Answer:
(E) The z-scores of the height measurements
Step-by-step explanation:
Mean is given by
[tex]\bar {x}=\frac{1}{n}\left(\sum _{i=1}^{n}{x_{i}}\right)=\frac{x_{1}+x_{2}+\cdots +x_{n}}{n}[/tex]
Where,
n = Number of people
[tex]x_{i}[/tex] = The heights of people
When converting m to cm the mean would be
[tex]\bar {x}=\frac{1}{n}\left(\sum _{i=1}^{n}{x_{i}}\right)\times 100[/tex]
So, the mean would change
The median gives us the middle data value when the data values are in ascending order.
So, the median would change
Standard deviation
[tex]s=\sqrt{\frac{1}{N-1}\sum_{i=1}^{N}(x_i-\bar{x})^2}[/tex]
When converting to centimeters
[tex]s=\sqrt{\frac{1}{N-1}\sum_{i=1}^{N}\left((x_i-\bar{x})\times 100\right)^2[/tex]
Hence, the standard deviation would change
When converting to centimeters the maximum height in meters would be the maximum height in centimeters also.
The z score is given by
[tex]z=\frac{x-\mu}{\sigma}[/tex]
where,
x = Data point
[tex]\mu[/tex] = Mean
[tex]\sigma[/tex] = Standard deviation
When converting to centimeters
[tex]z=\frac{(x-\mu)\times 100}{\sigma\times 100}\\\Rightarrow z=\frac{x-\mu}{\sigma}[/tex]
Hence, the z score would remain the same
