Math Problem Statement
39
45
48
43
44
44
37
50
41
45
40
44
48
40
47
41
48
39
41
42
42
41
40
40
54
42
41
39
41
39
48
42
43
44
60
36
39
36
38
42
what is the third quartile
Solution
To find the third quartile (Q3), also known as the 75th percentile, follow these steps:
- Sort the data: First, arrange the numbers in increasing order.
Sorted dataTo find the third quartile (Q3), also known as the 75th percentile, follow these steps:
- Sort the data: First, arrange the numbers in increasing order.
Sorted 36, 36, 37, 38, 39, 39, 39, 39, 40, 40, 40, 40, 41, 41, 41, 41, 41, 42, 42, 42, 42, 42, 43, 43, 44, 44, 44, 44, 44, 45, 45, 47, 48, 48, 48, 48, 50, 54, 60
-
Find the position of Q3: The formula to find the position of Q3 is:
where is the number of data points. In this case, there are 39 data points, so:
The 30th value in the sorted data is the third quartile.
-
Locate Q3: The 30th value in the sorted data is 44.
Thus, the third quartile (Q3) is 44.
Would you like further details or clarifications?
Here are five related questions:
- How do you find the median (Q2) in a dataset?
- What is the significance of quartiles in a dataset?
- How is the interquartile range (IQR) calculated?
- Can you calculate the first quartile (Q1) from this dataset?
- What are outliers, and how are they related to quartiles?
Tip: Quartiles divide a data set into four equal parts, helping to understand its spread and distribution.
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Math Problem Analysis
Mathematical Concepts
Statistics
Quartiles
Percentiles
Formulas
Q3 = 3(n+1)/4
Theorems
Quartile theorem
Suitable Grade Level
Grades 8-10