Here are the prices for biweekly lawn mowing services for 12 local companies:
15, 15, 20, 30, 30, 35, 40, 40, 40, 40, 50, 50, 50
Which measure of center—mean or median—best represents the shape of the distribution?
(1 point)
Responses
Median; the shape of the distribution is skewed to the right.
Median; the shape of the distribution is skewed to the right.
Mean; the shape of the distribution is close to symmetrical.
Mean; the shape of the distribution is close to symmetrical.
Median; the shape of the distribution is skewed to the left.
Median; the shape of the distribution is skewed to the left.
Mean; the shape of the distribution is skewed to the left.
Median; the shape of the distribution is skewed to the right.
To determine which measure of center — mean or median — best represents the shape of the distribution, we need to consider the characteristics of the dataset. In this case, the prices for biweekly lawn mowing services are given as follows:
15, 15, 20, 30, 30, 35, 40, 40, 40, 40, 50, 50, 50
To find the median, we arrange the prices in ascending order:
15, 15, 20, 30, 30, 35, 40, 40, 40, 40, 50, 50, 50
The median is the middle value, which in this case is 40.
To find the mean, we calculate the sum of all the prices and divide it by the total number of prices:
(15 + 15 + 20 + 30 + 30 + 35 + 40 + 40 + 40 + 40 + 50 + 50 + 50) / 13 = 475 / 13 ≈ 36.54
Based on the values obtained, we find that the median is 40 and the mean is approximately 36.54.
Considering the shape of the distribution, we observe that there are many values clustered around 40, with fewer values towards the lower and higher ends. This suggests that the distribution is skewed to the right.
Therefore, the best representation of the shape of the distribution is:
Median; the shape of the distribution is skewed to the right.