Question

a data set has the following characteristics: mean: 4.9 median: 6 mode: 6 variance: 4 the z - score is the number of standard deviations a data value is away from the mean. using the formula below, calculate the z - score for the listed data points. z - score: $z_x=\frac{x - mu}{sigma}$ $z_1=$ $z_5=$ $z_{6.5}=$

Explanation:

Step1: Calculate standard deviation

Since variance $\sigma^{2}=4$, then standard deviation $\sigma = \sqrt{4}=2$.

Step2: Calculate $z_1$

Given $\mu = 4.9$, $\sigma = 2$, and $x = 1$, using the formula $z_x=\frac{x - \mu}{\sigma}$, we have $z_1=\frac{1 - 4.9}{2}=\frac{- 3.9}{2}=-1.95$.

Step3: Calculate $z_5$

With $x = 5$, $z_5=\frac{5 - 4.9}{2}=\frac{0.1}{2}=0.05$.

Step4: Calculate $z_{6.5}$

For $x = 6.5$, $z_{6.5}=\frac{6.5 - 4.9}{2}=\frac{1.6}{2}=0.8$.

Answer:

$z_1=-1.95$
$z_5 = 0.05$
$z_{6.5}=0.8$