2.1 Measuring Position Flashcards
Interpret Percentile: what does it mean to say that your test score was in the 90th percentile?
90% of the students who took test scored less than or equal to my score.
Using a cumulative relative frequency graph, how do you find the median?
Find 50% on the y-axis and trace over to the line. Then go straight down to the x-axis. That value is the median. (feel free to draw right on the graph).
How do you find the IQR on a cumulative relative frequency graph?
Approximate where 25% and 75% are on the y-axis and trace over to the line to get the x-values for Q1 and Q3 respectively. IQR = Q3-Q1.
Using a cumulative relative frequency graph, how do you find what percentile a given x-value is at?
Trace up to the line from that x-value. The y-value at that point is the percentile.
Using a cumulative relative frequency graph, how can I tell where the most data lies?
The steeper the graph in-between any two x-values, the more data there is in that interval.
How do you find a z-score?
Take your value minus the mean and the divide by the standard deviation.
How do you interpret a z-score?
The (value) is (z-score) standard deviations (above/below) the mean (with context).
If you transform all your data (maybe converting units or something) by multiplying or dividing everything by some factor, how will this affect SOCS?
The shape will be the same but the center and spread will both be scaled accordingly. Example: if you convert everyone’s heights from feet to inches, the mean and s.d. would both be multiplied by 12 but the overall shape wouldn’t change.
If you transform all your data (maybe converting units or something) by adding or subtracting everything by some number, how will this affect SOCS?
The shape and the spread will be the same but the center will be adjusted accordingly. Example: if you everyone stood on a chair, the mean of their heights would increase by the height of the chair, but the s.d. and the overall shape wouldn’t change.
If you convert all of your data to z-scores, how will this affect SOCS?
Same question, different wording:
If you standardize all of the data…
The shape stays the same (IMPORTANT: it does not become normal just because we are talking about z-scores). The mean will be 0 and the S.D. will be 1 (always).
Why is a z-score called a standardized score?
It removes units and allows you to compare data from different distributions using the same standard (how many standard deviations a value is from the mean).
Relative to the distribution of heights of people their own age, how could I tell who was taller, me or my little brother?
Convert both of our heights to z-scores using the mean and s.d. for our separate distributions. Whichever z-score is bigger is “relatively” taller.
