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:

  1. 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:

  1. 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

  1. Find the position of Q3: The formula to find the position of Q3 is:

    Q3=3(n+1)4Q3 = \frac{3(n+1)}{4}

    where nn is the number of data points. In this case, there are 39 data points, so:

    Q3=3(39+1)4=1204=30Q3 = \frac{3(39+1)}{4} = \frac{120}{4} = 30

    The 30th value in the sorted data is the third quartile.

  2. 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:

  1. How do you find the median (Q2) in a dataset?
  2. What is the significance of quartiles in a dataset?
  3. How is the interquartile range (IQR) calculated?
  4. Can you calculate the first quartile (Q1) from this dataset?
  5. 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