67.65
I will restate your question as "Why are the mean and standard deviation of a sample so frequently calculated?". The standard deviation is a measure of the dispersion of the data. It certainly is not the only measure, as the range of a dataset is also a measure of dispersion and is more easily calculated. Similarly, some prefer a plot of the quartiles of the data, again to show data dispersal.t Standard deviation and the mean are needed when we want to infer certain information about the population such as confidence limits from a sample. These statistics are also used in establishing the size of the sample we need to take to improve our estimates of the population. Finally, these statistics enable us to test hypothesis with a certain degree of certainty based on our data. All this stems from the concept that there is a theoretical sampling distribution for the statistics we calculate, such as a proportion, mean or standard deviation. In general, the mean or proportion has either a normal or t distribution. Finally, the measures of dispersion will only be valid, be it range, quantiles or standard deviation, require observations which are independent of each other. This is the basis of random sampling.
Yes, the coefficient of variation (CV) can be greater than 100%. The CV is calculated as the ratio of the standard deviation to the mean, expressed as a percentage. If the standard deviation is greater than the mean, which can occur in certain datasets, the CV will exceed 100%, indicating high relative variability compared to the average value.
99.6% for
.820=82.0%
A z score is a value that is used to indicate the distance of a certain number from the mean of a normally distributed data set. A z score of -1.0 means that the number is one standard deviation below the mean. A z score of +1.0 means that the number is one standard deviation above the mean. Z scores normally range from -4.0 to +4.0. Hope this helps! =)
It's used in determining how far from the standard (average) a certain item or data point happen to be. (Ie, one standard deviation; two standard deviations, etc.)
To see how wide spread the results are. If the average (mean) grade for a certain test is 60 percent and the standard deviation is 30, then about half of the students are not studying. But if the mean is 60 and the standard deviation is 5 then the teacher is doing something wrong.
Usually, industrial use of standard deviation is involved in quality control and testing. A product such as cement, is produced in batches, and I assume, requires periodic testing to ensure consistent properties. The sample test variations can be evaluated using standard deviation. If the standard deviation is high, it is likely that inferior product could be shipped. Probability analysis can determine the chance that product below certain standards would be shipped.
I will restate your question as "Why are the mean and standard deviation of a sample so frequently calculated?". The standard deviation is a measure of the dispersion of the data. It certainly is not the only measure, as the range of a dataset is also a measure of dispersion and is more easily calculated. Similarly, some prefer a plot of the quartiles of the data, again to show data dispersal.t Standard deviation and the mean are needed when we want to infer certain information about the population such as confidence limits from a sample. These statistics are also used in establishing the size of the sample we need to take to improve our estimates of the population. Finally, these statistics enable us to test hypothesis with a certain degree of certainty based on our data. All this stems from the concept that there is a theoretical sampling distribution for the statistics we calculate, such as a proportion, mean or standard deviation. In general, the mean or proportion has either a normal or t distribution. Finally, the measures of dispersion will only be valid, be it range, quantiles or standard deviation, require observations which are independent of each other. This is the basis of random sampling.
Using standard deviations someone can tell how likely a person is to do something, or how often the majority do, e.g. how much electricity is used by 90% of people or how likely they are to use a certain amount.
Brand A
About 98% of the population.
99.6% for
.820=82.0%
Anything that is normally distributed has certain properties. One is that the bulk of scores will be near the mean and the farther from the mean you are, the less common the score. Specifically, about 68% of anything that is normally distributed falls within one standard deviation of the mean. That means that 68% of IQ scores fall between 85 and 115 (the mean being 100 and standard deviation being 15) AND 68% of adult male heights fall between 65 and 75 inches (the mean being 70 and I am estimating a standard deviation of 5). Basically, even though the means and standard deviations change, something that is normally distributed will keep these probabilities (relative to the mean and standard deviation). By standardizing these numbers (changing the mean to 0 and the standard deviation to 1) we can use one table to find the probabilities for anything that is normally distributed.
A z score is a value that is used to indicate the distance of a certain number from the mean of a normally distributed data set. A z score of -1.0 means that the number is one standard deviation below the mean. A z score of +1.0 means that the number is one standard deviation above the mean. Z scores normally range from -4.0 to +4.0. Hope this helps! =)
In a certain city the mean price of a quart of milk is 63 cents and the standard deviation is 8 cents. The average price of a package of bacon is $1.80 and the standard deviation is 15 cents. If we pay $0.89 for a quart of milk and $2.19 for a package of bacon at a 24-hour convenience store, which is relatively more expensive? To answer this, we compute Z-scores for each: