A class took an English test and a Math test. The test scores of 25 students for both tests are given below: English test score: 60, 35, 80, 88, 76, 30, 66, 50, 75, 78, 56, 50, 80, 47, 90, 78, 95, 75, 82, 86, 78, 72, 69, 55, 50. Math test score: 80, 40, 45, 85, 90, 95, 65, 75,55, 33, 86, 85, 70, 78, 55, 60, 65, 69, 45, 55, 90, 95, 85, 70, 80. a) Find out the five-number summary for the datasets above. b) Develop a box and whisker plot for the test scores of English and Maths. What conclusion can you make about the students' performance?
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.
A class took an English test and a Math test. The test scores of 25 students for both tests are given below:
English test score: 60, 35, 80, 88, 76, 30, 66, 50, 75, 78, 56, 50, 80, 47, 90, 78, 95, 75, 82, 86, 78, 72, 69, 55, 50.
Math test score: 80, 40, 45, 85, 90, 95, 65, 75,55, 33, 86, 85, 70, 78, 55, 60, 65, 69, 45, 55, 90, 95, 85, 70, 80.
a) Find out the five-number summary for the datasets above.
b) Develop a box and whisker plot for the test scores of English and Maths. What conclusion can you make about the students' performance?
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