Find the mean of the data set:
14, 19, 13, 22,7
The Correct Answer and Explanation is:
To find the mean of the data set ( 14, 19, 13, 22, 7 ), you follow a straightforward mathematical process that involves summing all the values and then dividing by the number of values.
Step 1: Sum the Values
First, you add all the numbers in the data set together:
[
14 + 19 + 13 + 22 + 7
]
Calculating this step-by-step:
- ( 14 + 19 = 33 )
- ( 33 + 13 = 46 )
- ( 46 + 22 = 68 )
- ( 68 + 7 = 75 )
So, the total sum of the values is ( 75 ).
Step 2: Count the Values
Next, you need to determine how many values there are in the data set. In this case, the numbers are ( 14, 19, 13, 22, ) and ( 7 ), which makes a total of 5 values.
Step 3: Calculate the Mean
Now, to find the mean, you divide the total sum by the number of values:
[
\text{Mean} = \frac{\text{Total Sum}}{\text{Number of Values}} = \frac{75}{5}
]
Performing the division:
[
\frac{75}{5} = 15
]
Conclusion
Thus, the mean of the data set ( 14, 19, 13, 22, 7 ) is ( 15 ).
Explanation of Mean
The mean, often referred to as the average, is a measure of central tendency that gives an indication of the typical value in a data set. It is calculated by summing all values and dividing by the number of values, as demonstrated above. The mean provides a quick snapshot of the data, helping to summarize the information into a single representative value. However, it is essential to be aware that the mean can be sensitive to extreme values, or outliers, which can skew the result and provide a misleading impression of the data. In this case, none of the values are extreme, and the mean accurately reflects the central point of the data set. Thus, the mean serves as a foundational statistical tool widely used in various fields, including finance, education, and scientific research, to analyze and interpret data efficiently.