2. The following table shows the IQ test scores of some students: IQ test score Frequency 9 50-59 60-69 13 70-79 27 80-89 13 90-99 9. (a) Construct the relative frequency, cumulative frequency and cumulative relative frequency distribution (b) What percentage of students have IQ (c) Find the mean and variance of IQ score of the students. ore under 60?
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 table shows the IQ test scores of some students:
IQ test score 50-59 60-69 70-79 80-89 90-99
Frequency 9 13 27 13 9
(a)Construct the relative frequency, cumulative frequency and cumulative relative frequency distribution
(b) What percentage of students have IQ score under 60?
(c) Find the mean and variance of IQ score of the students. (d)Construct the frequency histogram from the above data, and
comment on the shape of the distribution.
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(e) Using your answers of the above questions find the median and mode
IQ test score of students. Interpret the values of median and mode.
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(f) Find an interval so that test score will fall within two standard deviations of the mean. Using an appropriate rule, mention the
percentage of scores that this interval contains.
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