(i) Tabulate the marks as a frequency distribution grouping in interval of 10 marks, namely 0–9, 10–19, 20–29 etc., determine whether the general performance of students is low or high using coefficient of skewness p=3(mean-median)/standard deviation (II) If scoring at least 75% is to get distinction, determine the standard score of students who got distinctive mark. (iii) The headmaster wants you to compile students' scores within the interquartile range. For what range of marks would you report?
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 is a record of marks obtained by a group of 50 candidates in an examination.
48 63 62 59 12 57 37 38 81 43
44 28 18 23 2 25 42 40 90 63
62 83 8 27 58 54 81 91 45 31
43 19 93 72 25 63 82 71 38 63
46 17 7 9 23 38 45 88 15 19
(i) Tabulate the marks as a frequency distribution grouping in interval of 10 marks, namely 0–9, 10–19, 20–29 etc., determine whether the general performance of students is low or high using coefficient of skewness p=3(mean-
(II) If scoring at least 75% is to get distinction, determine the standard score of students who got distinctive mark.
(iii) The headmaster wants you to compile students' scores within the
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