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
(2 points)
mean:
; median:
; mode:
16 and 14.07
wrong
To find the measures of center for a dataset, we need to calculate the mean, median, and mode.
Mean:
To find the mean, we add up all the numbers in the dataset and then divide by the total number of values.
In this case, the dataset is: 10, 17, 11, 24, 12, 7, 15, 17, 20, 5, 11, 21, 16, 17.
1. Add up all the numbers: 10 + 17 + 11 + 24 + 12 + 7 + 15 + 17 + 20 + 5 + 11 + 21 + 16 + 17 = 208.
2. Divide the sum by the total number of values (14 in this case): 208 / 14 = 14.857.
So, the mean of the dataset is approximately 14.857.
Median:
To find the median, we need to arrange the dataset in ascending order and then find the middle value. If there is an odd number of values, the median is the middle number. If there is an even number of values, the median is the average of the two middle numbers.
In our dataset, 5, 7, 10, 11, 11, 12, 15, 16, 17, 17, 17, 20, 21, 24.
There are 14 values, so the middle two numbers are the 7th and 8th values: 15 and 16.
So, the median of the dataset is (15 + 16) / 2 = 15.5.
Mode:
The mode is the value that appears most frequently in the dataset. If there are multiple values that appear equally frequently and more often than any other, the dataset is multimodal.
In our dataset, the numbers 17 appear three times, which is more frequently than any other number.
So, the mode of the dataset is 17.
Therefore, the measures of center for the given dataset are:
Mean: approximately 14.857
Median: 15.5
Mode: 17