Marks Relative Frequency 0
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.
![1. College X organised a mid-semester test in last September. The marks of 135 students were recorded in the
following table.
Marks
Relative Frequency
8.
0<xs 20
135
31
20 < x< 40
135
41
40 < x S 60
135
60 < x S 80
45
34
80 <xs 100
135
a) Find the upper quartile.
b) Calculate the median, mean and the standard deviation of the marks.
c) Hence, find the Pearson's coefficient of skewness and interpret your answer.
d) State with reason, which of the above measures of location better describes the distribution of the data.
e) From the analysis of students' marks, Mr Adam decided to do one-to-one consultation with his low-ability
students and give 5 questions per week as a revision to the rest of his students. Calculate the mark
required to join the consultation if 55% of his students were assigned to do the revision.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F936a432c-cdf3-4d15-8d5a-7b8903a4a1b7%2F5f00f2cc-57f5-4c38-83ab-6c10d60db0ba%2F8mqu5y_processed.jpeg&w=3840&q=75)
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