3.3/ 3.4 Finding + Using Median

Question 1

Context for medians

Answer 1

Better represents the center value in data set (center value= most reported numerical variable-> NV being that which the whole graph is representing/ x-axis) for SKEWED distributions
!!! BUT mean is better for relatively symmetric distributions

Middle value when data is ordered from least to greatest (you dont even need every single data, just half of it/ dont need the outliers at the end of the list)
!!!!
Median helps you get an idea of distribution (how often the numerical values show up/ the important ideas-> NV is age 18 and how many ppl are 18 are numerical values) half of all the data is more or less than the median value ***(mean has this job too, but they are diff because of what they consider to establish a “typical value”)

When median and mean are ABOUT the same- data is evenly distributed from the lowest to highest (30-34 is only 4 datas outlying)
(No huge outlier to high values ratio)

!!!!!!! Half of all NV is less or more than this median #
Mean- this mean # is the average for EVERY NV, not just Half

Centers are not centers since data sets are sets with MULTIPLE values (skewed) -> they all provide singe-value summary/ each give a simple summary of data
Mean-> the outcome we expect on average
Median-> value that divides data in halves so we can compare values
Mode-> most common value

Question 2

Find median

Answer 2

Biggest to smallest (notice that values are already sited this wya on graph, so median stands there)
Cancel on both sides evenly until yo get middle number
* if two middle numbers-> find average by adding them/ 2

OR find location:
# of observations + 1/ 2
It will always be a 1!!
or just say “between 11th and 12th”

Question 3

Use median to compare

Answer 3

Pattern you will see is that mean values are bigger than medians _ of outliers
Although it isn’t an average of the values, it compares better because it doxxes the ACTUAL frequent values, not influenced by large outliers like averages which wont let the average joe know what they want to to know
Median shows the effectiveness/ worth it ness of things

Question 4

Median tips

Answer 4

Will ALWAYS be peak
Mean is always being pulled to the direction for the outlier (half of all datas are MORE than the median value/ the numerical VARIABLE/ x axis) -> this makes it skewed

Question 5

Skewed left and right

Answer 5

Skewed right= median is a smaller value (x axis) than the mena going right
Skewed left= median is greater value than mean going left

Question 6

What do with outlier

Answer 6

Check if they’re mistakes, if not do analysis with and w/o outlier

Question 7

Median definition

Answer 7

Half of violent crimes at rate per (x) are above MEDIAN VALUE and half are below MEDIAN VALUE