The following data represent the length of shaft life of machine, in years of 36 machines Table 1 19 21 12 11 23 14 12 19 18 13 15 7 20 11 14 18 17 12 12 19 15 6 15 6 10 6 25 20 16 9 8 11 6 14 14 10 a. Construct a cumulative and relative frequency distribution using 6 classes. b. Find the mean, median and mode for the life span of shaft. c. Find 4th deciles and 41th percentile d. Also construct the histogram and comment the shape of the data.
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 represent the length of shaft life of machine, in years of 36 machines
Table 1
19 21 12 11 23 14 12 19 18
13 15 7 20 11 14 18 17 12
12 19 15 6 15 6 10 6 25
20 16 9 8 11 6 14 14 10
a. Construct a cumulative and relative frequency distribution using 6 classes.
b. Find the mean,
c. Find 4th deciles and 41th percentile
d. Also construct the histogram and comment the shape of the data.
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