Unit 1: Stats

Individuals

objects described by a set of data

variable

any characteristic of an individual

categorical

places an individual into one of several groups or categories

quantitative

takes numerical values (aka numbers)

C-SOCS

C: context (what do the values represent)

S: spread (min and max)

O: outliers

C: center (mean/median)

S: shape (symmetric, skewed, ect)

Symmetric means…

mean=median

Skewed left

• mean is less than median

  • “clumped” on right with tail on the left

skewed right

• mean is greater than median

  • “clumped” on left with tail on the right

mean

• add all the values together

• divide by the number of values added

median

midpoint of all the data values (count in equally from both sides until you reach the center)

what is included in the 5-number summary

min, Q1, median, Q3, max

how to find Q1

middle of the values below the median

how to find Q3

middle of the values above the median

how to find IQR

Q3-Q1 (distance between the two)

how to find outliers

Lower outlier cutoff: Q1-(1.5 x IQR)

Higher outlier cutoff: Q3+(1.5 x IQR)

standard deviation

• definition

• how to find

• average distance that the data values are spread out from the MEAN

  • put values in calc and use ‘calc’ function to get 5-number summary

empirical rule (what values)

• 68% of data lies within 1 SD of the mean

• 95% of data lies within 2 SD of the mean

• 99.7% of data lies within 2 SD of the mean

z-score

(x - µ) divided by σ

how to use ‘table A’ (to find percentage/probability)

• calculate z-score

• match z-score to number in ‘table A’

  • turn 4 digit number into a percentage (x100) or keep as is for probability

how to use ‘table A’ (inverse normal calculations)

• find the z-score

• substitute it into z-score equation and solve for x (data value)

area to the left of z

use table entry

area to the right of z

1-table entry

area between z1 and z2

difference between table entries for z1 and z2