The following data set gives the Life Orientation marks of a sample of Matric students who applied for university admission. LO marks 84 76 80 93 81 68 69 59 76 73 66 60 53 51 78 (a) Calculate the arithmetic mean (average). (b) Find the mode. (c) Find the median. (d) Calculate the sample variance. (e) Find the value of first quartile .Q1/. (f) Find the value of the third quartile .Q3/: (g) Draw a box plot for the data. (h) Find the 90th percentile of the data set.
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 data set gives the Life Orientation marks of a sample of Matric students who applied for university admission.
LO marks
84 76 80 93 81
68 69 59 76 73
66 60 53 51 78
(a) Calculate the arithmetic mean (average).
(b) Find the
(c) Find the median.
(d) Calculate the sample variance.
(e) Find the value of first
(f) Find the value of the third quartile .Q3/:
(g) Draw a box plot for the data.
(h) Find the 90th percentile of the data set.
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