For 6 7 7 12 12 11 9 9 8 4 6 13 14: σ=3.0947
3.898717738 is the standard deviation.
For 51 11 21 394145: σ = 197,058.6674
2
No. The set of whole numbers does not include negative numbers. There are 11 integers in that range.
(85 - 58)/11 = 27/11 = 2.4545.. sd
It is approx 2.828
3.898717738 is the standard deviation.
5.142857143 is the mean.12.43956044 is the variance.3.526976104 is the standard deviation.
For 8 9 9 9 10 11 11 12: σ=1.3562
7.087547766 is the standard deviation for those figures.
For 51 11 21 394145: σ = 197,058.6674
If "standard" is meant to be standard deviation, the answer is the second.
11
The purpose of obtaining the standard deviation is to measure the dispersion data has from the mean. Data sets can be widely dispersed, or narrowly dispersed. The standard deviation measures the degree of dispersion. Each standard deviation has a percentage probability that a single datum will fall within that distance from the mean. One standard deviation of a normal distribution contains 66.67% of all data in a particular data set. Therefore, any single datum in the data has a 66.67% chance of falling within one standard deviation from the mean. 95% of all data in the data set will fall within two standard deviations of the mean. So, how does this help us in the real world? Well, I will use the world of finance/investments to illustrate real world application. In finance, we use the standard deviation and variance to measure risk of a particular investment. Assume the mean is 15%. That would indicate that we expect to earn a 15% return on an investment. However, we never earn what we expect, so we use the standard deviation to measure the likelihood the expected return will fall away from that expected return (or mean). If the standard deviation is 2%, we have a 66.67% chance the return will actually be between 13% and 17%. We expect a 95% chance that the return on the investment will yield an 11% to 19% return. The larger the standard deviation, the greater the risk involved with a particular investment. That is a real world example of how we use the standard deviation to measure risk, and expected return on an investment.
The average age is 11 to 12 years of age. Standard deviation is 2 years.
A large standard deviation indicates that the distribution is heavily weighted far from the mean. Take the following example: {1,1,1,1,1,19,19,19,19,19} Mean is 10 and StDev = 9.49 Now look at this data set: {5, 6, 7, 8, 9, 11, 12, 13, 14, 15} Mean is still 10, but StDev = 3.5
IQ is based on an average of 100 and a standard deviation of 15 for any group