Adjusted frequency 50 40 30 20 10 50 60 70 80 100 Mark 40 (a) Based on the histogram above, (i) give two comments for the students' performance in this test, construct a frequency distribution table, cumulative relative frequency and cumulative percentage of the marks. (ii) (b) Based on the frequency distribution table in part (a)(ii), (i) calculate the mean and standard deviation of the marks, (ii) draw a cumulative frequency curve. Hence, from the curve find the (A) value of X , if 30% of the data were at least X, (B) interquartile range (IQR) of the marks.
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 following histogram shows the mark distribution of the selected 200 students in a statistics test:
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