Given the box plot, will the mean or the median provide a better description of the center?
box plot with min at 6, Q1 at 7.5, median at 8, Q3 at 23, max at 32.5
The mean, because the data distribution is symmetrical
The median, because the data distribution is symmetrical
The mean, because the data distribution is skewed to the right
The median, because the data distribution is skewed to the right
which side is it skewed to?
well if you look at the problem it starts at around 5.5 causing a little space to be provided in between and then it ends at 25 causing the skewed point to be at the median because the distribution is symmetrical.
Will the mean or the median provide a better description of the center
left
To determine whether the mean or the median provides a better description of the center based on the provided box plot, we need to consider the symmetry or skewness of the data distribution.
Looking at the box plot, we can see that the median is represented by the line inside the box, which is located at 8. The median divides the data into two equal halves, with 50% of the values falling below it and 50% falling above it. It is not affected by extreme values or outliers.
The box plot does not provide information about the symmetry or skewness directly. However, we can analyze the position and size of the whiskers (lines extending from the box) to make an inference about the data distribution. In this case, the whiskers are relatively long, extending from the lower quartile (Q1 = 7.5) to the minimum (6) and from the upper quartile (Q3 = 23) to the maximum (32.5).
Based on this information, we can infer that the data distribution is skewed to the right, indicating that there are some high values pulling the distribution towards the right. Skewness indicates that the mean can be influenced by these extreme values, which can lead to a significant deviation from the typical central tendency.
Therefore, in this case, the median would provide a better description of the center because it is a robust measure that is not affected by extreme values or the skewness of the distribution.
6 7.5 8 23 32.5
The median because the data is skewed.
Look at the difference between
7.5 and 8 is only .5
Difference between 8 and 23 is 15
To use the mean, you want the difference between the median and Q1 and Q3 to be about the same. Otherwise use the median.