What is the mean of the data set?
85, 97, 84, 88, 95, 100, 81
The Correct Answer and Explanation is :
To calculate the mean of the data set, we use the following formula:
[
\text{Mean} = \frac{\text{Sum of all values}}{\text{Number of values}}
]
Step 1: Add the values in the data set.
The data set is: 85, 97, 84, 88, 95, 100, 81.
[
85 + 97 + 84 + 88 + 95 + 100 + 81 = 630
]
Step 2: Count the number of values in the data set.
There are 7 values in total.
Step 3: Divide the sum by the number of values.
[
\text{Mean} = \frac{630}{7} = 90
]
So, the mean of the data set is 90.
Explanation:
The mean is a measure of central tendency that represents the average of a data set. It is often used to summarize a set of numbers by providing a single value that reflects the overall distribution. The mean is calculated by adding up all the numbers in the data set and then dividing by how many values there are.
In this case, the data set represents a set of numbers (85, 97, 84, 88, 95, 100, and 81) that could be anything from test scores to measurements. We first added the values together to find the total sum of 630. Then, we divided that sum by the number of values in the data set, which is 7. The result is 90, which is the mean.
The mean is helpful when you want to understand the overall average of a set of numbers. However, it can be influenced by extreme values. For instance, if there were a much higher or lower number in the data set, it could skew the mean. This is why it’s sometimes useful to consider other measures of central tendency, such as the median or mode, which might give a better representation of the data in certain cases. In this case, the mean of 90 gives a clear, central value for this particular set.