The monthly income of employees in a small company is summarised in the table below: Monthly salary (N$) Number of employees [2000 – 2499] 10 [2500 – 2999] 6 [3000 – 3499] 12 [3500 – 3999] 2 Required: Calculate the following descriptive statistics for the random variable Monthly salary (N$): a) Standard deviation. b) 50th percentile and interpretation. c) Most common value and interpretation
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.
The monthly income of employees in a small company is summarised in the table below:
|
Monthly salary (N$) |
Number of employees |
|
[2000 – 2499] |
10 |
|
[2500 – 2999] |
6 |
|
[3000 – 3499] |
12 |
|
[3500 – 3999] |
2 |
Required:
Calculate the following
a) Standard deviation.
b) 50th percentile and interpretation.
c) Most common value and interpretation
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