Question

question 3 (1 point) the data represent the number of cans collected by different classes for a service project. 12 14 22 14 18 23 42 13 9 19 22 14 1. find the mean. 2. find the median. 3. eliminate the greatest value, 42, from the data set. explain how the measures of center change.

Explanation:

Step1: Calculate the sum of data

$12 + 14+22 + 14+18+23+42+13+9+19+22+14=222$

Step2: Calculate the mean

There are $n = 12$ data - points. The mean $\bar{x}=\frac{\sum_{i = 1}^{n}x_{i}}{n}=\frac{222}{12}=18.5$

Step3: Arrange data in ascending order

$9,12,13,14,14,14,18,19,22,22,23,42$

Step4: Calculate the median

Since $n = 12$ (even), the median is the average of the $\frac{n}{2}$ - th and $(\frac{n}{2}+1)$ - th ordered data - points. $\frac{n}{2}=6$ and $\frac{n}{2}+1 = 7$. The 6 - th value is $14$ and the 7 - th value is $18$. Median $=\frac{14 + 18}{2}=16$

Step5: Remove the value 42

The new data set is $9,12,13,14,14,14,18,19,22,22,23$. The new sum is $9+12+13+14+14+14+18+19+22+22+23 = 170$. There are $n=11$ data - points. The new mean is $\frac{170}{11}\approx15.45$.

Step6: Calculate the new median

Since $n = 11$ (odd), the median is the $\frac{n + 1}{2}$ - th ordered data - point. $\frac{11+1}{2}=6$ - th value, which is $14$.
The mean decreased from $18.5$ to approximately $15.45$ because the large value of $42$ was removed, reducing the total sum while the number of data - points decreased by 1. The median decreased from $16$ to $14$ because the removal of the large value of $42$ changed the position of the middle value in the ordered data set.

Answer:

1. Mean: $18.5$
2. Median: $16$
3. The mean decreased from $18.5$ to approximately $15.45$ and the median decreased from $16$ to $14$.