To find the mean, median, mode, and range of the given list of values: 1, 2, 4, 71, 2, 4, 71, 2, 4, 7, we can follow these steps:
1. Mean: To calculate the mean, we sum all the values and divide by the number of values.
- Sum = 1 + 2 + 4 + 71 + 2 + 4 + 71 + 2 + 4 + 7 = 168
- Number of values = 10
Mean = Sum / Number of values = 168 / 10 = 16.8
2. Median: To find the median, we first arrange the values in ascending order:
1, 2, 2, 2, 4, 4, 4, 7, 71, 71
Since there are 10 values (an even number), the median is the average of the 5th and 6th values.
5th value = 4 6th value = 4
Median = (4 + 4) / 2 = 4
3. Mode: The mode is the number that appears most frequently in the list.
- In the list 1, 2, 4, 71, 2, 4, 71, 2, 4, 7:
- 1 appears 1 time
- 2 appears 3 times
- 4 appears 3 times
- 71 appears 2 times
- 7 appears 1 time
Thus, both 2 and 4 are modes (multimodal).
4. Range: The range is the difference between the maximum and minimum values.
- Maximum value = 71
- Minimum value = 1
Range = Maximum - Minimum = 71 - 1 = 70
Summary of Results:
- Mean: 16.8
- Median: 4
- Mode: 2 and 4 (multimodal)
- Range: 70
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