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Why does the standard error become smaller simply by increasing the sample size?
Wiki User
∙ 11y ago
Because of the Law of Large Numbers. According to that law, the observations tends towards the mean. This increases the concentration of observations nears the mean thereby reducing the variance or standard error.
Wiki User
∙ 11y ago
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What does it mean when the standard error value is smaller than the standard deviation?
It simply means that you have a sample with a smaller variation than the population itself. In the case of random sample, it is possible.
How large a sample would be needed to have a standard error less than 2 points for population with a standard deviation of 20?
A sample of size 100.
If the standard error of a sample of 48 is equal to 14.25 the standard deviation is equal to?
98.73
Why is standard deviation of a statistic called standard error?
The standard error is the standard deviation divided by the square root of the sample size.
If the variance of the data values in a sample is 169 what is the standard deviation of the data values?
For a sample, the SD is 13.53, approx.
What does it mean when the standard error value is smaller than the standard deviation?
It simply means that you have a sample with a smaller variation than the population itself. In the case of random sample, it is possible.
Why is the standard error a smaller numerical value compared to the standard deviation?
Let sigma = standard deviation. Standard error (of the sample mean) = sigma / square root of (n), where n is the sample size. Since you are dividing the standard deviation by a positive number greater than 1, the standard error is always smaller than the standard deviation.
How does a sample size impact the standard deviation?
If I take 10 items (a small sample) from a population and calculate the standard deviation, then I take 100 items (larger sample), and calculate the standard deviation, how will my statistics change? The smaller sample could have a higher, lower or about equal the standard deviation of the larger sample. It's also possible that the smaller sample could be, by chance, closer to the standard deviation of the population. However, A properly taken larger sample will, in general, be a more reliable estimate of the standard deviation of the population than a smaller one. There are mathematical equations to show this, that in the long run, larger samples provide better estimates. This is generally but not always true. If your population is changing as you are collecting data, then a very large sample may not be representative as it takes time to collect.
Sample standard deviation?
Standard deviation in statistics refers to how much deviation there is from the average or mean value. Sample deviation refers to the data that was collected from a smaller pool than the population.
Describe how the sample size affects the standard error?
Standard error (which is the standard deviation of the distribution of sample means), defined as σ/√n, n being the sample size, decreases as the sample size n increases. And vice-versa, as the sample size gets smaller, standard error goes up. The law of large numbers applies here, the larger the sample is, the better it will reflect that particular population.
How does one calculate the standard error of the sample mean?
Standard error of the sample mean is calculated dividing the the sample estimate of population standard deviation ("sample standard deviation") by the square root of sample size.
How does increasing the sample size affect the sample error of the mean?
It should reduce the sample error.
What is the sample standard deviation of 27.5?
A single observation cannot have a sample standard deviation.
Does the standard deviation of x decrease in magnitude as the size of the sample gets smaller?
No. But a small sample will be a less accurate predictor of the standard deviation of the population due to its size. Another way of saying this: Small samples have more variability of results, sometimes estimates are too high and other times too low. As the sample size gets larger, there's a better chance that your sample will be close to the actual standard deviation of the population.
How does sample size affect the size of your standard error?
The standard error should decrease as the sample size increases. For larger samples, the standard error is inversely proportional to the square root of the sample size.The standard error should decrease as the sample size increases. For larger samples, the standard error is inversely proportional to the square root of the sample size.The standard error should decrease as the sample size increases. For larger samples, the standard error is inversely proportional to the square root of the sample size.The standard error should decrease as the sample size increases. For larger samples, the standard error is inversely proportional to the square root of the sample size.
Does the size of a sample affect the values of the frequency table?
Yes. If the sample is a random drawing from the population, then as the size increases, the relative frequency of each interval from the sample should be a better estimate of the relative frequency in the population. Now, in practical terms, increasing a small sample will have a larger effect than increasing a large sample. For example, increasing a sample from 10 to 100 will have a larger effect than increasing a sample from 1000 to 10,000. The one exception to this, that I can think of, is if the focus of the study is on a very rare occurrence.
Will margins of error for sample of size 80 be larger or smaller than those for sample size of 40?
They should be smaller for the sample size 80.
