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Difficulty: EasyMeasures of Central Tendency (Mean, Median, Mode)

A high school basketball team scored the following points in five consecutive games: 44, 66, 66, 77, and 1212. Which of the following statements regarding the measures of central tendency for these scores must be true? Select all such statements.

  1. The mean score is equal to 77.Answer
  2. The median score is equal to the mode score.Answer
  3. C
    The median score is equal to 77.
  4. The mode score is equal to 66.Answer
  5. E
    The mean score is less than the median score.

Answer

The statements asserting that the mean score is equal to 7, the median score is equal to the mode score, and the mode score is equal to 6 are all true.
For the dataset 4,6,6,7,124, 6, 6, 7, 12, the mean is 355=7\frac{35}{5} = 7, the median (middle score) is 66, and the mode (most frequent score) is 66. Consequently, the mean equals 77, the median and mode are equal (6=66 = 6), and the mode is 66.

Step-by-Step Solution

1
Calculate the mean of the dataset.
Mean = 4+6+6+7+125=355=7\frac{4 + 6 + 6 + 7 + 12}{5} = \frac{35}{5} = 7.
The mean is calculated by dividing the sum of all data points by the total count.
2
Determine the median of the dataset.
Median = 66.
The data is already arranged in ascending order: 4,6,6,7,124, 6, 6, 7, 12. The 3rd value (middle position) is 66.
3
Determine the mode of the dataset.
Mode = 66.
The value 66 occurs twice, whereas all other values occur only once.
4
Evaluate each given statement against the calculated metrics.
Mean = 77, Median = 66, Mode = 66. Thus: Mean (77) is true; Median = Mode (6=66 = 6) is true; Mode = 66 is true.
Direct comparison verifies which statements hold true.

Key Concept

Calculating and comparing mean, median, and mode for a discrete set of numerical data.
Estimated Time:1m 0s
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Topics

Measures of Central Tendency (Mean, Median, Mode)

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