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
Answer:
$z_1=\frac{1 - 4.9}{2}=-1.95$ $z_5=\frac{5 - 4.9}{2}=0.05$ $z_{6.5}=\frac{6.5 - 4.9}{2}=0.8$
Explanation:
Step1: Calculate standard - deviation
Given variance $\sigma^{2}=4$, so $\sigma=\sqrt{4}=2$.
Step2: Calculate $z_1$
Substitute $x = 1$, $\mu=4.9$, $\sigma = 2$ into $z_x=\frac{x-\mu}{\sigma}$, we get $z_1=\frac{1 - 4.9}{2}$.
Step3: Calculate $z_5$
Substitute $x = 5$, $\mu=4.9$, $\sigma = 2$ into $z_x=\frac{x-\mu}{\sigma}$, we get $z_5=\frac{5 - 4.9}{2}$.
Step4: Calculate $z_{6.5}$
Substitute $x = 6.5$, $\mu=4.9$, $\sigma = 2$ into $z_x=\frac{x-\mu}{\sigma}$, we get $z_{6.5}=\frac{6.5 - 4.9}{2}$.