87,89,90,90,98,99,99,101,102,103,104
Find the 25th and 75th percentiles.
25th percentile means 25% of score ≤ a score. Likewise for 75th percentile.
To find the 25th and 75th percentiles of a given data set, we need to first arrange the data in ascending order.
Let's rearrange the data set in ascending order:
87, 89, 90, 90, 98, 99, 99, 101, 102, 103, 104
Now, we can find the 25th and 75th percentiles using the formulas:
25th Percentile = (25/100) * (n + 1)
75th Percentile = (75/100) * (n + 1)
where n is the total number of observations.
In this case, we have n = 11, so we can calculate:
25th Percentile = (25/100) * (11 + 1) = (25/100) * 12 = 0.25 * 12 = 3
75th Percentile = (75/100) * (11 + 1) = (75/100) * 12 = 0.75 * 12 = 9
To find the values corresponding to the 25th and 75th percentiles, we count from the lowest to the highest number:
25th Percentile: The 3rd value in the sorted list is 90. Therefore, the 25th percentile is 90.
75th Percentile: The 9th value in the sorted list is 102. Therefore, the 75th percentile is 102.
So, the 25th percentile is 90 and the 75th percentile is 102.