To find the z-score for a given value, you can use the following formula:
z = (X - μ) / σ
In this formula:
- X is the value for which you want to calculate the z-score (in this case, 62).
- μ is the mean of the data set (here, it is 79).
- σ is the standard deviation of the data set (which is 4 here).
Now, let’s plug in the values:
- X = 62
- μ = 79
- σ = 4
Substituting these values into the z-score formula yields:
z = (62 - 79) / 4
Now, calculate the numerator:
62 - 79 = -17
Now divide by the standard deviation:
z = -17 / 4 = -4.25
So, the z-score for the value 62 when the mean is 79 and the standard deviation is 4 is -4.25.
This negative z-score indicates that the value 62 is 4.25 standard deviations below the mean of 79. Generally, a z-score tells you how far away a particular data point is from the mean, and in this case, a z-score of -4.25 suggests that 62 is quite far from the average of the dataset.