Find the median and mean of the data set below:
0,45,33,8,26,25,31
The Correct Answer and Explanation is :
The median of the data set (0, 45, 33, 8, 26, 25, 31) is (26.0), and the mean is (24.0).
Explanation
1. Understanding Median:
The median is a measure of central tendency that indicates the middle value of a data set when it is ordered. To find the median, the data points must first be arranged in ascending order. For the provided data set, the ordered values are:
[0, 8, 25, 26, 31, 33, 45]
Since there are seven data points (an odd number), the median is the middle number, which is the fourth value in the ordered list. Therefore, the median is (26.0).
2. Understanding Mean:
The mean, or average, is calculated by summing all the values in the data set and then dividing by the number of values. For this data set, the calculation proceeds as follows:
[
\text{Sum} = 0 + 45 + 33 + 8 + 26 + 25 + 31 = 168
]
To find the mean, we divide this sum by the total number of values:
[
\text{Mean} = \frac{168}{7} = 24.0
]
3. Comparing Median and Mean:
In this data set, the median (26.0) is higher than the mean (24.0). This difference can indicate the presence of outliers or skewness in the data. In this case, the higher values (like 45) can pull the mean downward, while the median remains relatively unaffected as it focuses solely on the central value.
In summary, while the median provides insight into the middle of the data, the mean gives an overall average, reflecting the impact of all values in the set. Together, they provide a more comprehensive view of the data’s distribution.