Given below are recent measurements from the Old Faithful geyser in Yellowstone National Park. The time intervals (in minutes) between eruptions are76 84 76 103 92 47 98 54 80 91 69 86 83 75 9389 96 65 94 85 94 60 94 86 93 88 61 96 52 981. Find the mean. Round to one significant digit.2. Find the mode(s).3. Find the standard deviation. Round to one significant digit.4. Based on the Empirical Rule, about 68% of measurements are between ______ minutes and _______ minutes.5. Using Chebyshev’s theorem, what do you know about the percentage of time intervals (in minutes) between eruptions are within 3 standard deviations of the mean, or between _________ minutes and ________ minutes?6. Determine whether there is any outlier. 7. Construct a boxplot for this data set.8. Based on the boxplot in #7, are the data approximately normally distributed?9. Find the percentile of 92 minutes.10. Find the 35th percentile.
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.
Given below are recent measurements from the Old Faithful geyser in Yellowstone National Park. The time intervals (in minutes) between eruptions are
76 84 76 103 92 47 98 54 80 91 69 86 83 75 93
89 96 65 94 85 94 60 94 86 93 88 61 96 52 98
1. Find the mean. Round to one significant digit.
2. Find the
3. Find the standard deviation. Round to one significant digit.
4. Based on the
5. Using Chebyshev’s theorem, what do you know about the percentage of time intervals (in minutes) between eruptions are within 3 standard deviations of the mean, or between _________ minutes and ________ minutes?
6. Determine whether there is any outlier.
7. Construct a boxplot for this data set.
8. Based on the boxplot in #7, are the data approximately
9. Find the percentile of 92 minutes.
10. Find the 35th percentile.
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