Find the third quartile Q3 of the list of 24 sorted values shown below.
30 32 33 34 37 37 40 42 43 48 49 50 50 52 57 59 60 61 63 65 67 71 72 7430 32 33 34 37 37 40 42 43 48 49 50 50 52 57 59 60 61 63 65 67 71 72 74
It looks like you have repeated the list of scores.
30 32 33 34 37 37 40 42 43 48 49 50 50 52 57 59 60 61 63 65 67 71 72 74
Q3 = 75th percentile = 62
To find the third quartile (Q3) of a list of values, you need to divide the list into two halves: the lower half and the upper half. Q3 represents the value below which approximately 75% of the data lies.
In this case, the list of values is:
30 32 33 34 37 37 40 42 43 48 49 50 50 52 57 59 60 61 63 65 67 71 72 74
The first step is to sort the list in ascending order:
30 32 33 34 37 37 40 42 43 48 49 50 50 52 57 59 60 61 63 65 67 71 72 74
Next, you need to determine the position of Q3. Since Q3 represents the value below which approximately 75% of the data lies, you need to find the index position corresponding to the 75th percentile. To do this, you can use the formula:
Index position = (75/100) * (n + 1)
where n is the number of values in the list.
In this case, n = 24, so the index position for Q3 is:
Index position = (75/100) * (24 + 1) = (0.75) * 25 = 18.75
Since the index position is not a whole number, you need to take the average of the values at the 18th and 19th index positions. In this case:
Q3 = (value at 18th index position + value at 19th index position) / 2
Q3 = (60 + 61) / 2 = 121 / 2 = 60.5
Therefore, the third quartile (Q3) of the given list of values is 60.5.