Please read the following instructions carefully before attempting any question: 1. Attempt all questions. Solve all questions on the Answer Script. 2. Draw neat sketches where necessary. Do not use pencil, except for diagrams/sketches. 3. Label the answers with proper question numbers. 4. All rough work must be done in the Answer Script. 5. Any attempt to use unfair means will disqualify from the examination. 6. All students must comply with any other instruction given in the Examination Hall. Q) Consider the following data: 33 2 43 47 34 38 38 20 33 9 36 2 14 3 5 42 35 16 48 22 20 39 40 10 25 23 33 36 38 14 34 33 9 6 25 48 18 30 12 Make frequency distribution using 5 classes and find the following: a) Arithmetic Mean b) Median c) Mode d) All quartiles e) 3rd Deciles f) 46th Percentile g) Coefficient of Skewness
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.
- Q) Consider the following data:
33 2 43 47 34 38 38 20 33 9 36 2 14 3 5 42 35 16 48 2 22 20 39 40 10 25 23 33 36 38 14 34 33 9 6 25 48 18 30 12
Make frequency distribution using 5 classes and find the following:
- Arithmetic Mean
Median Mode - All
quartiles - 3rd Deciles
- 46th Percentile
- Coefficient of Skewness
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