Finding Measures of Center

To begin, we should notice that $7$ bumble bees is significantly higher than the number of bees Benji saw on any other day. Thus, $7$ is probably an outlier. To see how this outlier affects the measures of center, we can calculate all three with and without the outlier.

Excluding $7$

First, we'll exclude the outlier. The mean can be calculated as follows. Thus, the mean is approximately $1.85.$ To find the median, we must write the data points in ascending order. The median will fall directly in the middle of the points. $$1111112222334$$ Thus, $2$ is the median. Most often, Benji only sees $1$ bumble bee. Thus, $1$ is the mode.

Including $7$

Next, we'll perform the same steps including the outlier. The mean can be calculated as follows. Thus, the mean is approximately $2.38.$ To find the median, we'll add $7$ to the end of the ordered list from above. The median still lies directly in the middle. $$11111122223347$$ Now that there are an even number of data points, the median will be the mean of the two middle numbers. Since these are the same, the median is $2.$ Although the additional data point shifted the location of the median, notice that the value did not change. Lastly, seeing $1$ bumble bee still occurred most. Thus, the mode is $1.$ $$\begin{array}{rlrl}\text{mean}& :1.85& & \to 2.38\\ \text{median}& :2& & \to 2\\ \text{mode}& :1& & \to 1\end{array}$$ Adding an additional data point, even when it was such an extreme data point, only affected the mean. The median and mode remained the same. This is because the mean is the only measure of center that takes into account the actual data points rather than just the number of data points. Thus, the outlier affects the mean.