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, add up all of the values in the dataset and divide by the number of values:
(10 + 17 + 11 + 24 + 12 + 7 + 15 + 17 + 20 + 5 + 11 + 21 + 16 + 17) ÷ 14 = 15.214...
The mean is approximately 15.21.
Median:
To find the median, first put the data in order by magnitude:
5, 7, 10, 11, 11, 12, 15, 16, 17, 17, 17, 20, 21, 24
Since there are an even number of values in the dataset, the median is the average of the two middle values, which are 15 and 16:
(15 + 16) ÷ 2 = 15.5
The median is 15.5.
Mode:
To find the mode, look for the value that appears most often in the dataset:
The number 17 appears three times, which is more than any other value. Therefore, the mode is 17.
To find the measures of center - mean, median, and mode - for the given dataset, follow these steps:
Step 1: Arrange the data in ascending order:
5, 7, 10, 11, 11, 12, 15, 16, 17, 17, 17, 20, 21, 24
Step 2: Find the mean:
To find the mean, add up all the numbers in the dataset and divide the sum by the total number of values.
Mean = (5+7+10+11+11+12+15+16+17+17+17+20+21+24) / 14
Mean = 221 / 14
Mean = 15.78 (rounded to two decimal places)
Step 3: Find the median:
The median is the middle value in a dataset. If the dataset has an odd number of values, the median is the middle number. If the dataset has an even number of values, the median is the average of the two middle numbers.
Since the dataset has 14 values, we can find the median by looking at the 7th and 8th numbers.
Median = (12 + 15) / 2
Median = 27 / 2
Median = 13.5
Step 4: Find the mode:
The mode is the value(s) that appear(s) most frequently in the dataset.
In the given dataset, the value 17 appears most frequently, occurring three times.
Mode = 17
So, the measures of center for the given dataset are:
Mean: 15.78 (rounded to two decimal places)
Median: 13.5
Mode: 17
To find the measures of center for the given dataset, we will calculate the mean, median, and mode.
1. Mean:
The mean is the average of all the numbers in the dataset. To calculate the mean, add up all the numbers and divide the sum by the total count of numbers.
First, add up all the numbers:
10 + 17 + 11 + 24 + 12 + 7 + 15 + 17 + 20 + 5 + 11 + 21 + 16 + 17 = 208
Next, divide the sum by the total count of numbers (which is 14 in this case):
Mean = 208 / 14 = 14.857
So, the mean of the given dataset is approximately 14.857.
2. Median:
The median is the middle number in a sorted list of numbers. To find the median, first sort the numbers in ascending order, and then find the middle number (or average of the two middle numbers if there is an even count of numbers).
First, sort the numbers:
5, 7, 10, 11, 11, 12, 15, 16, 17, 17, 17, 20, 21, 24
Since the count of numbers is odd (14 in this case), the median is the middle number, which is the 7th number in the sorted list:
Median = 12
So, the median of the given dataset is 12.
3. Mode:
The mode is the number(s) that occurs most frequently in the dataset. In this case, there is one mode if there is one number that occurs most frequently, or there can be multiple modes if multiple numbers occur with the same highest frequency.
In the given dataset, the number 17 occurs three times, which is more than any other number. Therefore, the mode of the given dataset is 17.
So, the measures of center for the given dataset are:
Mean: 14.857
Median: 12
Mode: 17