The test grades for a certain class were entered into a Minitab worksheet, and then “Descriptive Statistics” were requested. The results were: 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 dataset simply by studying the set of descriptive statistics above. (a) Write a brief description of what the results tell you about the distribution of grades. Be sure to address: the general shape of the distribution unusual features, including possible outliers the middle 50% of the data any significance in the difference between the mean and the median
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 “
MTB > Describe 'Grades'.
N
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 dataset simply by studying the set of descriptive statistics above.
(a) Write a brief description of what the results tell you about the distribution of grades. Be sure to address:
- the general shape of the distribution
- unusual features, including possible outliers
- the middle 50% of the data
- any significance in the difference between the mean and the median
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