Find the 45th percentile of the data set. Give your answer to three decimal places. Number of Hours My Classmates Spent Playing Video Games on Weekends 9.95 10 16.75 0 19.5 22.5 15 12.75 5.5 11 20.75 17.5 23 21.9 23.75 18 20 15 18.8 20.5 2.25 7.5 10 24 22.9
Answers 2
The 45th percentile of the data given above (P₄₅) is 16.225.
What is percentile in statistics?Percentile refers to the mathematical or statistical term that is used to indicate the position of a data in relation to others from the sample given.
How did we arrive at the above figure?Step 1 - First all data must be arranged in ascending order:
See the attached table for this.
Step 2 - We compute the position or rank of the 45th percentile.
The formula for percentile position is given as:((n +1 ) *P)/100
= ((25+1) * 45)/100
= 11.70
Step 3 - Deploy the interpolation method because the position above is not an integer.
The numbers in positions 11 and 12 are where you'll find the 45 percent percentile. Based on the data arranged in ascending order, the values are 15 and 16.75.
The percentile we're seeking for is situated at the value of 11.7 - 11 = 0.7, which is the percentage of the space between 15 and 16.75.
Therefore,
(P₄₅) = 15 + 0.7 x (16.75 - 15)
(P₄₅) =16.225.
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