Tables & Relative Frequency (College Board AP® Statistics): Study Guide

Naomi C

Written by: Naomi C

Reviewed by: Dan Finlay

Updated on

Frequency tables

How are frequency tables used for ungrouped data?

  • Frequency tables can be used for ungrouped data when you have lots of the same values within a data set

    • They can be used to collect and present data easily

  • If a particular value has a frequency of 3 this means that there are three of that value in the data set

  • For example, the number of pets owned by a group of individuals

    • could be presented as a list, e.g. 0, 0, 0, 1, 1, 1, 1, 1, 2, 2, 2, 2, 3, 3 , 3, 3, 3, 3

    • or alternatively, in a frequency table

Number of pets

0

1

2

3

Frequency

3

5

4

6

How are measures of center calculated from frequency tables with ungrouped data?

  • The mode is the data value that has the highest frequency

  • The median is the middle value of the data when put in order

    • Use cumulative frequencies (running totals) to find the median

      • The median is the data value that is halfway through the total frequency

  • The mean can be calculated by

    • multiplying each value x subscript i by its frequency f subscript i

    • summing these together to get sum for blank of f subscript i x subscript i

    • then dividing by the total frequency n equals sum for blank of f subscript i = Σfi

    • The formula, x with bar on top equals fraction numerator sum from i equals 1 to n of f subscript i x subscript i over denominator n end fraction, is not given in the exam

  • Your calculator can calculate these statistical measures by inputting the values and their frequencies into your calculator and calculating one-variable statistics

How are measures of variability calculated from frequency tables with ungrouped data?

  • The range is the largest value of the data minus the smallest value of the data

    • It is not the largest frequency minus the smallest frequency

  • The interquartile range, IQR, is the third quartile subtract the first quartile, IQR equals straight Q 3 minus straight Q 1

    • The quartiles can be found by listing out the data and calculating by hand

      • or by using that Q1 is the data value that is a quarter of the way through the total frequency etc.

    • or by inputting the values and their frequencies into your calculator and calculating one-variable statistics

  • The standard deviation and variance can also be calculated by hand using the formulas after listing out the values

    • or by inputting the values and their frequencies into your calculator and calculating one-variable statistics

How are frequency tables used for grouped data?

  • Frequency tables can be used for grouped data when you have lots of values within the same interval

    • Class intervals will be written using inequalities and without gaps

      • 10 less or equal than x less than 20 and 20 less or equal than x less than 30

  • If a particular class interval has a frequency of 3 this means that there are three data items in that class interval

    • You do not know the exact data values when you are given grouped data

  • For example, the heights of students within a class

    • could be presented in a grouped frequency table

Height, h

Frequency

150 less or equal than h less than 155

1

155 less or equal than h less than 160

3

160 less or equal than h less than 165

5

165 less or equal than h less than 170

4

170 less or equal than h less than 175

2

Relative frequency tables

What is a relative frequency table for ungrouped data?

  • A relative frequency table gives the proportion of data items falling into each category

    • This may be presented as a decimal, fraction or percentage

  • If a particular value has a relative frequency of 0.4 this means that 0.4 or 40% of the items in the data set have that value

    • We do not know the exact number of data items in each group

    • However, we can calculate this if we are also told the total frequency

  • For example, the ungrouped relative frequency table below shows the number of siblings that a particular group of individuals have

    • 30% of the group have no siblings

    • 50% of the group have 1 sibling

    • 15% of the group have 2 siblings

    • 5% of the group have 3 siblings

Number of siblings

0

1

2

3

Relative frequency

0.3

0.5

0.15

0.05

What is a relative frequency table for grouped data?

  • The same idea of relative frequency can be applied to grouped data

    • If a particular class interval has a relative frequency of 7 over 10 this means that 7 over 10 or 70% of the items in the data set have a value within that class interval

      • We do not know the exact number of data items in each group

      • However, we can calculate this if we are also told the total frequency

  • For example, the grouped relative frequency table below shows the number of weights of a sample of cats

    • 8% of the group weigh between 1 kg and 2 kg

    • 42% of the group weigh between 2 kg and 3 kg

    • 31% of the group weigh between 3 kg and 4 kg

    • 19% of the group weigh between 4 kg and 5 kg

Weight of cat, w (kg)

1 less than w less or equal than 2

2 less than w less or equal than 3

3 less than w less or equal than 4

4 less than w less or equal than 5

Relative frequency

8 over 100

42 over 100

31 over 100

19 over 100

👀 You've read 1 of your 5 free study guides this week
An illustration of students holding their exam resultsUnlock more study guides. It's free!

By signing up you agree to our Terms and Privacy Policy.

Already have an account? Log in

Did this page help you?

Naomi C

Author: Naomi C

Expertise: Maths Content Creator

Naomi graduated from Durham University in 2007 with a Masters degree in Civil Engineering. She has taught Mathematics in the UK, Malaysia and Switzerland covering GCSE, IGCSE, A-Level and IB. She particularly enjoys applying Mathematics to real life and endeavours to bring creativity to the content she creates.

Dan Finlay

Reviewer: Dan Finlay

Expertise: Maths Subject Lead

Dan graduated from the University of Oxford with a First class degree in mathematics. As well as teaching maths for over 8 years, Dan has marked a range of exams for Edexcel, tutored students and taught A Level Accounting. Dan has a keen interest in statistics and probability and their real-life applications.

Download notes on Tables & Relative Frequency