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: 21; median: 24; mode: 32
mean: 21; median: 24; mode: 32
mean: 22.5; median: 21; mode: 20
mean: 22.5; median: 21; mode: 20
mean: 24; median: 21; mode: 32
mean: 24; median: 21; mode: 32
Mean: 22.5; Median: 21; Mode: 32
To find the measures of center for this dataset, we need to calculate the mean, median, and mode.
First, let's find the mean. The mean is the sum of all the numbers in the dataset divided by the total number of values. In this case, we have 15 numbers.
So, add up all the numbers: 20 + 30 + 32 + 16 + 31 + 32 + 13 + 20 + 28 + 32 + 15 + 18 + 20 + 21 + 32 = 365
Now, divide the sum by the total number of values: 365 / 15 = 24.33 (approx)
Therefore, the mean of this dataset is approximately 24.
Next, let's find the median. The median is the middle value of the dataset when it is arranged in ascending order. If there is an even number of values, the median is the average of the two middle values.
First, let's sort the dataset in ascending order: 13, 15, 16, 18, 20, 20, 20, 21, 28, 30, 31, 32, 32, 32, 32
As we have 15 numbers, the middle value is the 8th number, which is 21. Therefore, the median is 21.
Finally, let's find the mode. The mode is the number that appears most frequently in the dataset.
In this dataset, the number 32 appears four times, which is more than any other number. Therefore, the mode is 32.
So, the measures of center for this dataset are:
Mean: 24
Median: 21
Mode: 32
To find the measures of center—mean, median, and mode—of the dataset provided, we can follow these steps:
Step 1: Calculate the mean (average):
Add up all the numbers and divide the sum by the total count. Let's do the calculation:
20 + 30 + 32 + 16 + 31 + 32 + 13 + 20 + 28 + 32 + 15 + 18 + 20 + 21 + 32 = 380
Now divide the sum by the total count:
380 / 15 = 25.33 (rounded to 2 decimal places)
So, the mean is approximately 25.33.
Step 2: Calculate the median (middle value):
To find the median, we arrange the numbers in ascending order:
13, 15, 16, 18, 20, 20, 20, 21, 28, 30, 31, 32, 32, 32, 32
Since there are 15 numbers, the middle value is the 8th number, which is 21.
So, the median is 21.
Step 3: Calculate the mode (most frequent value):
The mode is the value that appears most frequently in the dataset.
In this case, the number 32 appears most frequently, appearing 4 times.
So, the mode is 32.
Therefore, the measures of center for the provided dataset are as follows:
Mean: 25.33
Median: 21
Mode: 32