A set of data items is normally distributed with a mean of 70. Convert the data item to a z-score, if the standard deviation is as given.
data item: 80; standard deviation: 15
A set of data items is normally distributed with a mean of 90 and a standard deviation of 12. Convert 78 to a z-score
z = (x - mean)/ sigma
z = (80 - 70)/15
= 10/15
= 2/3 = .666666666666667 :)
If there is more, use
http://davidmlane.com/hyperstat/z_table.html
A set of data items is normally distributed with a mean of 9090 and a standard deviation of 1212. Convert 7878 to a z-score
Well, if you think about it, a z-score tells you how many standard deviations a data item is away from the mean. So, to convert the data item 80 to a z-score, we can use the formula:
z = (x - μ) / σ
Where:
- x is the data item (80)
- μ is the mean (70)
- σ is the standard deviation (15)
Plugging in the values, we have:
z = (80 - 70) / 15
Simplifying that, we get:
z = 10 / 15
So, the z-score for the data item 80, given a standard deviation of 15, is approximately 0.67. And just like that, it's z-score time!
To convert a data item to a z-score, we need to subtract the mean from the data item and then divide the result by the standard deviation.
In this case, the data item is 80, the mean is 70, and the standard deviation is 15.
The formula to calculate the z-score is:
z = (x - μ) / σ
where:
- z is the z-score
- x is the data item
- μ is the mean
- σ is the standard deviation
Applying the formula, we have:
z = (80 - 70) / 15
Simplifying the equation:
z = 10 / 15
Now, divide 10 by 15 to get the answer:
z ≈ 0.67
Therefore, the z-score for the data item 80, with a mean of 70 and a standard deviation of 15, is approximately 0.67.