Consider the following dataset: 22,29,31,30,22,23,18,29,25. What is the third quartiles value
To find the third quartile value (Q3), first we need to arrange the dataset in numerical order:
18, 22, 22, 23, 25, 29, 29, 30, 31
Since there are 9 data points, the median (Q2) is the fifth value, which is 25.
Next, we divide the dataset into two halves:
Lower half: 18, 22, 22, 23
Upper half: 29, 29, 30, 31
To find the first quartile (Q1), we calculate the median of the lower half, which is the average of the 2nd and 3rd values: (22+23)/2 = 22.5
To find the third quartile (Q3), we calculate the median of the upper half, which is the average of the 2nd and 3rd values: (29+30)/2 = 29.5
Therefore, the third quartile value (Q3) is 29.5.