A set of 50 data values has a mean of 15 and a variance of 25. Find the standard score of a data value = 20
The "standard score" is more commonly called the "z-score".
It is the number of "standard deviations" above the mean.
The standard deviation is the square root of the variance, or 5 in this case.
The number of data values is not needed to answer the question.
A data point of 20 is one standard deviation above the mean of 15, so the standard or "z" score is 1.0
Statistics confuses me....thank you for your help :)
A z-score is 0.6 standard deviations above the mean.
To find the standard score of a data value, you need to calculate the z-score. The z-score measures how many standard deviations an individual data value is from the mean.
The formula to calculate the z-score is:
z = (x - μ) / σ
Where:
- z is the standard score (z-score)
- x is the data value you want to find the standard score for
- μ is the mean of the data set
- σ is the standard deviation of the data set
In this case, you are given the mean (μ = 15) and the data value (x = 20). However, you are not given the standard deviation (σ). Instead, you are given the variance (25), which is the square of the standard deviation.
The formula to calculate the standard deviation from the variance is:
σ = √variance
So, in this case, you can find the standard deviation by taking the square root of the variance:
σ = √25 = 5
Now that you have all the necessary values, you can calculate the z-score:
z = (x - μ) / σ
= (20 - 15) / 5
= 5 / 5
= 1
Therefore, the z-score (standard score) of the data value 20 is 1.