Question

question 8 (3 points)
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. ______ cans
2. find the median. ______ cans
3. eliminate the greatest value, 42, from the data set. explain how the measures of center change.

the mean ____ (increases, decreases) to about __ 16.36 cans and the median __ (increases, decreases) to ____ 14 cans.
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Explanation:

Step1: Calculate sum of data

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

Step2: Find number of data points

There are 12 data - points.

Step3: Calculate the mean

The mean $\bar{x}=\frac{222}{12}=18.5$

Step4: Arrange data in ascending order

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

Step5: Calculate the median

Since there are 12 data - points (an even number), the median is the average of the 6th and 7th ordered values. $\text{Median}=\frac{14 + 18}{2}=16$

Step6: Remove 42 and recalculate mean

The new sum is $222-42 = 180$, and there are 11 data - points. The new mean is $\frac{180}{11}\approx16.36$.

Step7: Remove 42 and recalculate median

The new ordered data set is $9,12,13,14,14,14,18,19,22,22,23$. The median (the 6th value) is 14.

Answer:

1. 18.5
2. 16
3. decreases; 16.36; decreases; 14