Select the mean, median mode and range of the following list of values.

​ 1,2,4,71,2,4,71,2,4,7
Averages 3.5 None 3 6
Mean
Media
Range
Mode

2 answers

Let's calculate the mean, median, mode, and range of the list of values: 1, 2, 4, 71, 2, 4, 71, 2, 4, 7.

  1. Mean: \[ \text{Mean} = \frac{\text{Sum of all values}}{\text{Number of values}} \] \[ \text{Sum} = 1 + 2 + 4 + 71 + 2 + 4 + 71 + 2 + 4 + 7 = 168 \] \[ \text{Number of values} = 10 \] \[ \text{Mean} = \frac{168}{10} = 16.8 \]

  2. Median: To find the median, we first sort the list: 1, 2, 2, 2, 4, 4, 4, 7, 71, 71 Since there are 10 values (even number), the median will be the average of the 5th and 6th values. \[ \text{Median} = \frac{4 + 4}{2} = 4 \]

  3. Mode: The mode is the value that appears most frequently. In the sorted list:

    • 1 appears 1 time
    • 2 appears 3 times
    • 4 appears 3 times
    • 7 appears 1 time
    • 71 appears 2 times

    The modes are 2 and 4 (both appear 3 times).

  4. Range: The range is calculated as: \[ \text{Range} = \text{Maximum value} - \text{Minimum value} \] \[ \text{Maximum} = 71, \quad \text{Minimum} = 1 \] \[ \text{Range} = 71 - 1 = 70 \]

To summarize:

  • Mean: 16.8
  • Median: 4
  • Mode: 2 and 4 (bimodal)
  • Range: 70
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