Mathematics - 0580 CIE

Relative And Expected Frequencies

Muhtasari

Not every probability can be worked out by counting equally likely outcomes. What is the chance a drawing pin lands point up, or that a particular footballer scores a penalty? For these we have to experiment, and that is where relative frequency comes in: we run trials, record what happens, and use the results to estimate the probability.

In this lesson you will learn how relative frequency estimates a probability from real data, and why more trials give a better estimate. You will then turn the idea around: given a probability and a number of trials, you will predict how often an event should happen using expected frequency. Together these two ideas connect probability to the real world of experiments and surveys.

Malengo

Understand relative frequency as an estimate of probability.
Calculate expected frequencies.

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Maelezo ya Somo

Theory only takes you so far. When outcomes are not equally likely, or when you simply do not know the true probability, you have to gather evidence. Manufacturers test products, scientists run experiments and pollsters survey voters precisely so they can estimate probabilities from real results. Relative and expected frequencies are the bridge between the tidy world of theory and the messy world of data.

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A spinner is spun 200 times and lands on red 50 times. Estimate the probability of red. A. 0.1 B. 0.25 C. 0.4 D. 0.5 Answer: B
The probability of an event is 0.2. In 50 trials, what is the expected frequency? A. 5 B. 10 C. 20 D. 25 Answer: B
A fair die is rolled 120 times. How many times would you expect to roll a 4? A. 6 B. 12 C. 20 D. 24 Answer: C
Which gives the most reliable estimate of a probability from an experiment? A. 5 trials B. 20 trials C. 100 trials D. 1000 trials Answer: D
A bag of seeds has a germination probability of 0.9. Out of 300 seeds, how many are expected to germinate? A. 27 B. 90 C. 210 D. 270 Answer: D

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Vitabu Vinavyopendekezwa

Cambridge IGCSE Mathematics Core and Extended Coursebook

Manukuu: Second edition

Mchapishaji: Cambridge University Press

Mwaka: 2018

ISBN: 978-1-108-43718-9

Maelezo: Endorsed coursebook with full coverage of the 0580/0980 syllabus, worked examples and practice exercises.

Cambridge IGCSE Core and Extended Mathematics

Manukuu: Fifth edition

Mchapishaji: Hodder Education

Mwaka: 2023

ISBN: 978-1-398-37391-4

Maelezo: Endorsed textbook with worked examples and graded questions across Core and Extended content.

Jifunze zaidi kutoka vyanzo huria

Sehemu ya kitabu Frequency, Frequency Tables, and Levels of Measurement OpenStax · Introductory Statistics
Once you have a set of data, you will need to organize it so that you can analyze how frequently each datum occurs in the set. However, when calculating the frequency, you may need to round your answers so that they are as precise as possible. A simple way to round off answers is to carry your final

"Introductory Statistics: Frequency, Frequency Tables, and Levels of Measurement" by OpenStax, OpenStax, Rice University, licensed under CC BY 4.0 (https://creativecommons.org/licenses/by/4.0/). Source: https://openstax.org/books/introductory-statistics/pages/1-3-frequency-frequency-tables-and-levels-of-measurement. Access for free at https://openstax.org/books/introductory-statistics/pages/1-introduction

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