after teaching a science unit on sound waves,...
after teaching a science unit on sound waves, mr. conway gave his students a quiz, and he recorded each students score. sound waves quiz number of correct answers complete the sentences. the median of the data is _ correct answers. the mean is about _ correct answers. if the outlier in this distribution were removed, the ______ would change. 8 ... 9 ... median 8 ... 9 ... mean 9 ... 8 ... median 9 ... 8 ... mean
Answer
# Answer:
8 ... 9 ... mean
# Explanation:
## Step1: Count data - point number
There are 1 + 1+ 1+ 2+ 3+ 6+ 4 = 18 data - points.
## Step2: Find the median
Since \(n = 18\) (even), the median is the average of the \(\frac{n}{2}=9\)th and \((\frac{n}{2}+ 1)=10\)th ordered data - points. Counting the data from the left, the 9th and 10th values are both 8, so the median is 8.
## Step3: Calculate the mean
\[
\begin{align*}
\text{Mean}&=\frac{2\times1 + 6\times1+7\times2 + 8\times3+9\times6+10\times4}{18}\\
&=\frac{2 + 6+14 + 24+54+40}{18}\\
&=\frac{140}{18}\approx7.78\approx8
\end{align*}
\]
## Step4: Analyze the outlier effect
The outlier is the value 2. If we remove the outlier, the sum of the data and the number of data - points change. The median may or may not change (in some cases when the number of data is still even and the middle values remain the same), but the mean will change because the mean is sensitive to extreme values. So if the outlier in this distribution were removed, the mean would change.