Consider a sample with data values of 10, 20, 12, 17, and 16. Perform the following computations WITH and WITHOUT using the Excel commands. Compute the range and interquartile range. Compute the variance and the standard deviation. Create and interpret a box-plot (i.e. interpret such characteristics as the width of the boxplot, the line in the box etc.). Are there any outliers in this distribution? Why (not)?
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.
Problem Set 4: Measures of Dispersion
Consider a sample with data values of 10, 20, 12, 17, and 16. Perform the following computations WITH and WITHOUT using the Excel commands.
- Compute the
range andinterquartile range . - Compute the variance and the standard deviation.
- Create and interpret a box-plot (i.e. interpret such characteristics as the width of the boxplot, the line in the box etc.). Are there any outliers in this distribution? Why (not)?
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