Question

1. The weights of four 32 ounce bags of almonds were actually found to 28, 32, 35, and 33 ounces. a. Find the sample mean. (5) b. Find the population standard deviation. (8) c. Find the sample variance. (5)

Answer 1

1.

Given data,

28,32,33,35

Mean = Sum of observations/ Count of observations
Mean = (28 + 32 + 35 + 33 / 4) = 32
Variance
Step 1: Add them up
28 + 32 + 35 + 33 = 128
Step 2: Square your answer
128*128 =16384
…and divide by the number of items. We have 4 items , 16384/4 = 4096
Set this number aside for a moment.
Step 3: Take your set of original numbers from Step 1, and square them individually this time
28^2 + 32^2 + 35^2 + 33^2 = 4122
Step 4: Subtract the amount in Step 2 from the amount in Step 3
4122 - 4096 = 26
Step 5: Subtract 1 from the number of items in your data set, 4 - 1 = 3
Step 6: Divide the number in Step 4 by the number in Step 5. This gives you the variance
26 / 3 = 8.6667
Step 7: Take the square root of your answer from Step 6. This gives you the standard deviation
2.9439
a.
sample mean = 32
b.
population standard deviation = 2.9439
c.
variance = 8.6667