Summarize the dataset by finding its measures of center—mean, median, and mode.
20, 30, 32, 16, 31, 32, 13, 20, 28, 32, 15, 18, 20, 21, 32
(1 point)
Responses
mean: 24; median: 24.5; mode: 20
mean: 24; median: 24.5; mode: 20
mean: 22.5; median: 21; mode: 20
mean: 22.5; median: 21; mode: 20
mean: 21; median: 24; mode: 32
mean: 21; median: 24; mode: 32
mean: 24; median: 21; mode: 32
The correct response is:
mean: 24; median: 24.5; mode: 32
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 close to symmetrical.
Mean; the shape of the distribution is close to symmetrical.
Mean; 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 left.
Median; the shape of the distribution is skewed to the left.
The correct response is:
Median; the shape of the distribution is skewed to the right.
To find the measures of center for this dataset, we need to calculate the mean, median, and mode.
Mean: The mean is calculated by finding the sum of all the values in the dataset and dividing it by the total number of values.
Sum of values = 20 + 30 + 32 + 16 + 31 + 32 + 13 + 20 + 28 + 32 + 15 + 18 + 20 + 21 + 32 = 370
Total number of values = 15
Mean = Sum of values / Total number of values = 370 / 15 = 24.67 (rounded to 2 decimal places)
Median: The median is the middle value of a sorted dataset. To find the median, we need to arrange the values in ascending order.
13, 15, 16, 18, 20, 20, 20, 21, 28, 30, 31, 32, 32, 32, 32
Since there are 15 values, the middle value is the 8th value, which is 21.
Mode: The mode is the value(s) that appear(s) most frequently in the dataset.
In this dataset, the value 32 appears most frequently, so the mode is 32.
Therefore, the measures of center for this dataset are:
Mean: 24.67 (rounded to 2 decimal places)
Median: 21
Mode: 32