Question

consider the following two data sets.
set 1
9
10
6
7
5
set 2
9
10
6
7
200

1. compute the mean and the median of data set 1. enter your answer as an integer or rounded to 1 decimal place as appropriate.

o mean
o median

1. compute the mean and the median of data set 2. enter your answer as an integer or rounded to 1 decimal place as appropriate.

o mean
o median

1. what do these data sets reveal about the mean and the median?

both the mean and the median are resistant to outliers.
the mean is sensitive to outliers.
the median is sensitive to outliers.
both the mean and the median are sensitive to outliers.

Explanation:

Step1: Calculate mean of Data Set 1

The formula for the mean $\bar{x}=\frac{\sum_{i = 1}^{n}x_{i}}{n}$. For Data Set 1 with $x_1 = 9,x_2=10,x_3 = 6,x_4=7,x_5 = 5$ and $n = 5$. $\sum_{i=1}^{5}x_{i}=9 + 10+6+7+5=37$. So, $\bar{x}=\frac{37}{5}=7.4$.

Step2: Calculate median of Data Set 1

Arrange Data Set 1 in ascending - order: $5,6,7,9,10$. Since $n = 5$ (odd), the median is the middle - value. So the median is $7$.

Step3: Calculate mean of Data Set 2

For Data Set 2 with $x_1 = 9,x_2=10,x_3 = 6,x_4=7,x_5 = 200$ and $n = 5$. $\sum_{i=1}^{5}x_{i}=9 + 10+6+7+200=232$. So, $\bar{x}=\frac{232}{5}=46.4$.

Step4: Calculate median of Data Set 2

Arrange Data Set 2 in ascending - order: $6,7,9,10,200$. Since $n = 5$ (odd), the median is the middle - value. So the median is $9$.

Step5: Analyze the effect of outliers

In Data Set 1, there are no outliers. In Data Set 2, 200 is an outlier. The mean of Data Set 1 is $7.4$ and the mean of Data Set 2 is $46.4$, which is greatly affected by the outlier 200. The median of Data Set 1 is $7$ and the median of Data Set 2 is $9$, and the change in the median due to the outlier is relatively small. So, the mean is sensitive to outliers.

Answer:

1. Mean: $7.4$, Median: $7$
2. Mean: $46.4$, Median: $9$
3. The mean is sensitive to outliers.