consider the data set.\n41 47 50 46 43 41\n66 48 45 50 42 43\ndescribe what would happen if the outlier was…

consider the data set.\n41 47 50 46 43 41\n66 48 45 50 42 43\ndescribe what would happen if the outlier was removed from the data set.\nthe mean would decrease and the range would increase.\nthe mean and the median would increase.\nthe mode and range would decrease.\nthe mean, median, and range would decrease.

consider the data set.\n41 47 50 46 43 41\n66 48 45 50 42 43\ndescribe what would happen if the outlier was removed from the data set.\nthe mean would decrease and the range would increase.\nthe mean and the median would increase.\nthe mode and range would decrease.\nthe mean, median, and range would decrease.

Answer

Explanation:

Step1: Identify the outlier

The outlier is 66 as it is much larger than other values.

Step2: Calculate original mean

Original data set: 41, 47, 50, 46, 43, 41, 66, 48, 45, 50, 42, 43. Mean = $\frac{41 + 47+50+46+43+41+66+48+45+50+42+43}{12}=\frac{562}{12}\approx46.83$.

Step3: Calculate new mean after removing 66

New data set: 41, 47, 50, 46, 43, 41, 48, 45, 50, 42, 43. Mean = $\frac{41 + 47+50+46+43+41+48+45+50+42+43}{11}=\frac{496}{11}\approx45.09$. Mean decreases.

Step4: Calculate original median

Arrange original data in ascending - order: 41, 41, 42, 43, 43, 45, 46, 47, 48, 50, 50, 66. Median = $\frac{45 + 46}{2}=45.5$.

Step5: Calculate new median after removing 66

Arrange new data in ascending - order: 41, 41, 42, 43, 43, 45, 46, 47, 48, 50, 50. Median = 45. Median decreases.

Step6: Calculate original range

Original range = 66 - 41 = 25.

Step7: Calculate new range after removing 66

New range = 50 - 41 = 9. Range decreases.

Answer:

The mean, median, and range would decrease.