Here are the scores of 16 students on a history test. 61, 63, 70, 72, 75, 75, 76, 79, 79, 81, 82, 84, 84, 89, 91, 95. Notice that the scores are ordered from least to greatest. Make a box-and-whisker plot for the data. +++D 60 65 70 75 80 85 90 95 Score
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.
This box-and-whisker plot visually represents the distribution of the scores.
- **Whiskers**: These extend to the minimum score (61) and the maximum score (95).
- **Box**: The ends of the box represent the first quartile (around 72) and the third quartile (around 84).
- **Median**: The line inside the box indicates the median score (around 79).
The plot helps to identify the spread and the central tendency of the scores, as well as any potential outliers. The whiskers indicate the range of the data set, while the box shows the interquartile range.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff603335b-518a-4d3a-a76f-67abdbef85df%2F925a83e5-95d2-44ff-ad5b-347a942a42db%2Fme14pgg_processed.jpeg&w=3840&q=75)
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