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Example: Find the median of the following numbers. a) 6, 5, 2, 8, 9, 4. b) 2, 1, 8, 3, 5, 8.

Mathematics

ScanSolve AI Answer

Answers

2 parts
a

5.5\text{5.5}

b

4\text{4}

Step-by-step solution

10 steps

The problem asks us to find the median for two sets of numbers.

Part a· 5 steps

The numbers are: 2, 6, 5, 8, 9, 4.

  1. Arrange the numbers in ascending order.

    2,4,5,6,8,92, 4, 5, 6, 8, 9
  2. Count the total number of values (nn).

    There are 6 numbers in the set, so n=6n = 6.

  3. Determine the position of the median.

    Since nn is an even number, the median is the average of the two middle values. These are the values at positions n2\frac{n}{2} and n2+1\frac{n}{2} + 1.
    The positions are 62=3\frac{6}{2} = 3 and 62+1=4\frac{6}{2} + 1 = 4.
    So, we need to find the 3rd and 4th values in the ordered list.

  4. Identify the 3rd and 4th values.

    The ordered list is: 2, 4, 5, 6, 8, 9
    The 3rd value is 5.
    The 4th value is 6.

  5. Calculate the median.

    The median is the average of the 3rd and 4th values.

    Median=5+62\text{Median} = \frac{5 + 6}{2} Median=112\text{Median} = \frac{11}{2} Median=5.5\text{Median} = 5.5

    The median for part a) is 5.5\boxed{\text{5.5}}.

Part b

4\text{4}

The numbers are: 1, 2, 8, 3, 5, 8.

  1. Arrange the numbers in ascending order.

    1,2,3,5,8,81, 2, 3, 5, 8, 8
  2. Count the total number of values (nn).

    There are 6 numbers in the set, so n=6n = 6.

  3. Determine the position of the median.

    Since nn is an even number, the median is the average of the two middle values. These are the values at positions n2\frac{n}{2} and n2+1\frac{n}{2} + 1.
    The positions are 62=3\frac{6}{2} = 3 and 62+1=4\frac{6}{2} + 1 = 4.
    So, we need to find the 3rd and 4th values in the ordered list.

  4. Identify the 3rd and 4th values.

    The ordered list is: 1, 2, 3, 5, 8, 8
    The 3rd value is 3.
    The 4th value is 5.

  5. Calculate the median.

    The median is the average of the 3rd and 4th values.

    Median=3+52\text{Median} = \frac{3 + 5}{2} Median=82\text{Median} = \frac{8}{2} Median=4\text{Median} = 4

    The median for part b) is 4\boxed{\text{4}}.

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