Find the measures of center—mean, median, and mode—for the given dataset.
10, 17, 11, 24, 12, 7, 15, 17, 20, 5, 11, 21, 16, 17
Mean:
To find the mean (average), we add up all the numbers and divide by the total number of values:
10 + 17 + 11 + 24 + 12 + 7 + 15 + 17 + 20 + 5 + 11 + 21 + 16 + 17 = 198
There are 14 values in the dataset, so
mean = 198/14 ≈ 14.14
Median:
To find the median, we need to first put the values in order:
5, 7, 10, 11, 11, 12, 15, 16, 17, 17, 17, 20, 21, 24
There are 14 values, so the median is the middle value. In this case, the middle two values are 16 and 17.
median = (16 + 17)/2 = 16.5
Mode:
The mode is the value that appears most frequently in the dataset. In this case, the number 17 appears three times, which is more than any other number.
mode = 17
To find the measures of center for the given dataset, we will calculate the mean, median, and mode.
Step 1: Arrange the data in ascending order:
5, 7, 10, 11, 11, 12, 15, 16, 17, 17, 17, 20, 21, 24
Step 2: Calculate the mean:
The mean (or average) is calculated by summing up all the numbers in the dataset and dividing it by the total number of values.
In this case, the sum of all the numbers is 5 + 7 + 10 + 11 + 11 + 12 + 15 + 16 + 17 + 17 + 17 + 20 + 21 + 24 = 208.
There are 14 values in the dataset, so the mean is 208/14 = 14.857.
Step 3: Calculate the median:
The median is the middle value in the dataset when it is arranged in ascending order. If there are two middle values, the median is the average of the two.
In this case, the median is the 7th value, which is 12. So the median is 12.
Step 4: Calculate the mode:
The mode is the value(s) that appear most frequently in the dataset. In this case, the mode is 17, as it appears three times, more than any other number in the dataset.
Therefore, the measures of center for the given dataset are:
Mean: 14.857
Median: 12
Mode: 17