Question

question 35
a sample of n = 5 scores has a mean of m = 7. after one score is removed from the sample, the mean for the remaining scores is found to be m = 6. what was the score that was removed?
x = 6
x = 9
x = 11
cannot be determined from the information provided

question 36
what is the mode for the following sample of n = 11 scores? scores: 1,2,2,2,3,3,4,5,6,6,7
6
3
2
2.5

question 37
after every score in a sample of n = 5 is multiplied by 2, the mean is calculated and found to be m = 8. what was the mean of the original sample?
m = 10
m = 4
m = 16
m = 3

Explanation:

Question 35

Step1: Find the sum of the original 5 - scores

The formula for the mean $\bar{x}=\frac{\sum_{i = 1}^{n}x_{i}}{n}$. Given $n = 5$ and $\bar{x}=7$, then $\sum_{i=1}^{5}x_{i}=n\times\bar{x}=5\times7 = 35$.

Step2: Find the sum of the remaining 4 - scores

After one score is removed, $n = 4$ and $\bar{x}=6$. So the sum of the remaining 4 scores is $4\times6=24$.

Step3: Calculate the removed score

Let the removed score be $x$. We know that the sum of the original 5 scores minus the removed score equals the sum of the remaining 4 scores. So $x=35 - 24=11$.

The mode is the score that appears most frequently in a data - set. In the data - set 1, 2, 2, 2, 2, 3, 3, 4, 5, 6, 6, 7, the number 2 appears 4 times, which is more frequently than any other number.

Let the original scores be $x_1,x_2,x_3,x_4,x_5$ and their mean be $\bar{x}=\frac{\sum_{i = 1}^{5}x_{i}}{5}$. The new scores are $y_i = 2x_i$ for $i = 1,2,\cdots,5$. The mean of the new scores $\bar{y}=\frac{\sum_{i = 1}^{5}y_{i}}{5}=\frac{\sum_{i = 1}^{5}2x_{i}}{5}=2\times\frac{\sum_{i = 1}^{5}x_{i}}{5}=2\bar{x}$. Given $\bar{y}=8$, then $\bar{x}=\frac{\bar{y}}{2}=\frac{8}{2}=4$.

Answer:

$X = 11$

Question 36