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
A. mean: 24; median: 21; mode: 32
B. mean: 22.5; median: 21; mode: 20
C. mean: 21; median: 24; mode: 32
D. mean: 24; median: 24.5; mode: 20
A. mean: 24; median: 21; mode: 32
To find the measures of center, we need to calculate the mean, median, and mode of the dataset given:
Dataset: 20, 30, 32, 16, 31, 32, 13, 20, 28, 32, 15, 18, 20, 21, 32
Mean:
To find the mean, we sum up all the numbers in the dataset and divide it by the total count.
Mean = (20 + 30 + 32 + 16 + 31 + 32 + 13 + 20 + 28 + 32 + 15 + 18 + 20 + 21 + 32) / 15
Mean = 398 / 15
Mean = 26.53 (approx)
Median:
To find the median, we arrange the numbers in ascending order and find the middle value.
The dataset arranged in ascending order: 13, 15, 16, 18, 20, 20, 20, 21, 28, 30, 31, 32, 32, 32, 32
There are 15 numbers in the dataset, so the middle value is at the 8th position.
Therefore, the median is 21.
Mode:
The mode is the value(s) that appear(s) most frequently in the dataset.
In the given dataset, the number 32 appears the most frequently (4 times).
Therefore, the mode is 32.
Summarizing the dataset by finding the measures of center, we get:
Mean: 26.53 (approx), Median: 21, Mode: 32.
So, the correct answer is: A. mean: 26.53; median: 21; mode: 32.