Unit 3

center

typical value, central tendency, kind of average

shape

can either be symmetric or skewed

spread

• varied, dispersed, scattered from the center

∑

capital sigma

summation operator — adds up

ⁱ

index — keep observation straight ,

[1,2,3,4,… n] kept consistent

∑xⁱ

• sum of all n values of x

• i = variable represents x+y values

square sum of variables

• (sigma x index)² (x₁+x₂+x₃+….x_n)²

square each variable

• sigma x index ² x²₁+x²₂+x²₃+… x²_n

what is more: square sum of variables or square each variable

square sum of variables

how can you control which observation to sum over

number on top of sigma means where to stop

number below sigma means where to start

mean

average — typical central tendency

x bar

another term for mean , can be sample mean (stats) or population mean: μ

computing the mean (with frequency data)

sum of values/ n

sigma x index/ n

how to compute x bar

add all y values then divide by the different variables given (n)

multiplie each value (x) by the frequency (f)

add the products then divide by “n”

group frequency distribution

need to find the x values sepereatley

how: midpoint of each measurement interval to stand

whats the error with group frequency distribution when finding the mean

• gives us a different mean compared to ungrouped data

distribution point

• deviation around the sum to zero

x_i- xbar

deviation of the mean (sum) minus the mean

above the mean is positive

below the mean is negative

deviation around the mean must equal 0

subtract the given x values by the mean

x- mean

mean minimizes the squared deviations around it

(x_i-x)^-2

squared deviation (x_n-x)²

spread out version of squared deviation

• sigma (x_i - x)² = (x-x bar)²+ (x₂-x bar)²

most likely to get use to the smallest number

x bar

mean , number that minimizes the square deviation around it

squared deviation

refers to the process of calculating the squared difference between a data point and the mean of a dataset

outliers

can effect the mean, a number in the graph that is really seperated from the other points

right tail , right skewed

means there is large outliers in the graph

left tail, left skewed

means there is small outliers in the graph

best type of variable for means

requires quantitative data, not for nominal variable, ok for ordinal not the best, affected by outliers

the median

the middle of the graph

distribution in half from the lowest and highest where the data falls

50th percentil of distribution

calculate the median when its odd

use middle value of the medican

(n+1)/ 2

calculate the median when its even

the average of the two middle numbers , most likely will result in a decimal

when to find median data

not for nominal data ok with ordinal and interval data , not affected by outliers

mode

variables most frequently occuring in a data set - basically highest y value

visually — highest point in a bar chart , biggest slice in pie chart

what type of graph doesn’t have a mode

• uniform distribution graph

right skewed and left skewed

• right: mode , median, mean

• left: mean, median , mode