Find the outlier in the data: 32, 40, 34, 31, 20, 36, 40, 31. How does the outlier affect the mean? If necessary, round to the nearest tenth.
20; lowers it by 1.9.
20; raises it by 1.9.
45; lowers it by 1.7.
45; raises it by 1.7.
if the mean is m = ∑x/8
then removing the outlier (20) makes the new mean
(8m-20)/7
Not sure just what your choices mean. There is no 45 in the data.
To find the outlier in the given data, we can first calculate the mean of the data set. The mean is calculated by summing up all the numbers and dividing by the total count.
Sum of the numbers = 32 + 40 + 34 + 31 + 20 + 36 + 40 + 31 = 264
Total count = 8
Mean = 264/8 = 33
Now, let's compare each number to the mean to find the outlier.
32 - mean = 32 - 33 = -1
40 - mean = 40 - 33 = 7
34 - mean = 34 - 33 = 1
31 - mean = 31 - 33 = -2
20 - mean = 20 - 33 = -13
36 - mean = 36 - 33 = 3
40 - mean = 40 - 33 = 7
31 - mean = 31 - 33 = -2
As we can see, the number 20 is the outlier because it deviates the most from the mean, with a difference of -13.
To determine how the outlier affects the mean, we need to consider whether the outlier is higher or lower than the mean. In this case, the outlier (20) is lower than the mean (33).
If we remove the outlier, the new data set would be: 32, 40, 34, 31, 36, 40, 31.
Now, let's calculate the new mean:
Sum of the numbers (without the outlier) = 32 + 40 + 34 + 31 + 36 + 40 + 31 = 244
Total count (without the outlier) = 7
New Mean = 244/7 ≈ 34.9 (rounded to the nearest tenth)
Comparing the new mean (34.9) with the original mean (33), we can determine the effect of the outlier.
The outlier (20) lowers the mean by approximately 1.9 (rounded to the nearest tenth). Therefore, the correct answer is: 20; lowers it by 1.9.