To determine whether the mean or median better describes the shape of the data set \(46, 54, 43, 57, 50, 62, 78, 42\), we need to compare both measures and consider the distribution of the data:
1. **Calculate the median**:
- Arrange the data in ascending order: \(42, 43, 46, 50, 54, 57, 62, 78\).
- The median (the middle value) for an even number of data points is the average of the two middle numbers.
- The two middle numbers are \(50\) and \(54\).
- Median = \(\frac{50 + 54}{2} = \frac{104}{2} = 52\).
2. **Calculate the mean**:
- Sum of all data points = \(42 + 43 + 46 + 50 + 54 + 57 + 62 + 78 = 432\).
- Number of data points = \(8\).
- Mean = \(\frac{432}{8} = 54\).
3. **Determine the best measure**:
- The mean (\(54\)) and the median (\(52\)) are close, but since the data set includes a noticeable higher outlier value (\(78\)), the mean might be slightly influenced by this outlier, making it less representative of the central tendency of the majority of the data points.
Considering these points, the median is generally a better measure when outliers are present, as it is less affected by extremely high or low values. Thus, the correct response is:
The median value of 52 is the best measure of center that describes the shape of the data set.
Does the mean or median better describe the shape of this data set? 46, 54, 43, 57, 50, 62, 78, 42(1 point) Responses The median value of 54 is the best measure of center that describes the shape of the data set. The median value of 54 is the best measure of center that describes the shape of the data set. The mean value of 52 is the best measure of center that describes the shape of the data set. The mean value of 52 is the best measure of center that describes the shape of the data set. The median value of 52 is the best measure of center that describes the shape of the data set. The median value of 52 is the best measure of center that describes the shape of the data set. The mean value of 54 is the best measure of center that describes the shape of the data set.
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