1. Standard Deviation, Variance, Z-Score
Algebra 1B Lesson 43
Instructional material 1

2. Review
Standard Deviation is a number that tells us how a value in the data set differs from the mean. It also tells us how spread out the numbers are. The bigger the standard deviation, the more widespread the data is.
The Greek letter sigma, , will represent Standard Deviation

3. To find the Z-Score use this formula:
The Z-Score tells how many standard deviations a specific number in the data set is away from the mean.
If the z-score is positive, the data value will be above the mean. If the z-score is negative, the data value will be below the mean.
To find the Z-Score use this formula:
𝑧= 𝑥−µ  , where 𝑥 = the data value, µ = mean, and  = standard deviation.

4. The Standard Deviation and Variance describe how spread out data values are from each other, as well as from the mean. Given the variance, take the square root to find the standard deviation.

5. The Z-Score measures how far a data value is away from the mean in terms of Standard Deviation.
The Standard Deviation is what you add/subtract to the mean while the z-score is how many times you add/subtract to the mean.

6. Example 1
Determine if the following test score is valid given the following:
A student scored a 75 on an Algebra 1 chapter test. The class average was a 83 with a standard deviation of 2. The student’s z-score was -3.

7. The test score is invalid, because if the student has a z-score of -3, the test score would have been a 77.
−3≠ 75− −3= 𝑥−83 2
𝑥=77

8. Example 2
An ivy league college only accepts applicants if they score 2 standard deviations above the mean on the SAT. What does an applicant have to score on the SAT in order to be accepted if the average SAT score is 1026 and the standard deviation is 206.

9. 2= 𝑥−
𝑥=1438