What is the third quartile Q3 for data 2, 5, 5, 9, 11, 12, 13, 16, 17, 19, 22, 23, 24, 25,
28 ?
To find the third quartile Q3, we need to divide the data set into two halves and find the median of the upper half.
First, we find the median of the entire data set:
2, 5, 5, 9, 11, 12, 13, 16, 17, 19, 22, 23, 24, 25, 28
The median is the middle value of this sorted set of numbers, which is 16.
Next, we divide the data set into two halves:
Lower half: 2, 5, 5, 9, 11, 12, 13
Upper half: 16, 17, 19, 22, 23, 24, 25, 28
The median of the upper half is the third quartile Q3.
The median of the upper half is the middle value of this sorted set of numbers:
16, 17, 19, 22, 23, 24, 25, 28
The middle two numbers are 22 and 23, so we take their average:
(22 + 23) / 2 = 22.5
Therefore, the third quartile Q3 is 22.5.
To find the third quartile (Q3), also known as the upper quartile, you need to first arrange the data in ascending order.
The given data in ascending order:
2, 5, 5, 9, 11, 12, 13, 16, 17, 19, 22, 23, 24, 25, 28
1. Calculate the position of Q3:
Q3 position = (3/4) * (total number of data points + 1)
Total number of data points = 15
Q3 position = (3/4) * (15 + 1) = (3/4) * 16 = 12
2. Since the position is not a whole number, you need to take the average of the values at the 12th and 13th position.
Values at the 12th and 13th position: 22 and 23
3. Calculate Q3 by taking the average of the two values:
Q3 = (22 + 23) / 2 = 45 / 2 = 22.5
Therefore, the third quartile (Q3) for the given data is 22.5.