What is the mean of the data set?
85, 97, 84, 88, 95, 100, 81
The Correct Answer and Explanation is :
To find the mean of the given data set (85, 97, 84, 88, 95, 100, 81), we follow these steps:
- Sum the data points: Add all the numbers together.
[
85 + 97 + 84 + 88 + 95 + 100 + 81 = 630
] - Count the number of data points: There are 7 numbers in this set.
- Calculate the mean: Divide the sum by the count of the data points.
[
\text{Mean} = \frac{\text{Sum}}{\text{Number of data points}} = \frac{630}{7} = 90
]
Thus, the mean of the data set is 90.
Explanation
The mean, also known as the average, is a measure of central tendency that summarizes a set of numbers. To calculate it, we begin by summing all the individual data points. In our example, we have a data set consisting of seven scores: 85, 97, 84, 88, 95, 100, and 81. Adding these values together gives us a total of 630.
Next, we determine how many values we have in the data set. Here, we see that there are 7 individual scores. The final step is to divide the total sum (630) by the number of scores (7) to find the mean. This division results in a mean value of 90.
The mean provides a quick snapshot of the overall performance represented by the data set. In contexts like test scores or assessments, the mean can help identify trends and evaluate performance against set standards. However, it’s essential to note that the mean can be sensitive to outliers—extremely high or low values can skew the average. For example, if one score were significantly lower or higher than the rest, it might misrepresent the typical score of the group. Therefore, while the mean is useful, it is often complemented with other statistical measures like the median and mode to provide a fuller picture of the data.