Understanding Statistics 1#14 z-score
- 2. Z-Score - You want to know how close are you to the mean, for grades as an example - If you are above you are ok if you are far away to mean you are outstanding - I want to know how far I am in front of the mean OR how many std. deviation in front of the mean Remember: 1 ϭ = 68% of the data, 2ϭ = 95% (Empiric Rule) - So you are 2ϭ away from the mean you are doing very well, you are in the top 5% - If you are 3ϭ you are outstanding Z-Score aka Standard Score - tells us how many ϭ is above or below the mean Z= 𝑥−µ ϭ (population as we have µ) Z = 𝑋−x̅̅̅̅ 𝑆 (sample as we have x̅̅̅̅ )
- 3. Z-Score - Let’s suppose I want to know how far above the mean I am then I will subtract the mean from my score - But this is not very useful with the subtraction alone because if I have different populations with different mean and different std deviation (different spread among the data) then is not very helpful just to know how far ahead of the mean I am - For this I divide by std. dev. so I know how many std. dev. I am above or below from the mean - This allow me to compare myself with other schools or other classes Problem: SAT average score is 500 with std dev of 150 points. What is the std score for a person who score a 630? - You can conclude that yes the score is above median but not really very good but is not even 1 std dev Z= 𝑥−µ ϭ = 630−500 150 = 0.87ϭ
- 4. Z-Score Problem: Person A scored 87 on a phisics test. Class average was 80 with a std dev of 5. Person B scored 82. Her class average was 73 with std dev of 6. who scored better with respect to their class? ZA= 𝑥−µ ϭ = 87−80 5 = 1.4ϭ ZB= 𝑥−µ ϭ = 82−73 6 = 1.5ϭ Both students done well, however Student B score better than Student A in term of Z-Score WITH RESPECT TO THEIR CLASS!!!