Movie budget amounts (in million of dollars) 4.5 5 6.5 7 20 20 29 30 35 40 40 41 50 52 60 65 68 68 70 70 70 72 74 75 80 100 113 116 120 125 132 150 160 200 225 Find the value of the 78th percentile, P78 113 116 114.5 120
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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Movie budget amounts (in million of dollars)
4.5 5 6.5 7 20 20 29 30 35 40
40 41 50 52 60 65 68 68 70 70
70 72 74 75 80 100 113 116 120 125
132 150 160 200 225
Find the value of the 78th percentile, P78
113
116
114.5
120
In this problem, you want to find the 78th percentile in the data set. At least 78% of the data values will be less than this number.
Take note that there are 35 data values in this data set. Therefore, N= 35
We need to sort them in ascending order.
4.5,5,6.5,7,20,20,29,30,35,40,40,41,50,52,60,65,68,68,70,70,70,72,74,75,80,100,113,116,120,125,132,150,160,200,225
The index of the sorted data set represents the position. The first number, 4.5 has an index of 1, the second, 5 has an index of 2, etc. To find the index of the 78th percentile, apply the formula
where i represents the index. Substituting in the values for this problem, we have
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