Complete the table. Ages Sample mean, ¯x 80, 80 80 80, 55 67.5 80, 57 68.5 55, 80 67.5 55, 55 55 55, 57 56 57, 80 68.5 57, 55 56 57, 57 57 This shows that the mean of all the sample means equals the population mean. f) What is the the standard deviation of all the sample means? g) What is the standard error, σ√nσn where σσ is the population standard deviation and nn is the sample size? This shows that the standard error equals the standard deviation of all the possible sample means.
Inverse Normal Distribution
The method used for finding the corresponding z-critical value in a normal distribution using the known probability is said to be an inverse normal distribution. The inverse normal distribution is a continuous probability distribution with a family of two parameters.
Mean, Median, Mode
It is a descriptive summary of a data set. It can be defined by using some of the measures. The central tendencies do not provide information regarding individual data from the dataset. However, they give a summary of the data set. The central tendency or measure of central tendency is a central or typical value for a probability distribution.
Z-Scores
A z-score is a unit of measurement used in statistics to describe the position of a raw score in terms of its distance from the mean, measured with reference to standard deviation from the mean. Z-scores are useful in statistics because they allow comparison between two scores that belong to different normal distributions.
Complete the table.
| Ages | Sample |
|---|---|
| 80, 80 | 80 |
| 80, 55 | 67.5 |
| 80, 57 | 68.5 |
| 55, 80 | 67.5 |
| 55, 55 | 55 |
| 55, 57 | 56 |
| 57, 80 | 68.5 |
| 57, 55 | 56 |
| 57, 57 | 57 |
This shows that the mean of all the sample means equals the population mean.
f) What is the the standard deviation of all the sample means?
g) What is the standard error, σ√nσn where σσ is the population standard deviation and nn is the sample size?
This shows that the standard error equals the standard deviation of all the possible sample means.
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