Answer :
The mean of the data set is 5.41, the median is 5.1, and the mode is 8.3.
The question asks us to find the mean, median, and mode of a given set of numbers: 8.1, 6.3, 4.4, 8.3, 5.6, 2.2, 8.3, 3.6, 4.6, 2.4. To calculate the mean, we sum all the numbers and divide by the total count.
To find the median, we first need to order the numbers and then locate the central value(s). The mode is the number(s) that occur most frequently in the data set.
- To calculate the mean, add all the numbers together and then divide by the number of values: (8.1 + 6.3 + 4.4 + 8.3 + 5.6 + 2.2 + 8.3 + 3.6 + 4.6 + 2.4) / 10 = 54.1 / 10 = 5.41.
- For the median, arrange the numbers in ascending order: 2.2, 2.4, 3.6, 4.4, 4.6, 5.6, 6.3, 8.1, 8.3, 8.3. Since there are 10 numbers (an even amount), we take the average of the 5th and 6th numbers: (4.6 + 5.6) / 2 = 5.1.
- When identifying the mode, look for the number that appears most frequently. In this case, it's 8.3 as it appears twice in the list. The mean is 5.41, the median is 5.1, and the mode is 8.3.
Mean is 5.48, median is 5.1, and mode is 8.3 for the given numbers.
Mean: The mean is calculated by summing all the numbers and dividing by the total count of numbers.
Sum = 8.1 + 6.3 + 4.4 + 8.3 + 5.6 + 2.2 + 8.3 + 3.6 + 4.6 + 2.4
Sum = 54.8.
There are 10 numbers, so:
Mean = 54.8 / 10
= 5.48.
Median: To find the median, we first sort the numbers: 2.2, 2.4, 3.6, 4.4, 4.6, 5.6, 6.3, 8.1, 8.3, 8.3.
With 10 numbers (even), the median is the average of the 5th and 6th numbers:
Median = (4.6 + 5.6) / 2
= 10.2 / 2
= 5.1.
Mode: The mode is the number that appears most frequently. Here, 8.3 appears twice, while others appear once. Mode = 8.3.
