The test grades for a certain class were entered into a Minitab worksheet, and then DescriptiveStatistics were requested. The results were:MTB> Describe ‘Grades’.N MEAN MEDIAN TRMEAN STDEV SEMEANGrades 28 74.71 76.00 75.50 12.61 2.38MIN MAX Q1 Q3Grades 35.00 94.00 68.00 84.00You happened to see, on a scrap of paper, that the lowest grades were 35, 57, 59, 60, …but you don’t know what the other individual grades are. Nevertheless, a knowledgeable user ofstatistics can tell a lot about the data set simply by studying the set of descriptive statistics above.a. Write a description of what the results in the box tell you about the distribution of grades. Besure to address the general shape of the distribution, any unusual features, including possibleoutliers, the location of the middle 50% of the data and any significance in the differencebetween the mean and the median.b. Construct a boxplot for the test grades.
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 test grades for a certain class were entered into a Minitab worksheet, and then
Statistics
MTB> Describe ‘Grades’.
N MEAN MEDIAN TRMEAN STDEV SEMEAN
Grades 28 74.71 76.00 75.50 12.61 2.38
MIN MAX Q1 Q3
Grades 35.00 94.00 68.00 84.00
You happened to see, on a scrap of paper, that the lowest grades were 35, 57, 59, 60, …
but you don’t know what the other individual grades are. Nevertheless, a knowledgeable user of
statistics can tell a lot about the data set simply by studying the set of descriptive statistics above.
a. Write a description of what the results in the box tell you about the distribution of grades. Be
sure to address the general shape of the distribution, any unusual features, including possible
outliers, the location of the middle 50% of the data and any significance in the difference
between the mean and the median.
b. Construct a boxplot for the test grades.
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