three graphs

Question

graph A: 5through 12 5-1, 6-1, 7-3, 8-3, 9-2, 10-0, 11-0, 12-0
Graph B: 5 through 12 5-1, 6-0, 7-1, 8-1, 9-3, 10-2, 11-1, 12-1
graph C: 5 through 12 5-0, 6-0, 7-0, 8-0, 9-0, 10-1, 11-3, 12-6

The median is the best measure of center for which data set?

(1 point)
Responses

data set A because the distribution is nearly summetric
data set A because the distribution is nearly summetric

data set B because the range is the largest
data set B because the range is the largest

data set B because the distribution is the flattest
data set B because the distribution is the flattest

data set C because the distribution is skewed
data set C because the distribution is skewed

Answer 1

To determine which data set is best described by the median, we need to consider the characteristics of the distributions in each graph.

1. Data Set A: The values appear to cluster around the 7-9 range, and there are a few zeros at the higher end (10-12). The distribution looks somewhat balanced and not heavily skewed, suggesting the mean could be a valid measure of center as well.

2. Data Set B: The distribution has a varied spread with some values concentrated around 5-9, but there is a small number of occurrences for each value, making the distribution more uniform across the data range.

3. Data Set C: This distribution is heavily skewed to the right (with 1, 3, and 6 at the highest values), indicating that the mean could be influenced by the outliers at the higher end of the data. In this case, the median would be a better representation of the central tendency because it is less affected by the extreme values.

Given the characteristics of each data set, the most appropriate answer would be:

data set C because the distribution is skewed.

This is because the median is robust to skewness and is a better measure of center for skewed distributions.