Question

The prices of backpacks are $37 $43 $41 $36 $44 and $70 calculate the mean in the medium within without the outlier round to the nearest 10th if necessary then State whether the mean or the median best describes the center

Answer 1

To find the mean and median of the given data, we first need to arrange the data in order:

$36, 37, 41, 43, 44, 70$

Without the outlier, the data becomes:

$36, 37, 41, 43, 44$

To find the mean, we add up all the data points and divide by the total number of data points:

Mean = $(36 + 37 + 41 + 43 + 44 + 70)/6 \approx 45.17$

Without the outlier, the mean becomes:

Mean = $(36 + 37 + 41 + 43 + 44)/5 \approx 40.2$

To find the median, we need to find the middle value of the data. Since we have an even number of data points, we take the average of the two middle values:

Median = $(41 + 43)/2 = 42$

Without the outlier, the median becomes:

Median = $(36 + 37 + 41 + 43 + 44)/5 = 41$

Comparing the mean and median, we can see that the outlier has a significant effect on the mean, pulling it up to $45.17$. The median, on the other hand, is less affected by outliers and remains close to the center of the data. Therefore, the median is a better measure of the center in this case.