A study examined how long aircraft air conditioning units operated after being repaired. Here are the operating times (in hours) for one unit: 97 51 11 4 141 18 142 68 77 80 1 16 106 206 82 54 31 216 46 111 39 63 18 191 18 163 24 (a) Make a histogram, using classes that are 40 hours wide, beginning with: 0 time 40, 40 time 80, . . . (b) Describe the overall shape of the distribution: Is it roughly symmetric, skewed to the right, or skewed to the left? Are there any outliers? (c) Is the five-number summary or the mean and standard deviation a better brief summary for this distribution? Explain your choice. Calculate the one of these summaries that you choose
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.
A study examined how long aircraft air conditioning units operated after being repaired. Here are the operating times (in hours) for one unit: 97 51 11 4 141 18 142 68 77 80 1 16 106 206 82 54 31 216 46 111 39 63 18 191 18 163 24
(a) Make a histogram, using classes that are 40 hours wide, beginning with: 0 time 40, 40 time 80, . . .
(b) Describe the overall shape of the distribution: Is it roughly symmetric, skewed to the right, or skewed to the left? Are there any outliers?
(c) Is the five-number summary or the mean and standard deviation a better brief summary for this distribution? Explain your choice. Calculate the one of these summaries that you choose.
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