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Which data set has the highest median?(1 point)

Responses

{8, 20, 13, 14, 12, 9}
  left brace 8 comma 20 comma 13 comma 14 comma 12 comma 9 right brace

{11, 15, 16, 8, 12, 14}
  left brace 11 comma 15 comma 16 comma 8 comma 12 comma 14 right brace

{1, 6, 15, 7, 15, 18, 14}
left brace 1 comma 6 comma 15 comma 7 comma 15 comma 18 comma 14 right brace

{1, 10, 8, 29, 14, 17, 3}

:)

1 answer

To determine which data set has the highest median, we need to find the median of each set. The median is the middle number in a sorted list. If there is an even number of observations, the median is the average of the two middle numbers.

Let's calculate the median for each set:

  1. {8, 20, 13, 14, 12, 9}

    • Sorted: {8, 9, 12, 13, 14, 20}
    • Median = (12 + 13) / 2 = 12.5

  2. {11, 15, 16, 8, 12, 14}

    • Sorted: {8, 11, 12, 14, 15, 16}
    • Median = (12 + 14) / 2 = 13

  3. {1, 6, 15, 7, 15, 18, 14}

    • Sorted: {1, 6, 7, 14, 15, 15, 18}
    • Median = 14 (the middle value)

  4. {1, 10, 8, 29, 14, 17, 3}

    • Sorted: {1, 3, 8, 10, 14, 17, 29}
    • Median = 10 (the middle value)

Now we compare the medians:

  • Median of the first set = 12.5
  • Median of the second set = 13
  • Median of the third set = 14
  • Median of the fourth set = 10

The highest median is from the third data set: {1, 6, 15, 7, 15, 18, 14} with a median of 14.