Please enable JavaScript.
Coggle requires JavaScript to display documents.
Standard Deviation, Example for Population Data:, You grow 20 crystals…
Standard Deviation
Formula for Standard Deviation from Population Data:
Formula for Standard Deviation from Sample Data:
Example for Sample Data:
The red blood cell counts (in 10^5 cells per microliter) of a healthy adult measured on 6 days are as follows:55, 51, 52, 49, 50, 49
Find the standard deviation of this sample of counts.
Answer:
Step 1: Sample data={55,51,52,49,50,49}
Step 2:
The sample mean of the given cell counts is:
(55+51+52+49+50+49)/6=51
Step 3:
The Standard deviation
={[(55-51)^2+(51-51)^2+(52-51)^2+(49-51)^2+(50-51)^2+(49-51)^2]/6-1}^1/2
=2.2804
Step 4:The sample standard deviation of the red blood cell counts is found to be 2.2804
Definition:
Standard deviation is a number used to tell how measurements for a group are spread out from the average (mean or expected value).
Example for Population Data:
9, 2, 5, 4, 12, 7, 8, 11, 9, 3, 7, 4, 12, 5, 4, 10, 9, 6, 9, 4
Subtract the mean from each data point (or the other way around, if you prefer... you will be squaring this number, so it does not matter if it is positive or negative).(9 - 7)2 = (2)2 = 4
(12 - 7)2 = (5)2 = 25
(7 - 7)2 = (0)2 = 0
(8 - 7)2 = (1)2 = 1
(3 - 7)2 = (-4)22 = 16
(7 - 7)2 = (0)2 = 0
(4 - 7)2 = (-3)2 = 9
(12 - 7)2 = (5)2 = 25
(5 - 7)2 = (-2)2 = 4
(4 - 7)2 = (-3)2 = 9
(10 - 7)2 = (3)2 = 9
(9 - 7)2 = (2)2 = 4
(6 - 7)2 = (-1)2 = 1
(9 - 7)2 = (2)2 = 4
(4 - 7)2 = (-3)22 = 9
You grow 20 crystals from a solution and measure the length of each crystal in millimeters. Here is your data:
(2 - 7)2 = (-5)2 = 25
(5 - 7)2 = (-2)2 = 4
(4 - 7)2 = (-3)2 = 9
(11 - 7)2 = (4)22 = 16
(9 - 7)2 = (2)2 = 4
Calculate the mean of the squared differences.(4+25+4+9+25+0+1+16+4+16+0+9+25+4+9+9+4+1+4+9) / 20 = 178/20 = 8.9This value is the variance. The variance is 8.9
The population standard deviation is the square root of the variance. Use a calculator to obtain this number.(8.9)1/2 = 2.983The population standard deviation is 2.983
