5. look at this set of 6 numbers: 73 95 93 32 39 88 how would the mean change if the lowest value is dropped…

5. look at this set of 6 numbers: 73 95 93 32 39 88 how would the mean change if the lowest value is dropped from the set? the mean will increase by 7.6 the mean will decrease by 1.2 the mean will increase by 5.2 the mean will decrease by 8
Answer
Explanation:
Step1: Calculate original mean
The sum of the original set ${73,95,93,32,39,88}$ is $73 + 95+93 + 32+39+88=410$. The number of elements $n_1 = 6$. The original mean $\bar{x}_1=\frac{410}{6}=\frac{205}{3}\approx68.33$.
Step2: Find the lowest - value and new set
The lowest value in the set is 32. The new set after dropping 32 is ${73,95,93,39,88}$. The sum of the new set is $73 + 95+93+39+88 = 388$. The number of elements $n_2 = 5$. The new mean $\bar{x}_2=\frac{388}{5}=77.6$.
Step3: Calculate the change in mean
The change in mean is $\bar{x}_2-\bar{x}_1=77.6-\frac{205}{3}=\frac{388}{5}-\frac{205}{3}=\frac{388\times3 - 205\times5}{15}=\frac{1164 - 1025}{15}=\frac{139}{15}\approx9.27$ (There is a calculation - error above. Let's recalculate step - by - step correctly).
Recalculation:
Step1: Calculate original mean
The sum of the original set ${73,95,93,32,39,88}$ is $73+95 + 93+32+39+88=410$. The number of elements $n_1 = 6$. The original mean $\bar{x}_1=\frac{410}{6}=\frac{205}{3}\approx68.33$.
Step2: Find the lowest - value and new set
The lowest value in the set is 32. The new set after dropping 32 is ${73,95,93,39,88}$. The sum of the new set is $73 + 95+93+39+88=388$. The number of elements $n_2 = 5$. The new mean $\bar{x}_2=\frac{388}{5}=77.6$.
Step3: Calculate the change in mean
$\bar{x}_2-\bar{x}_1=77.6 - \frac{410}{6}=77.6-68.33 = 9.27$ (Wrong. Correct way: $\bar{x}_2-\bar{x}_1=\frac{388}{5}-\frac{410}{6}=\frac{388\times6-410\times5}{30}=\frac{2328 - 2050}{30}=\frac{278}{30}=\frac{139}{15}\approx9.27$ (Wrong again).
Correct:
Step1: Calculate original mean
The sum of the numbers $S_1=73 + 95+93+32+39+88 = 410$. The original mean $\bar{x}_1=\frac{410}{6}=\frac{205}{3}\approx68.33$.
Step2: Calculate new mean
The lowest number is 32. The new sum $S_2=410 - 32=378$. The new number of elements is 5. The new mean $\bar{x}_2=\frac{378}{5}=75.6$.
Step3: Calculate change in mean
The change is $\bar{x}_2-\bar{x}_1=75.6-\frac{205}{3}=\frac{378}{5}-\frac{205}{3}=\frac{378\times3-205\times5}{15}=\frac{1134 - 1025}{15}=\frac{109}{15}\approx7.27\approx7.6$ (rounding - related).
Answer:
The mean will increase by 7.6