Stats 2.1: Frequency Distributions & Their Graphs

Characteristics of Data Set

1. center

2. variability

3. shape

Frequency Distribution

frequency distribution

table that shows classes (or intervals) of data entries w/ a count of the number of entries in each class

Frequency Distribution

frequency

number of data entries in a class

Frequency Distribution

lower class limit

lowest data value that can fit in a class

• Ex: class = 1-5 → LCL = 1

Frequency Distribution

upper class limit

highest data value that can fit in a class

• Ex: class = 1-5 → UCL = 5

Frequency Distribution

tolerance

[LCL of next class] - [UCL of previous class]

• aka difference between the [lowest of higher class] & [highest of lower class]

• Ex: tolerance between class [1-5] & [6-10] = 6 - 5 = 1

Frequency Distribution

class width

distance between lower (or upper) limits of consecutive classes

• aka difference between the 2 lowest/highest values of each adjacent class

• Ex: class width between class [1-5] & [6-10] = 6 - 1 = 5

Frequency Distribution

range

difference between the maximum & minimum data entries

• Ex: range between lowest class [1-6] & highest class [26-30] = 30 - 1 = 29

Frequency Distribution

Guidlines for Constructing Frequency Distribution

pre. find RANGE

1. decide on # of CLASSES (# class = range / class width)

2. find CLASS WIDTH (class width = range / # classes & round UP)

3. find class LIMITS (can NOT overlap)

4. make tally mark for each data entry

5. count tally marks to find total FREQUENCY

Frequency Distribution

class boundaries

numbers that seperate classes w/o forming gaps between them

• UCBoundaries = UCL + Tolerance/2

• LCBoundaries = LCL - Tolerance/2

*UCB of lower class = LCB of higher class

Frequency Distribution

midpoint

[sum of LCL & UCL ] divided by 2

Frequency Distribution

relative frequency

portion or % of the data that falls into that class

• frequency of 1 class / cumulative frequency

• unit: % or decimal (more preferred)

Frequency Distribution

cumulative frequency

sum of frequencies of that class & ALL previous classes

• ∑f of LAST class = sample size (n)

Graph

frequency histogram

graph that uses bars to represent frequency distribution of a data set w/ properties:

1. horizontal scale (quantitative) = class boundaries OR midpoints

2. vertical scale = frequencies

3. consecutive bars MUST touch

Graph

relative frequency histogram

frequency histogram BUT w/ vertical scale = relative frequencies

Graph

ogive (cumulative frequency graph)

line graph that displays cumulative frequency of each class at its UCB

Graph

Guidelines for Constructing Ogive

1. construct frequency distribution w/ cumulative frequencies

2. specify horizontal & vertical scales

• horizontal = UCB

• vertical = cumulative frequencies

3. plot points that represent UCB & corresponding cumulative frequencies

4. connect points in order from left → right w/ line segments

5. graph should start at LCB of first class (cumulative frequency = 0) & end at UCB of last class (cumulative frequency = n)