The data set below represents the ages of 30 executives. Which ages are above the 75th percentile? 42 59 66 48 57 42 56 52 60 54 56 49 66 56 49 62 48 41 49 44 55 41 49 44 27 36 37 43 43 43 Determine the values in the data set above the 75th percentile. If a data value above the 75th percentile appears more than once in the data set, make sure to include that value in your answer the appropriate number of times.
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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59
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66
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48
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42
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56
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49
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66
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56
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62
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55
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41
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27
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Given information:
The data set representing the ages of n = 30 executives is provided below:
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42
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59
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66
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48
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57
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42
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56
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52
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60
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54
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56
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49
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66
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56
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49
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62
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48
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41
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49
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44
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55
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41
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49
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44
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27
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36
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37
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43
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43
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43
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To determine all those values that are above the k = 75th percentile.
In order to obtain the requirement of the problem, it is essential to evaluate the 75th percentile first. The computational work for the 75th percentile consists of the steps provided below:
- Arrange the data in increasing order.
- Multiply the value of k (in percent) with the total number of values (n). The number so obtained is known as an index.
- If the index does not result in a whole number, then round (up or down) it up to the nearest whole number.
- Count the values in the data set until the index value is obtained. The corresponding value is the kth percentile.
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