Question

what effect does eliminating the lowest value, -6, from the data set have on the mean and median? -6, 3, 3, 3, 3, 5, 6, 6, 8, 10 the mean increases from to approximately the median increases from to 4 4.1 5 5.22

Explanation:

Step1: Calculate original mean

The original data - set is \(-6,3,3,3,3,5,6,6,8,10\). The sum of the data - set is \(-6 + 3+3+3+3+5+6+6+8+10=41\). There are \(n = 10\) data points. The mean \(\bar{x}_1=\frac{41}{10}=4.1\).

Step2: Calculate new mean

After eliminating \(-6\), the new data - set is \(3,3,3,3,5,6,6,8,10\). The sum of the new data - set is \(3+3+3+3+5+6+6+8+10 = 47\). There are \(n = 9\) data points. The new mean \(\bar{x}_2=\frac{47}{9}\approx5.22\).

Step3: Calculate original median

The original data - set has \(n = 10\) (an even number of data points). First, order the data: \(-6,3,3,3,3,5,6,6,8,10\). The median is the average of the 5th and 6th ordered values. So, \(M_1=\frac{3 + 5}{2}=4\).

Step4: Calculate new median

The new data - set has \(n = 9\) (an odd number of data points). Order the new data: \(3,3,3,3,5,6,6,8,10\). The median is the 5th ordered value, so \(M_2 = 5\).

Answer:

The mean increases from 4.1 to approximately 5.22.
The median increases from 4 to 5.