The mean defined in the text is sometimes called the arithmetic mean to distinguish it from other possible means. For example, a different mean, called the harmonic mean (H.M.), is used to find average speeds. This mean is defined to be the sum of the reciprocals of all scores divided into the number of scores. For example, the harmonic mean of the numbers 4, 5, 6, 6, 7, 8 is H.M. = 1 1 + + + + 6. 1 1 1 1 + 8 4 5 = 5.7. (a) Find the arithmetic and harmonic mean of the numbers 2, 2, 4, 4, 7, 8, 8, 9, 9, 10. (Round your harmonic mean to one decimal place.) arithmetic mean harmonic mean (b) A trip from San Francisco to Disneyland is approximately 460 miles. If the southbound trip averaged 55 mph and the return trip averaged 61 mph, what is the average speed for the round trip? Compare the arithmetic and harmonic means. (Round your harmonic mean to one decimal place.) arithmetic mean mph harmonic mean mph
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.
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