Brian’s math test scores are: 86, 90, 93, 85, 79, 92. What is the mean and median?
The Correct Answer and Explanation is:
To find the mean and median of Brian’s math test scores (86, 90, 93, 85, 79, 92), we first need to calculate the mean and then the median.
Mean Calculation
The mean is calculated by adding all the scores together and then dividing by the number of scores.
- Sum of scores:
( 86 + 90 + 93 + 85 + 79 + 92 = 525 ) - Number of scores:
There are 6 scores. - Mean:
[
\text{Mean} = \frac{\text{Total Sum}}{\text{Number of Scores}} = \frac{525}{6} = 87.5
]
Median Calculation
The median is the middle value of a data set when the numbers are arranged in ascending order.
- Order the scores:
Arranging the scores from smallest to largest gives us:
( 79, 85, 86, 90, 92, 93 ) - Identify the middle value:
Since there is an even number of scores (6), the median will be the average of the two middle numbers. The two middle numbers are the 3rd and 4th values in the ordered list, which are 86 and 90. - Calculate the median:
[
\text{Median} = \frac{86 + 90}{2} = \frac{176}{2} = 88
]
Summary of Results
- Mean: 87.5
- Median: 88
Explanation
The mean provides a measure of the central tendency of the scores, representing the average performance across all tests. It is influenced by every score in the data set. In contrast, the median gives a better representation of the middle score, especially in cases where there are outliers (very high or low scores) that could skew the mean. In this case, both the mean and median are relatively close, suggesting that Brian’s scores are fairly consistent. The slight difference between the two values (mean = 87.5 and median = 88) indicates that while his scores are generally high, there is a small range in variability. Understanding both measures can help in evaluating Brian’s overall performance in math and determining if his scores indicate consistent improvement or fluctuations.