Compare the data sets using the mean and the median of each data set. SHOW ALL OF YOUR WORK!
Data Set 1:
1, 1, 2, 3, 7, 9, 15, 17, 18, 20, 22, 29
Mean: 12
Median: 12
Data Set 2:
2, 2, 3, 9, 13, 17, 20, 20, 22, 23, 26, 35
Mean: 16
Median: 18.5
First, let's calculate the mean (average) and median (middle value) for each data set to ensure the given values are correct.
Mean for Data Set 1:
(1+1+2+3+7+9+15+17+18+20+22+29) / 12 = 144 / 12 = 12
Mean for Data Set 2:
(2+2+3+9+13+17+20+20+22+23+26+35) / 12 = 192 / 12 = 16
Median for Data Set 1:
There are 12 values in Data Set 1, so to find the median, we need the average of the 6th and 7th values.
(9+15) / 2 = 24 / 2 = 12
Median for Data Set 2:
There are 12 values in Data Set 2, so to find the median, we need the average of the 6th and 7th values.
(17+20) / 2 = 37 / 2 = 18.5
So, the given mean and median values are correct for both data sets.
Now, let's compare the mean and median of each data set:
Data Set 1:
Mean: 12
Median: 12
Data Set 2:
Mean: 16
Median: 18.5
From the comparison, we can see that Data Set 2 has a higher mean and median than Data Set 1, which means that the values in Data Set 2 are generally larger than the values in Data Set 1.
Note that the difference between the mean and median in Data Set 1 is 0, indicating a more symmetric distribution, whereas the difference between the mean and median in Data Set 2 is 2.5, implying possible skewness in the distribution.