.16
Step 3: Find the average of the squared differences.
Variance = (17.05 + 17.05 + 9.77 + 9.77 + 9.77 + 1.28 + 1.28 + 1.28 + 1.28 + 0.76 + 0.76 + 3.50 + 8.24 + 8.24 + 118.16) / 15
Variance = 224.82 / 15
Variance = 14.98 (rounded to two decimal places)
To calculate the standard deviation, take the square root of the variance.
Standard Deviation = √14.98
Standard Deviation = 3.87 (rounded to two decimal places)
Therefore, the correct answer is:
Range = 15; Variance = 14.98; Standard Deviation = 3.87