Compute the range and standard deviation for strength of the

Compute the range and standard deviation for strength of the concrete (in psi)

3940, 4080, 3300, 3200, 2910, 3810, 4080, 4020

The range is __ psi

s=__ psi

Solution

a)
Range = Max - Min = 1170

b)
Mean= 3940 + 4080 + 3300 + 3200 + 2910 + 3810 + 4080 + 4020/8 = 3667.5

Step 1:Add them up:
3940 + 4080 + 3300 + 3200 + 2910 + 3810 + 4080 + 4020 = 29340

Step 2: Square your answer:
29340 × 29340 = 860835600
…and divide by the number of items. We have 8 items in our example so:
860835600 / 8 = 107604450
Set this number aside for a moment.

Step 3: Take your set of original numbers from Step 1+and square them individually this time:
3940^2 + 4080^2 + 3300^2 + 3200^2 + 2910^2 + 3810^2 + 4080^2 + 4020^2 = 109091000

Step 4: Subtract the amount in Step 2 from the amount in Step 3.
109091000 – 107604450 = 1486550
Set this number aside for a moment.

Step 5: Subtract 1 from the number of items in your data set. For our example:
8 – 1 = 7

Step 6: Divide the number in Step 4 by the number in Step 5. This gives you the variance:
1486550/ 7 = 212364.28
How to find the sample variance and standard deviation: Standard Deviation

Step 7: Take the square root of your answer from Step 6. This gives you the standard deviation:

212364.28= 460.829