Readers ask: Explain how two samples can have the same mean but different standard deviations?

Can 2 sets of data have the same mean but a different standard deviation?

Yes, absolutely! Both the median and mean are measures of “central tendency”, whereas the standard deviation measures spread around this measure. So yes, it’s definitely possible to have the same mean/median but completely different spreads around this.

Could two samples have the same mean but different ranges explain?

a. Could two samples have the same mean but different ranges? Yes, the mean does not reflect the distribution of numbers.

How do you compare standard deviations with different means?

It tells us how far, on average the results are from the mean. Therefore if the standard deviation is small, then this tells us that the results are close to the mean, whereas if the standard deviation is large, then the results are more spread out.

Is it possible for two or more sets of values to have the same standard deviation and variance?

It is possible for two or more sets of values to have the same standard deviation and variance. The variance is equal to the square of standard deviation. The standard deviation is equal to the square of the variance.

What does the standard deviation tell you?

The standard deviation is the average amount of variability in your data set. It tells you, on average, how far each score lies from the mean.

When standard deviation increases what happens to your standard error?

Standard error increases when standard deviation, i.e. the variance of the population, increases. Standard error decreases when sample size increases – as the sample size gets closer to the true size of the population, the sample means cluster more and more around the true population mean.

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How is mean different from median?

The mean is the sum of all the numbers in the set (167) divided by the amount of numbers in the set (5). The median is the middle point of a number set, in which half the numbers are above the median and half are below.

How do I calculate mean?

The mean is the average of the numbers. It is easy to calculate: add up all the numbers, then divide by how many numbers there are. In other words it is the sum divided by the count.

How do you compare two datasets with different sample sizes?

One way to compare the two different size data sets is to divide the large set into an N number of equal size sets. The comparison can be based on absolute sum of of difference. THis will measure how many sets from the Nset are in close match with the single 4 sample set.

How do you find the standard deviation between two groups?

Population standard deviation

  1. Step 1: Calculate the mean of the data—this is μ in the formula.
  2. Step 2: Subtract the mean from each data point.
  3. Step 3: Square each deviation to make it positive.
  4. Step 4: Add the squared deviations together.
  5. Step 5: Divide the sum by the number of data points in the population.

How do you compare mean scores?

The four major ways of comparing means from data that is assumed to be normally distributed are:

  1. Independent Samples T-Test.
  2. One sample T-Test.
  3. Paired Samples T-Test.
  4. One way Analysis of Variance (ANOVA).
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What is the most frequently used measure of variability?

The standard deviation is the most commonly used and the most important measure of variability. Standard deviation uses the mean of the distribution as a reference point and measures variability by considering the distance between each score and the mean.

How would you interpret a very small variance or standard deviation but not equal to zero?

A variance of zero indicates that all of the data values are identical. All nonzero variances are positive. A small variance indicates that the data points tend to be very close to the mean, and to each other. A high variance indicates that the data points are very spread out from the mean, and from one another.

How do you find the standard deviation in statistics?

  1. The standard deviation formula may look confusing, but it will make sense after we break it down.
  2. Step 1: Find the mean.
  3. Step 2: For each data point, find the square of its distance to the mean.
  4. Step 3: Sum the values from Step 2.
  5. Step 4: Divide by the number of data points.
  6. Step 5: Take the square root.

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