AS2 - Measures of location and spread Flashcards
Name some measures of spread and central tendency:
-variance
-standard deviation
-range/IQR/interpercentile ranges
-mean
-median
-mode
Explain what a percentile is:
-imagine the data is ordered, then split up into 100 parts
-the 23rd percentile would be 23% of its way into the data
How do you find quartiles for discrete data?
Q1 - n/4 and round up if fractional (if integer, take item halfway between this data point and the one above)
Q2 - same rules as Q1 but n/2
Q3 - same rules as Q1 but 3n/4
For the median, you can also do (n+1)/2 and not round, but using (n+1) for the other quartiles will not work - it is best to stay consistent with the method above.
When should you round location values?
only round up location values when given raw data
When given grouped data, use exact values and interpolate for measures of location
When should you interpolate data?
when you have grouped data, as interpolation assumes the unknown raw data is evenly distributed within a class
How do you interpolate data from a table?
-identify the class your measure of location is in
-start with the lower bound of the class (not the rounded value, the actual value)
-add on the fraction of the way into the class your item is, and multiply the fraction by the class width
https://www.youtube.com/watch?v=dZZu3sDVU5A
What is variance and standard deviation, and how do they relate to each other?
-standard deviation, σ, is the average deviation from the mean
-variance is just σ²
Give the formula for standard deviation:
What is coding, and how does it affect the data’s summary statistics?
-changing the data by some linear function as below
-the coded mean can be found by inputting the original mean into the function
-the coded SD can be found by multiplying it by the linear factor that the data was spread out by
