Download The Simplest Way to Standard Deviation

The Simplest Way to Standard Deviation
(For those who struggle with Math and Statistics but still need to know the process for the Psychology)
1. Donotpanic.
2. Lineyourdata(example:testscores)upinnumericalorder.Thismakesyourworka
littleeasier.{50,75,25,100}=___________________________________________________________
3. Findthemean(average)ofyourdatasetbyaddingeachnumberanddividingitby
thenumber(4)ofscores.
_________+__________+_________+___________=___________/4=_____________
4. Takeeachscoreandsubtractthemeanfromit.Negativenumbersareok;donot
panic!
Score
Mean(average)
Result1
25
50
75
100
5. Squareeachnumberinthe“Result1”column.Squaringmeanswemultiplythe
numberbyitself(2squared=2x2;3squared=3x3).Ifthenumberisnegative,
squaringitwillturnitintoapositive.Donotpanic.Itisok.
Result1
xitself(positively)
Result2
6. Takeallofthenumbersinthe“Result2”column(thesquares)andaddthem
together.
Result2
+
+
+
+
Result3=
7. Takethe“Result3”numberanddividebythenumberofscores.
Result3
Divideby#ofscores
Result4
4
=
8. Findthe√squareroot(whatnumbermultipliedbyitself=Result4)of“Result4”
and…
9. THATisyourstandarddeviation!
Now What?
Here is a brief article describing the next step in understanding standard deviation and distributions. Read and highlight/
annotate this and then complete the practice problems after it.
Psychological research involves measurement of behavior. This measurement results in numbers that differ from one
another individually but that are predictable as a group. One of the common patterns of numbers involves most of the
measurements being clustered together near the mean of the distribution, with fewer cases occurring as they deviate
farther from the mean. When a frequency distribution is drawn in pictorial form, the resulting pattern produces the bellshaped curve that scientists call a normal distribution.
When measurements produce a normal distribution, certain things are predictable. First, the mean, median, and mode are
all equal. Second, a scientist can predict how far from the mean most scores are likely to fall. Thus, it is possible to
determine which scores are more likely to occur and the proportion of scores likely to be above or below any given score.
Many behavioral measurements result in normal distributions. For example, scores on intelligence tests are likely to be
normally distributed. The mean is about 100 and a typical person is likely to score within about 15 points of the mean, that
is, between 85 and 115. If the psychologist knows the mean and the typical deviation from the mean (called the standard
deviation), the researcher can determine what proportion of scores is likely to fall in any given range. For instance, in the
range between one standard deviation below the mean (about 85 for IQ scores) and one deviation above the mean (about
115 for IQ scores), one expects to find the scores of about two thirds of all test takers. Further, only about two and a half
percent of test takers will score higher than two standard deviations above the mean (about 130).
Read more: Normal Distribution - Statistics In Psychology, Example Of Mean, and Psychology Statistics - JRank
Articles http://psychology.jrank.org/pages/454/Normal-Distribution.html#ixzz3lrdR4p7X
PRACTICE: Using standard deviation in a normal curve.
A study of statistical data reveals that when a normal distribution occurs, 68% of the population will have a
value within one standard deviation of the mean, and 95% of the population will have a value within two
standard deviations of the mean.
←68%→ ←←←←95%→→→→ ‐2 sd ‐1 sd mean +1 sd +2 sd This information can be used to analyze data when original values are unknown.
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Given that the scores on a test are normally distributed, that the mean score is 80 and the standard deviation is 7,
1. What percent scored less than 87? ________
2. What percent scored less than 73? ________
3. What percent scored more than 94? ________
4. 2.5% scored less than what value? ________
Given the times required for a group of students to complete the physical fitness obstacle course result in a
normal curve, and that the mean time 21 minutes and the standard deviation is 4,
5. What percent took longer than 29 minutes? __________
6. What percent took less than 29 minutes? __________
7. What percent took between 13 and 29 minutes? __________
8. What percent took between 13 and 25 minutes? _________
9. What percent took longer than 17 minutes? _________
A set of data with a normal distribution has a mean of 50 and standard deviation of 10.
10. __________ and __________ 68% of the data is between what two numbers?
11. __________ and __________
95% of the data is between what two numbers?
A set of data with a normal distribution has a mean of 35 and standard deviation of 5.
12. __________ and __________
68% of the data is between what two numbers?
13. __________ and __________
95% of the data is between what two numbers?
14. __________ About what percent of the population (data) is above 40?
A set of data with a normal distribution has a mean of 16.4 and standard deviation of 3.2.
15. __________ and __________
68% of the data is between what two numbers?
16. __________ and __________
95% of the data is between what two numbers?
17. __________
What percent of the population (data) is below 13.2?
A set of data with a normal distribution has a mean of 120 and standard deviation of 15.
18. __________ 2.5% of the data is above what value?
19. __________ 16% of the data is below what value?
20. __________
What percent of the data is above 135?
21. __________
What percent of the data is below 90?