a data set has the following characteristics: mean: 4.9 median: 6 mode: 6 variance: 4 the z - score is the…
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: $z_x=\frac{x - mu}{sigma}$ $z_1=$ $z_5=$ $z_{6.5}=$
Answer
Explanation:
Step1: Calculate standard deviation
Given variance $\sigma^{2}=4$, so standard - deviation $\sigma=\sqrt{4}=2$.
Step2: Calculate $z_1$
Substitute $x = 1$, $\mu=4.9$, $\sigma = 2$ into $z_x=\frac{x - \mu}{\sigma}$. Then $z_1=\frac{1 - 4.9}{2}=\frac{-3.9}{2}=-1.95$.
Step3: Calculate $z_5$
Substitute $x = 5$, $\mu=4.9$, $\sigma = 2$ into $z_x=\frac{x - \mu}{\sigma}$. Then $z_5=\frac{5 - 4.9}{2}=\frac{0.1}{2}=0.05$.
Step4: Calculate $z_{6.5}$
Substitute $x = 6.5$, $\mu=4.9$, $\sigma = 2$ into $z_x=\frac{x - \mu}{\sigma}$. Then $z_{6.5}=\frac{6.5 - 4.9}{2}=\frac{1.6}{2}=0.8$.
Answer:
$z_1=-1.95$ $z_5 = 0.05$ $z_{6.5}=0.8$