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To find the numerator of the variance for the class population, first calculate the mean of the test scores: (90 + 75 + 72 + 88 + 85) / 5 = 82. The numerator is the sum of the squared differences between each score and the mean. Calculating these differences: (90 - 82)² = 64, (75 - 82)² = 49, (72 - 82)² = 100, (88 - 82)² = 36, (85 - 82)² = 9. Adding these squared differences gives 64 + 49 + 100 + 36 + 9 = 258. Thus, the value of the numerator is 258.
What else can I help you with?
What does n-1 indicate in a calculation for variance?
The n-1 indicates that the calculation is being expanded from a sample of a population to the entire population. Bessel's correction(the use of n − 1 instead of n in the formula) is where n is the number of observations in a sample: it corrects the bias in the estimation of the population variance, and some (but not all) of the bias in the estimation of the population standard deviation. That is, when estimating the population variance and standard deviation from a sample when the population mean is unknown, the sample variance is a biased estimator of the population variance, and systematically underestimates it.
What is n-1in statistics?
In statistics, "n-1" refers to the degrees of freedom used in the calculation of sample variance and sample standard deviation. When estimating variance from a sample rather than a whole population, we divide by n-1 (the sample size minus one) instead of n to account for the fact that we are using a sample to estimate a population parameter. This adjustment corrects for bias, making the sample variance an unbiased estimator of the population variance. It is known as Bessel's correction.
Is sample variance unbiased estimator of population variance?
No, it is biased.
How do you prove that the sample variance is equal to the population variance?
You cannot prove it because it is not true.The expected value of the sample variance is the population variance but that is not the same as the two measures being the same.
Why the sample variance is an unbiased estimator of the population variance?
The sample variance is considered an unbiased estimator of the population variance because it corrects for the bias introduced by estimating the population variance from a sample. When calculating the sample variance, we use ( n-1 ) (where ( n ) is the sample size) instead of ( n ) in the denominator, which compensates for the degree of freedom lost when estimating the population mean from the sample. This adjustment ensures that the expected value of the sample variance equals the true population variance, making it an unbiased estimator.
How to calculate narrow sense heritability in a population?
To calculate narrow sense heritability in a population, you can use the formula: h (Vg / Vp), where h is the narrow sense heritability, Vg is the genetic variance, and Vp is the total phenotypic variance. This calculation helps estimate the proportion of phenotypic variation that is due to genetic factors.
What does it mean to say that the sample variance provides an unbiased estimate of the population variance?
It means you can take a measure of the variance of the sample and expect that result to be consistent for the entire population, and the sample is a valid representation for/of the population and does not influence that measure of the population.
What is the variance of 6.6 8.5 4.6 1.7 2.4?
(Population) variance = 6.4664
What is the proof that the sample variance is an unbiased estimator?
The proof that the sample variance is an unbiased estimator involves showing that, on average, the sample variance accurately estimates the true variance of the population from which the sample was drawn. This is achieved by demonstrating that the expected value of the sample variance equals the population variance, making it an unbiased estimator.
The sample variance is always smaller than the true value of the population variance is always larger than the true value of the population variance could be smaller equal to or?
yes, it can be smaller, equal or larger to the true value of the population varience.
When the null hypothesis is true the ratio of the between groups population variance estimate to the within groups population variance estimate should be about?
1
In analysis of variance the magnitude of the mean differences from one treatment to another will contribute to the numerator of the f-ratio the denominator of the f-ratio both neither?
the numerator of the F-ratio
