   # Population Standard Deviation

Satisfactory Essays
The population standard deviation σ of a discrete random variable
,
Measure how close a random variable tends to be the population mean μ, so you must understand μ before you understand σ

If you have a random variable like a bet at a casino or and investment then the standard deviation σ measure the risk, if there is a lot of risk then the standard deviation is high

The formulas for standard deviation are given below but you should look at the examples first

Population mean
Population variance method 1 ,
Population variance method 2 ,
(it does not matter what method you use both give the same answer, the only thing you need to know about variance is that it is population standard deviation squared so if variance is high then standard deviation is high

Population standard deviation σ =

Example 1 find the population mean μ and population standard deviation σ of the gambling game with distribution.
Profit x
-2
2
Probability p(x)
0.5
0.5

This is a gambling game were there is a 50% chance of losing \$2 and a 50% chance of winning \$2
Solution
mean μ= -2×0.5+2×0.5=0
There are two methods for finding the population standard deviation squared σ2, they give the same answer and you can use either method in the exam
Method 1 σ2= (-2-0)2×0.5+(2-0)2×0.5 = 4
Method 2 σ2= (-2)2×0.5+22×0.5-02 = 4
So population standard deviation σ==2

Example 2 Consider an ordinary dice the common singular of dice is “die”
If you throw a dice you can get the numbers 1,2,3,4,5 or 6.
The probability of each of these events is 1/6 so the value of a dice has distribution
Ff x
1
2
3
4
5
6
Prp(x)
1/6
1/6
1/6
1/6
1/6
1/6
find the population mean μ and population standard deviation σ
Solution
Mean= μ=1×1/6+2×1/6+3×1/6+4×1/6+5×1/6+6×1/6=3.5
There are two methods for finding the population standard deviation squared σ2, they give the same answer and you can use either method in the exam
Method 1 for finding population standard deviation squared.
σ2=

## You May Also Find These Documents Helpful

• Powerful Essays

entering the actuarial field and finds the average salary to be \$41,000. The population standard deviation is \$3000. Can her claim be supported at 0.05? x¯=14.7, μx¯=13.77, ox¯=5.34, n=29, α=.01 3. Monthly Home Rent. The average monthly rent for a one bedroom in San Francisco is \$ 1229. A random sample of 15 one bedroom homes about 15 miles outside of San Francisco had a mean rent of \$1350. The population standard deviation is \$250. At a=0.05 can we conclude that the monthly rent outside San Francisco…

• 809 Words
• 4 Pages
Powerful Essays
• Good Essays

Inferences for One Population Standard Deviation The Standard deviation is a measure of the variation (or spread) of a data set. For a variable x, the standard deviation of all possible observations for the entire population is called the population standard deviation or standard deviation of the variable x. It is denoted σx or, when no confusion will arise, simply σ. Suppose that we want to obtain information about a population standard deviation. If the population is small, we can often determine…

• 466 Words
• 2 Pages
Good Essays
• Good Essays

Standard deviation can be difficult to interpret as a single number on its own. Basically, a small standard deviation means that the values in a statistical data set are close to the mean of the data set, on average, and a large standard deviation means that the values in the data set are farther away from the mean, on average. The standard deviation measures how concentrated the data are around the mean; the more concentrated, the smaller the standard deviation. A small standard deviation can…

• 507 Words
• 2 Pages
Good Essays
• Satisfactory Essays

Standard Deviation objective • Describe standard deviation and it’s importance in biostatistics. Measure of Dispersion • Indicates how widely the scores are dispersed around the central point (or mean.) -Standard deviation Standard Deviation. • The most commonly used method of dispersion in oral hygiene. • The larger the standard deviation, the wider the distribution curve. Standard Deviation • SD,  ,  (sigma) • Indicates how subjects differ from the average of the group/ the more they…

• 406 Words
• 4 Pages
Satisfactory Essays
• Good Essays

Deviation Definition: Behavior commonly seen in children that is the result of some obstacle to normal development such behavior may be commonly understand as negative (a timid child, a destructive child) or positive (a quite child), both positive and negative deviation will disappear once the child begins to concentrate on a piece of work freely chosen by him. The physical deforms are easier to identify. This can be by birth due to an accident etc… and most such physical deforms…

• 1161 Words
• 5 Pages
Good Essays
• Better Essays

I 'll be honest. Standard deviation is a more difficult concept than the others we 've covered. And unless you are writing for a specialized, professional audience, you 'll probably never use the words "standard deviation" in a story. But that doesn 't mean you should ignore this concept. The standard deviation is kind of the "mean of the mean," and often can help you find the story behind the data. To understand this concept, it can help to learn about what statisticians call normal distribution…

• 1144 Words
• 5 Pages
Better Essays
• Satisfactory Essays

Standard Deviation (continued) L.O.: To find the mean and standard deviation from a frequency table. The formula for the standard deviation of a set of data is [pic] Recap question A sample of 60 matchboxes gave the following results for the variable x (the number of matches in a box): [pic]. Calculate the mean and standard deviation for x. Introductory example for finding the mean and standard deviation for a table: The table shows the number of children living…

• 427 Words
• 2 Pages
Satisfactory Essays
• Good Essays

a. standard deviation b. mean c. variance d. range Answer: b 2. A numerical value used as a summary measure for a sample, such as sample mean, is known as a a. population parameter b. sample parameter c. sample statistic d. population mean Answer: c 3. Since the population size is always larger than the sample size, then the sample statistic a. can never be larger than the population parameter b. can never be equal to the population parameter…

• 2958 Words
• 12 Pages
Good Essays
• Good Essays

STANDARD DEVIATION The standard deviation is a popular measure of variability. It is used both as a separate entity and as a part of other analyses, such as computing confidence intervals and in hypothesis testing. The standard deviation is the square root of the variance. The population standard devia¬tion is denoted by σ. Like the variance, the standard deviation utilizes the sum of the squared deviations about the mean (SSx). It is computed by averaging these squared deviations (SSX/N) and…

• 539 Words
• 3 Pages
Good Essays
• Good Essays

A. What is the mean age of this sample? What is the standard deviation? The mean age is 47.5 years old. The standard deviation is 10.74832 years. http://www.calculator.net/standard-deviation-calculator.html Sample Standard Deviation, s: 10.748316881702 Sample Standard Variance, s2 115.52631578947 Total Numbers, N 20 Sum: 950 Mean (Average): 47.5 Population Standard Deviation, σ 10.476163419878 Population Standard Variance, σ2 109.75 If it follows the normal distribution The…

• 883 Words
• 4 Pages
Good Essays