Here are the prices for biweekly lawn mowing services for 13 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 skewed to the left.
Mean; the shape of the distribution is skewed to the left.
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 right.
To determine which measure of center best represents the shape of the distribution, you need to consider the characteristics of the data set. In this case, the data set represents the prices for biweekly lawn mowing services for 13 local companies. The prices are as follows:
15, 15, 20, 30, 30, 35, 40, 40, 40, 40, 50, 50, 50
To calculate the mean, you would add up all the values and divide by the total number of values. In this case, the mean would be (15+15+20+30+30+35+40+40+40+40+50+50+50)/13 = 39.23 (rounded to two decimal places).
To calculate the median, you would arrange the values in ascending order and find the middle value. In this case, the median would be the middle value of the sorted list, which is 40.
Looking at the data set, you can observe that there are several values of 40 and 50, which is pulling the mean towards the higher end. This suggests that the distribution is skewed to the right. Since the mean is affected by outliers or extreme values, it may not best represent the shape of the distribution.
On the other hand, the median is less affected by outliers as it only considers the middle value. In this case, the median is 40, which is a central value and is not greatly influenced by the outliers on the higher end of the distribution. Therefore, the better representation of the shape of the distribution in this case would be the median, which suggests that the shape of the distribution is skewed to the right.