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
Mean: (20 + 30 + 32 + 16 + 31 + 32 + 13 + 20 + 28 + 32 + 15 + 18 + 20 + 21 + 32) / 15 = 24.4
Median: Arrange the data in order: 13, 15, 16, 18, 20, 20, 20, 21, 28, 30, 31, 32, 32, 32, 32. The median is the middle number, which in this case is 24.
Mode: The mode is the number that appears most frequently in the dataset. In this case, the mode is 32, which appears four times.
To find the measures of center for the given dataset, we need to calculate the mean, median, and mode.
Mean:
To find the mean, we sum up all the numbers in the dataset and divide it by the total number of values.
Mean = (20 + 30 + 32 + 16 + 31 + 32 + 13 + 20 + 28 + 32 + 15 + 18 + 20 + 21 + 32) / 15
Mean = 392 / 15
Mean = 26.13 (rounded to two decimal places)
Median:
The median is the middle value of a dataset when it is arranged in ascending order. In this case, we have 15 values, so the middle value would be the 8th value.
Ascending order: 13, 15, 16, 18, 20, 20, 20, 21, 28, 30, 31, 32, 32, 32, 32
Median = 20
Mode:
The mode is the value that appears most frequently in the dataset.
In this dataset, the value 32 appears the most number of times (4 times).
Mode = 32
Summary of Measures of Center:
Mean = 26.13
Median = 20
Mode = 32