To determine which measure of center—mean or median—best represents the shape of the distribution, we first need to examine the data and identify the shape of the distribution.
The provided prices for biweekly lawn mowing services are: 15, 15, 20, 30, 30, 35, 40, 40, 40, 40, 50, 50, 50
Step 1: Calculate the median. To find the median, we need to order the data (which is already ordered in this case) and find the middle value. Since there are 13 data points (an odd number), the median is the 7th value.
- Ordered data: 15, 15, 20, 30, 30, 35, 40, 40, 40, 40, 50, 50, 50
- Median: 40
Step 2: Calculate the mean. To find the mean, we sum all the data values and divide by the number of values.
Mean = (15 + 15 + 20 + 30 + 30 + 35 + 40 + 40 + 40 + 40 + 50 + 50 + 50) / 13 = 410 / 13 ≈ 31.54.
Step 3: Analyze the shape of the distribution. Looking at the distribution, we see that there are several lower values (15 and 20) with more frequent occurrences of middle values (30, 35, and 40) and then some higher values (50). Most values cluster around the lower and middle portions, and there are a few higher values (50). This suggests that the distribution is skewed to the right.
Conclusion: Since the distribution is skewed to the right, the median is a better measure of center because it is less influenced by extreme values in the right tail.
Therefore, the best answer is:
Median; the shape of the distribution is skewed to the right.