Numerical Summaries of Data

Descriptive Statistics def

tools that are used to organize and summarize data numerically

measures of central tendency def

used to represent “central” or “typical values in a data set”

three most common measures of central tendency

mean, median, and mode

mean def

the arithmetic average of a set of data values

Mean forumla

X₁+ X₂+…X_n/n

mean example

actually do it love

advantage of the mean (3)

1. it is easy to compute

2. it is a unique descriptive

3. it is the most representative measure of center because it takes every score value into account

Disadvantage of the mean

because it takes every score value into account, the mean is sensitive to extreme scores and outliers

outlier def

a data value that is “far away” from the majority of other values in a data set

Median def

the value that divides a dataset into two equal parts such that the same number of scores in the dataset fall above and below this value

Steps to finding a median

1. arrange all data values in ascending order from least to greatest

   1. given an ODD number of data values, the median is the exact middle value in the ordered list

   2. Given an EVEN number of data values, the median is the average of the middle 2 values in the ordered list

Median EX

do ittttt

Advantage of the Median

Because the median only looks at vlaues in the middle of a dataset, it is less sensitive to extreme scores/outliers than the mean

Disadvantage of the Median

Because it only looks at values in the middle of a dataset, the median is not as representative a measure as the mean

Mode def

the score value that occurs most frequently in a dataset

Mode example

lol do it gurl

if two scores have the same frequency

bimodal

if more than 2 scores have the same greatest frequency

multimodal

advantage of mode

it is the only measure of central tendency appropriate for use with qualitative data

disadvantage of mode

it tends to be less informative than the mean or median when dealing with quantitive data

symmetric distribution def

a distribution of data where the left half of its graph is a mirror image of the right half, and vice versa

Bell shaped distribution shape

positively skewed distribution def

a distribution that is not symmetric because it has a long tail to the right

score values in positively skewed distributions

the majority of score values fall on the low end of the score scale and the outliers extend the tail to the right

how do mean, median, and mode interact in a pos skewed distribution

mode < median < mean

Negatively asked distributions def

a distribution that is not symmetric because its graph extends further to the left

negatively skewed distributions score values

majority of score values fall on the high end and a small number of extreme scores trail the tails to the left

neg skewed distribution image

negatively skewed distribution mean, median and mode

mean < median < mode