SOLUTION: What the calculation range,variance, and standard deviation of 7,4,2,3,4,5,8,1,9,4

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Question 1184953: What the calculation range,variance, and standard deviation of 7,4,2,3,4,5,8,1,9,4
Answer by MathLover1(20850) About Me  (Show Source):
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What the calculation range,variance, and standard deviation of 7,4,2,3,4,5,8,1,9,4

Range:
The range is found by subtracting the smallest data value from the largest data value. Here, the smallest data value is 1 and the largest is 9. Therefore, the range is:
9-1=8

Variance:
1. The steps that follow are also needed for finding the standard deviation. Start by writing the computational formula for the variance of a sample:

s%5E2=%28sum%28x%5E2%29-%28sum%28x%29%29%5E2%2Fn%29%2F%28n-1%29
Create a table of 2 columns and 11 rows. There will be a header row and a row for each data value. The header row should be labeled with x and x%5E2.
Enter the data values in the x+column, with each data value in its own row. In the second column, put the square of each of the data values, x%5E2.
.
x....|....x%5E2
7....|....49
4....|....16
2....|....4
3....|....9
4....|....16
5....|....25
8....|....64
1....|....1
9....|....81
4....|....16
3. Find the sum of all the values in the first column,

sum%28x%29=7%2B4%2B2%2B3%2B4%2B5%2B8%2B1%2B9%2B4=47

.%28sum%28x%29%29%5E2%2Fn=47%5E2%2F10=2209%2F10=220.9+
sum%28x%5E2%29=49%2B16%2B4%2B9%2B16%2B25%2B64%2B1%2B81%2B16=281
s%5E2=%28281-220.9%29%2F%2810-1%29
s%5E2=60.1%2F9
s%5E2=6.677777777777777
Standard Deviation
s=sqrt%286.677777777777777%29
s=2.584139659108574


Answer:
Range: 8
Variance: 6.67777777777777
Standard deviation: 2.584139659108574