{ 77, 80, 84, 85, 86, 88, 93, 95, 96, 100, 104, 104, 105, 107, 107, 107, 108, 108, 108, 108, 110, 111, 112…

{ 77, 80, 84, 85, 86, 88, 93, 95, 96, 100, 104, 104, 105, 107, 107, 107, 108, 108, 108, 108, 110, 111, 112, 113, 114, 114, 118, 120, 132, 137 }. first, give the mean of the data set. part 2 of 6 next, give the median of the data set. part 3 of 6 now give the mode of the data set. if there is more than one, write them in order, separated by commas. part 4 of 6 finally, give the midrange of the data set. part 5 of 6 given the relationship between the mean and median above, what shape is the distribution likely to be? the distribution will be roughly symmetric. the distribution will probably be skewed to the left. the distribution will probably be skewed to the right. part 6 of 6 suppose the first value in the data set is mistakenly recorded as 0.0. how would this affect the mean? the mean would not change. the mean would get larger. the mean would get smaller. how would this affect the median? the median would get smaller. the median would not change. the median would get larger.

{ 77, 80, 84, 85, 86, 88, 93, 95, 96, 100, 104, 104, 105, 107, 107, 107, 108, 108, 108, 108, 110, 111, 112, 113, 114, 114, 118, 120, 132, 137 }. first, give the mean of the data set. part 2 of 6 next, give the median of the data set. part 3 of 6 now give the mode of the data set. if there is more than one, write them in order, separated by commas. part 4 of 6 finally, give the midrange of the data set. part 5 of 6 given the relationship between the mean and median above, what shape is the distribution likely to be? the distribution will be roughly symmetric. the distribution will probably be skewed to the left. the distribution will probably be skewed to the right. part 6 of 6 suppose the first value in the data set is mistakenly recorded as 0.0. how would this affect the mean? the mean would not change. the mean would get larger. the mean would get smaller. how would this affect the median? the median would get smaller. the median would not change. the median would get larger.

Answer

Explanation:

Step1: Calculate the mean

The mean $\bar{x}=\frac{\sum_{i = 1}^{n}x_{i}}{n}$, where $n = 27$ and $\sum_{i=1}^{27}x_{i}=77 + 80+84+\cdots+137=2797$. So $\bar{x}=\frac{2797}{27}\approx103.6$.

Step2: Find the median

The data - set has $n = 27$ values. The median is the $\left(\frac{n + 1}{2}\right)$-th value when the data is arranged in ascending order. $\frac{27+1}{2}=14$-th value, which is $107$.

Step3: Determine the mode

The mode is the value that appears most frequently. In this data - set, $108$ appears $4$ times, more frequently than any other value.

Step4: Calculate the mid - range

The mid - range is $\frac{\text{minimum value}+\text{maximum value}}{2}=\frac{77 + 137}{2}=\frac{214}{2}=107$.

Step5: Analyze the distribution shape

Since the mean ($103.6$) is less than the median ($107$), the distribution is probably skewed to the left.

Step6: Analyze the effect on the mean

The original sum is $2797$. If the first value $77$ is changed to $0$, the new sum is $2797-77 + 0=2720$. The new mean is $\frac{2720}{27}\approx100.74$. So the mean would get smaller.

Step7: Analyze the effect on the median

The median is the $14$-th value. Changing the first value from $77$ to $0$ does not change the position of the $14$-th value in the ordered data - set. So the median would not change.

Answer:

Part 1: $103.6$ Part 2: $107$ Part 3: $108$ Part 4: $107$ Part 5: The distribution will probably be skewed to the left. Part 6: The mean would get smaller. Part 7: The median would not change.