9
It is approx 2.828
The absolute deviation of 10, 7, 13, 10, 8 is 9.6.
The mode is the data set element(s) that is(are) repeated the most. If every data set element occurs the same number of times, there is no mode. As there is only one occurrence of each data set element in {11, 12, 13} there is no mode. If your data set read {11, 12, 12, 13, 13, 12} your mode would be 12. If your data set read {11, 12, 12, 13, 13} your modes would be 12 & 13.
It is 3.045
156
It is approx 2.828
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.
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
It means that all of the ten numbers are 15!Standard deviation tells you how spread out the data is from the mean value. Or in other words, it tells you how far the numbers in your data are away from the mean value.If the standard deviation is a high number, it means the data is largely spread out and that there are big differences in the data. The numbers in the data would be quite far from each other. For example, if you had data like: 8, 35, 13, 47, 22, 64, this would probably mean that you'll get a high standard deviation because each of the numbers are very spread out.On the other hand, if the standard deviation is small, it tells you that the numbers in the data are quite close together and that there is only a small difference between the numbers in the data. For example, if you had data like: 19, 25, 20, 22, 23, 18, this would probably mean that you'll get a low standard deviation because each of the numbers aren't that spread outIn the scenario you've given, the standard deviation is ZERO. This means that there is no spread or variation AT ALL with the numbers in your data. This means every single number in the data is the same.Since your mean is 15 and every number in your data is the same, that means that all the ten numbers in your data have to be 15!Hope that makes sense.Jamz159
The mean of the 10th and 11th values
The mean of the 3rd and 4th values
The absolute deviation of 10, 7, 13, 10, 8 is 9.6.
The mean absolute deviation is 2
The variance is 13.5833
It is 52.
The mode is the data set element(s) that is(are) repeated the most. If every data set element occurs the same number of times, there is no mode. As there is only one occurrence of each data set element in {11, 12, 13} there is no mode. If your data set read {11, 12, 12, 13, 13, 12} your mode would be 12. If your data set read {11, 12, 12, 13, 13} your modes would be 12 & 13.
It is 2.8