The standard deviation is approximately 0.01307. See the explanation below.
The square root of the variance is used to calculate the standard deviation, a statistic that expresses how widely distributed a dataset is in relation to its mean.
By calculating the departure of each data point from the mean, the standard deviation may be determined as the square root of variance.
Step 1: First, lets calculate the variance.
The formula for variance is:
[tex]\sigma^2 = \frac{\sum_{i=1}^{n}(x_i - \mu)^2} {n-1}[/tex]
To get the variance ( s2 ) we must first get the mean. Our mean is 0.99892.
We subtract each value by the mean and square the difference.
(0.978-0.99892)² = 0.0004376464
(0.982-0.99892)² = 0.0002862864
(0.983-0.99892)² = 0.0002534464
(0.984-0.99892)² = 0.0002226064
(0.987-0.99892)² = 0.0001420864
(0.988-0.99892)² = 0.0001192464
(0.989-0.99892)² = 9.84064e-05
(0.99-0.99892)² = 7.95664e-05
(0.992-0.99892)² = 4.78864e-05
(0.992-0.99892)² = 4.78864e-05
(0.993-0.99892)² = 3.50464e-05
(0.994-0.99892)² = 2.42064e-05
(0.996-0.99892)² = 8.5264e-06
(0.997-0.99892)² = 3.6864e-06
(1-0.99892)² = 1.1664e-06
(1.001-0.99892)² = 4.3264e-06
(1.006-0.99892)² = 5.01264e-05
(1.007-0.99892)² = 6.52864e-05
(1.011-0.99892)² = 0.0001459264
(1.015-0.99892)² = 0.0002585664
(1.015-0.99892)² = 0.0002585664
(1.015-0.99892)² = 0.0002585664
(1.018-0.99892)² = 0.0003640464
(1.02-0.99892)² = 0.0004443664
(1.02-0.99892)² = 0.0004443664.
Step 2: Add all these numbers above
0.0004376464+0.0002862864+0.0002534464+0.0002226064+0.0001420864+0.0001192464+9.84064e-05+7.95664e-05+4.78864e-05+4.78864e-05+3.50464e-05+2.42064e-05+8.5264e-06+3.6864e-06+1.1664e-06+4.3264e-06+5.01264e-05+6.52864e-05+0.0001459264+0.0002585664+0.0002585664+0.0002585664+0.0003640464+0.0004443664+0.0004443664
=0.00410184
Step 3: Now we divide the sum by how many numbers there are. In this case we have 25.
We'll call this number n.
So n=25
For a sample (use 0.00410184 divided by (n-1) ):
So s2 =0.00410184 divided by 24
s2 = 0.00017091
Step 4 - Solve for Standard deviation:
The standard deviation is the square root of the variance. Our variance is 0.00017091.
So we only apply a square root on the variance.
= √ 0.00017091
s = 0.0130732551
Learn more about Standard Deviation:
https://brainly.com/question/475676
#SPJ1
Full Question:
A statistical process control monitoring system samples the inside diameter of ball bearing every hour. Measurements were taken every hour for 25 hours. The target thickness, T, is the average.
0.992 1.015 0.988 0.996 1.015 1.000 0.989 0.994 1.018 0.997 1.020 1.007 1.006 0.982 1.001 0.992 1.020 0.993 0.978 0.984 0.990 1.015 0.983 1.011 0.987
What is the population standard deviation, σ?
