Here is a frequency distribution table (HDI) data value frequency 24 18 25 27 26 19 27 26 28 24 Find the following measures of central tendency. mean (z) = (Please show your answer to one decimal place.)
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.
Given data:
| Data value (x) | Frequency (f) |
| 24 | 18 |
| 25 | 27 |
| 26 | 19 |
| 27 | 26 |
| 28 | 24 |
(a) Calculation of mean:
Formula:
| Data value (x) | Frequency (f) | |
| 24 | 18 | 432 |
| 25 | 27 | 675 |
| 26 | 19 | 494 |
| 27 | 26 | 702 |
| 28 | 24 | 672 |
| 114 | 2975 |
Substitute the values in the formula:
Thus, the value of mean is 26.1
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