Question

Height, in meters, is measured for each person in a sample. After the data are collected, all the height measurements

Answer 1

Answer:

(E) The z-scores of the height measurements

Step-by-step explanation:

Mean is given by

$\bar {x}=\frac{1}{n}\left(\sum _{i=1}^{n}{x_{i}}\right)=\frac{x_{1}+x_{2}+\cdots +x_{n}}{n}$

Where,

n = Number of people

$x_{i}$ = The heights of people

When converting m to cm the mean would be

$\bar {x}=\frac{1}{n}\left(\sum _{i=1}^{n}{x_{i}}\right)\times 100$

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

$s=\sqrt{\frac{1}{N-1}\sum_{i=1}^{N}(x_i-\bar{x})^2}$

When converting to centimeters

$s=\sqrt{\frac{1}{N-1}\sum_{i=1}^{N}\left((x_i-\bar{x})\times 100\right)^2$

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

$z=\frac{x-\mu}{\sigma}$

where,

x = Data point

$\mu$ = Mean

$\sigma$ = Standard deviation

When converting to centimeters

$z=\frac{(x-\mu)\times 100}{\sigma\times 100}\\\Rightarrow z=\frac{x-\mu}{\sigma}$

Hence, the z score would remain the same