what is the third quartile, Q3 of the following distribution: 4,5,33,10,12,14,34,43,21,22,21,22,44,29,16,18,20,24,26,29?
It’s 29
Please arrange these in numerical order. Then we can help you find the third quartile.
Once they are arranged in order of value, Q3 is the 75 percentile, 3/4 of the scores have value ≤ Q3.
To find the third quartile (Q3) of a distribution, you first need to arrange the numbers in ascending order. Here is the given distribution in ascending order: 4, 5, 10, 12, 14, 16, 18, 20, 21, 21, 22, 22, 24, 26, 29, 29, 33, 34, 43, 44.
Since there are 20 numbers in the distribution, Q3 will be the median of the second half of the numbers. In this case, the second half is from the 11th number to the 20th number.
Looking at the ordered list, the 11th number is 21 and the 20th number is 44. Therefore, the second half of the distribution is 21, 21, 22, 22, 24, 26, 29, 29, 33, 34, 43, 44.
To find the median of this second half, calculate the average of the two middle numbers. The middle numbers in this case are the 6th and 7th numbers: 26 and 29.
Add these two numbers together: 26 + 29 = 55. Then, divide the sum by 2: 55 / 2 = 27.5.
Thus, the third quartile (Q3) of the given distribution is 27.5.