how do you find the quartile Q3 of the list of 24 sorted values: 30,33,35,38,40,46,46,47,47,49,50,51,53,53,54,56,60,65,73,74,77,78. what is the formuala and how do you work it?
If they are in order of value lowest to highest, the value at the 75th percentile is Q3, the 18th score.
Find the list quartile of 11 22 14 48 46 54 62 72
To find the quartile Q3, also known as the third quartile, of a list of sorted values, you need to follow these steps:
Step 1: Arrange the list of values in ascending order.
The given list of values is already sorted, so we can proceed to the next step.
Step 2: Calculate the position of Q3 using the formula:
Position of Q3 = (3 * n + 1) / 4, where n is the total number of values in the list.
In this case, n = 24, so substituting it into the formula:
Position of Q3 = (3 * 24 + 1) / 4
Position of Q3 = 73 / 4
Position of Q3 ≈ 18.25
Step 3: Identify the values at the calculated position.
Since we have a fractional position, we need to interpolate to find the actual values at the 18th and 19th positions, considering the values surrounding them.
The value at position 18: 65
The value at position 19: 73
Step 4: Calculate the Q3 value.
Q3 is the average of the values at the 18th and 19th positions:
Q3 = (65 + 73) / 2
Q3 = 138 / 2
Q3 = 69
Therefore, the third quartile (Q3) of the given list of sorted values is 69.