The following table gives the scores of 30 students in a mathematics examination. Scores 90–99 80–89 70–79 60–69 50–59 Students 3 8 15 3 1 Find the mean and the standard deviation of the given data. Hint: Assume that all scores lying within a group interval take the middle value of that group. (Round your answers to two decimal places.) mean standard deviation
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 following table gives the scores of 30 students in a mathematics examination.
| Scores | 90–99 | 80–89 | 70–79 | 60–69 | 50–59 |
|---|---|---|---|---|---|
| Students | 3 | 8 | 15 | 3 | 1 |
Find the
| mean | |
| standard deviation |
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