To determine whether the mean or median better describes the shape of the data set (46, 54, 43, 57, 50, 62, 78, 42), let's calculate both the mean and the median.
Step 1: Calculate the mean.
Sum of the values: 46 + 54 + 43 + 57 + 50 + 62 + 78 + 42 = 392
Number of values: 8
Mean = Total Sum / Number of Values = 392 / 8 = 49
Step 2: Calculate the median.
To find the median, we must first arrange the data in ascending order: 42, 43, 46, 50, 54, 57, 62, 78
Since there are 8 numbers (even amount), the median will be the average of the 4th and 5th numbers: (50 + 54) / 2 = 52
Summary of Results:
- Mean = 49
- Median = 52
Conclusion: The mean (49) is lower than the median (52), which suggests that the data set may be slightly skewed due to the presence of lower values. In cases of skewed data, the median is typically a better measure of center because it is less affected by extreme values.
Thus, the best choice is: The median value of 52 is the best measure of center that describes the shape of the data set.