this data represents 12 scored on a math test: 1,5,9,10,16,16,22,23,25,30,33,34
the cut-off for.the upper quartile lies between which two scores?
25 and 30
Thank you
You're welcome.
To find the cutoff for the upper quartile, we first need to determine the quartiles of the data set. Let's walk through the process step by step.
Step 1: Sort the data in ascending order:
1, 5, 9, 10, 16, 16, 22, 23, 25, 30, 33, 34
Step 2: Calculate the 1st quartile (Q1):
To find Q1, we need to find the median of the lower half of the data. Since we have 12 data points, the median will be the middle value of the lower 6 values:
1, 5, 9, 10, 16, 16
The median of this lower half is (9 + 10) / 2 = 9.5. So, Q1 = 9.5.
Step 3: Calculate the 3rd quartile (Q3):
To find Q3, we need to find the median of the upper half of the data. The median of the upper 6 values is:
22, 23, 25, 30, 33, 34
The median of this upper half is (25 + 30) / 2 = 27.5. So, Q3 = 27.5.
Now, we have Q1 = 9.5 and Q3 = 27.5.
Step 4: Determine the cutoff for the upper quartile:
The upper quartile (Q3) represents the 75th percentile of the data. To find the value between which the cutoff lies, we can look at the scores immediately above and below Q3.
In this case, the two scores surrounding Q3 are 25 and 30.
Therefore, the cutoff for the upper quartile lies between 25 and 30.