To determine which measure of center—mean or median—best represents the shape of the distribution of the lawn mowing service prices, we first examine the prices provided:
Prices: 15, 15, 20, 30, 30, 35, 40, 40, 40, 40, 50, 50, 50
Steps to Analyze:
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Calculate the Median:
- There are 13 data points. The median is the middle value, which is the 7th value when the data is ordered.
- Ordering the data: 15, 15, 20, 30, 30, 35, 40, 40, 40, 40, 50, 50, 50
- Median = 40
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Calculate the Mean:
- Mean = (Sum of all values) / (Number of values)
- Sum = 15 + 15 + 20 + 30 + 30 + 35 + 40 + 40 + 40 + 40 + 50 + 50 + 50 = 440
- Mean = 440 / 13 ≈ 33.85
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Skewness of the Distribution:
- Examining the values, we see that there is a concentration of lower values (many values below 40) and a few higher values (50). This indicates that there are outliers on the high end.
- Hence, the distribution is skewed to the right (positive skewness) since the tail on the right side (higher values) is longer or fatter than on the left side.
Conclusion:
- When the distribution is skewed to the right, the mean is typically greater than the median. In this case: Mean ≈ 33.85 is less than 40 (Median).
- Since the distribution is skewed, the median is a better representation of the center than the mean.
Therefore, the correct response is:
Median; the shape of the distribution is skewed to the right.