use Theorem 6.2 to determine whether W is a subspace of V.V 2, W 5a bx cx 2 : abc 06

STA 100 NOTES WEEK 2 FALL 2016 LECTURE 2 Data Visualization:​ Categorical variables (labels, categories) that help to find trends. I) Pie Charts ***Melcon does not like these -takes a circle, splits it into pieces, and makes each slice a representative of a percentage. Example Pros​: Cons​: ● Gives the highest and lowest of the ● Difficult to compare slices data set ● Becomes cluttered with many categories ● Cannot easily have more than 1 categorical variable II) Bar Plot (Bar Chart) -Allows for 2 categorical variables. Example Pros​: ● Much easier to compare Cons​: ● Can get crowded, which is difficult to avoid **Can use relative frequencies. Relative Frequency = frequency / n A B C D Male 8 10 2 4 Female 7 10 8 1 Male Rel. .16 .20 .04 .08 Female Rel. .14 .20 .16 .02 III) Mosaic Plot -Horizontally stacked bar plot -Can have between 1 and 3 categorical variables. -1 categorical variable means we are only com