Question

use the image to answer the question. compare the mean and the median. is the data symmetrical?

Explanation:

Step1: Count the data points

There are 12 data points.

Step2: Find the median

Since there are 12 data points (an even number), the median is the average of the 6th and 7th ordered data points. Ordering the data: -1,0,0,1,1,1,1,2,2,2,3. The 6th value is 1 and the 7th value is 1. Median = $\frac{1 + 1}{2}=1$.

Step3: Calculate the mean

Mean = $\frac{(-1)+0 + 0+1+1+1+1+2+2+2+3}{12}=\frac{13}{12}\approx1.08$.

Step4: Check for symmetry

A symmetric data - set has the mean equal to the median. Here, mean $\approx1.08$ and median = 1. Also, looking at the dot - plot, if we fold the plot along a vertical line, the left and right sides do not match exactly.

Answer:

The mean ($\approx1.08$) is slightly greater than the median (1). The data is not symmetric.