Range (and Approximation to Standard Deviation) Find the range for each of the following data sets a) (n= 6), M = 2.5 118, 127, 97, 152, 141, 104 b) (n= 10), M = 3 49, 53, 60, 60, 62, 63, 64, 69, 73, 87 c) (n= 28), M = 4 294, 276, 315, 341, 286, 254, 365, 333, 284, 295, 308, 317, 328, 342 251, 284, 295, 302, 319, 327, 372, 351, 274, 314, 335, 287, 291, 353
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 range for each of the following data sets
a) (n= 6), M = 2.5
118, 127, 97, 152, 141, 104
b) (n= 10), M = 3
49, 53, 60, 60, 62, 63, 64, 69, 73, 87
c) (n= 28), M = 4
294, 276, 315, 341, 286, 254, 365, 333, 284, 295, 308, 317, 328, 342
251, 284, 295, 302, 319, 327, 372, 351, 274, 314, 335, 287, 291, 353
The standard deviation can be (simply) approximated by the followin simple formula
where n varies depending on the size of the data set, as given in the following table.
data points divisor
n=4 M=2
n=6 M=2.5
n=10 M=3
n=28 M=4
n=50 M=4.5
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