To determine whether the mean or median better describes the shape of the given data set, we can begin by calculating both.
Data set: 46, 54, 43, 57, 50, 62, 78, 42
Step 1: Calculate the mean.
- Sum of the data: 46 + 54 + 43 + 57 + 50 + 62 + 78 + 42 = 392
- Number of data points: 8
- Mean = Total Sum / Number of Data Points = 392 / 8 = 49
Step 2: Calculate the median. To find the median, we first arrange the data in ascending order:
- Sorted data: 42, 43, 46, 50, 54, 57, 62, 78
Since there are 8 data points (even number), the median will be the average of the 4th and 5th numbers:
- 4th number: 50
- 5th number: 54
- Median = (50 + 54) / 2 = 52
Now we have:
- Mean = 49
- Median = 52
Step 3: Choose the best measure of center.
- Consider the shape of the data: The data has a noticeable higher value (78) compared to the others, which could skew the mean down.
- The median is less affected by extremes and may better represent the center for this data set.
Based on this analysis, the best measure of center for this data set is the median.
Thus, the correct response is:
The median value of 52 is the best measure of center that describes the shape of the data set.