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Read the mini lesson doc and/or watch the lesson video in the Message Board then answer this question on measure of central tendency.

Find the mean, median and mode for the test scores on a math exam:

88, 89, 65, 62, 83, 63, 84, 63, 74, 64, 71, 82

(1 point)
Responses

mean = 74, median = 72.5, mode = 63
mean = 74, median = 72.5, mode = 63

mean = 74, median = 77, mode = 62
mean = 74, median = 77, mode = 62

mean = 74.5, median = 63, mode = 72
mean = 74.5, median = 63, mode = 72

mean = 74, median = 74, mode = 72
mean = 74, median = 74, mode = 72

1 answer

To find the mean, median, and mode of the test scores:

Test Scores: 88, 89, 65, 62, 83, 63, 84, 63, 74, 64, 71, 82

  1. Mean:

    • Add all the scores together: \( 88 + 89 + 65 + 62 + 83 + 63 + 84 + 63 + 74 + 64 + 71 + 82 = 882 \)
    • Divide by the number of scores (12): \( \text{Mean} = \frac{882}{12} = 73.5 \)

  2. Median:

    • First, arrange the scores in ascending order: 62, 63, 63, 64, 65, 71, 74, 82, 83, 84, 88, 89
    • Since there are 12 scores (even), the median will be the average of the 6th and 7th values: \( \text{Median} = \frac{71 + 74}{2} = \frac{145}{2} = 72.5 \)

  3. Mode:

    • The mode is the score that appears most frequently. The score 63 appears twice, while all others appear once. \( \text{Mode} = 63 \)

Summary:

  • Mean = 73.5
  • Median = 72.5
  • Mode = 63

Considering the available response options, none of them match the calculated mean. The closest response based on the calculated median and mode would be:

  • mean = 74, median = 72.5, mode = 63

However, realize the mean I calculated does not match exactly. It is important to ensure an accurate calculation or check if approximate values were accepted.