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

Responses

{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

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

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

1 answer

To find which data set has the highest median, we'll first calculate the median for each dataset. The median is the middle value of a sorted data set. If the number of values is odd, the median is the middle value. If the number of values is even, the median is the average of the two middle values.

  1. Data Set: {11, 15, 16, 8, 12, 14}

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

  2. Data Set: {1, 6, 15, 7, 15, 18, 14}

    • Sorted: {1, 6, 7, 14, 15, 15, 18}
    • Median: 14 (the fourth value in the sorted list)

  3. Data Set: {8, 20, 13, 14, 12, 9}

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

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

    • Sorted: {1, 3, 8, 10, 14, 17, 29}
    • Median: 10 (the fourth value in the sorted list)

Now we can summarize the medians:

  • First data set: 13
  • Second data set: 14
  • Third data set: 12.5
  • Fourth data set: 10

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