Find the mean, median, and mode for each of the following sets of scores. a) 3, 4, 4, 6, 6, 6, 6, 7, 7, 9, 9 b) 6, 8, 5, 5, 8, 9, 6, 28, 4 In which of the sets of scores in question #1 is the mean a poor measure of central tendency? Why?
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.
- Find the
mean ,median , andmode for each of the following sets of scores.
a) 3, 4, 4, 6, 6, 6, 6, 7, 7, 9, 9
b) 6, 8, 5, 5, 8, 9, 6, 28, 4
- In which of the sets of scores in question #1 is the mean a poor measure of
central tendency ? Why?
Measures of Dispersion (Variability)
3. For the following sets of scores, calculate the sum of squares, the variance, and the standard deviation (2 points per set). (Please calculate the standard deviation and variance based on a SAMPLE.)
a) 2, 4, 7, 3, 8, 9, 10, 26
b) 3, 5, 6, 7, 8, 9, 10, 11
4. Why is the standard deviation in Question 3a so large? Describe the effects of extreme deviations on the standard deviation.
Locating Scores in the Population
5. For a population with μ = 70 and σ = 10
a) the proportion of the
z = -.35
z = 1.00
b) the proportion of the normal distribution that is located above the following z-scores
z = -.55
z = 1.25
c) the proportion of the normal distribution that is located between the two z-score values
z = .75 and z = 1.50
z = -0.50 and z = 0.75
6. Scores on the SAT form a normal distribution with μ = 500 and σ = 100. What is the minimum score necessary to be in the top 25% of the SAT distribution?
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