Question

a data set has the following characteristics:

mean: 4.9

median: 6

mode: 6

variance: 4

the z-score is the number of a data value is away from the .

Explanation:

Define the z-score concept

Using the Z-Score Formula knowledge point

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

Identify the components of the formula

Using the Z-Score Formula knowledge point

• \(x\) is the data value.
• \(\mu\) is the mean.
• \(\sigma\) is the standard deviation, which is the square root of the variance: \(\sigma = \sqrt{4} = 2\).

Determine the fill-in-the-blank terms

Using the Z-Score Formula knowledge point

• The numerator \(x - \mu\) represents the distance of the data value from the mean.
• Dividing by \(\sigma\) measures this distance in units of standard deviations.
• Therefore, the z-score is the number of standard deviations a data value is away from the mean.

Answer:

A data set has the following characteristics:

Mean: 4.9

Median: 6

Mode: 6

Variance: 4

The z-score is the number of <blank>standard deviations</blank> a data value is away from the <blank>mean</blank>.