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1.3.1: The mean and the median

This subsection looks at two ways of finding an ‘average’. The first produces the mean, which is what was originally meant by ‘average’, and what most people think of when they talk about an average. The second gives the median, which might more accurately be described as a ‘typical’ or middle value. They will be illustrated using the following batch of heights.

The heights in metres (measured to the nearest centimetre) of a group of seven people are as follows
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1.3: A statistical interlude—averages

Aims The main aim of this section is to discuss several ways of finding averages and to introduce you to the statistical facilities of your calculator.

A single number which is typical or representative of a collection (or batch - statistical term for a set of collected data.) of numbers is commonly referred to as an average. There are several different ways of defining such a number. Two are discussed briefly in Author(s): The Open University

1.2.3: A typical shopping basket

This subsection discusses using a typical basket of goods to analyse price changes over time. However, what is meant by ‘typical’?

Think back to the last time you went shopping. What did you buy? The electric light bulbs that you have just stocked up on are unlikely to be in your shopping basket next week, whereas milk may well be there every week. And there may be items—a new toothbrush for example—that you buy from time to time, but not this week.

To monitor price change
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1.2.1: Using your loaf

Cade: There shall be in England seven halfpenny loaves sold for a penny; the three-hooped pot shall have ten hoops; and I will make it felony to drink small beer.

(William Shakespeare, Henry VI, Part 2, written in 1594)

In this quotation, the character Cade anticipates the good times that are sure to follow after the revolution. The notion of the ‘halfpenny loaf’ is interesting, as is t
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1.2: Are we getting better off?

Aims The main aim of this section is to introduce some ideas about making valid comparisons and to focus on ways of extracting information from tables and graphs.


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7 OpenMark quiz

Hopefully, thinking about how your solution to a mathematical problem might be marked, will help you to produce better solutions for yourself, as well as for somebody else. Now try the quiz  and see if there are any areas you need to work on.


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6.5 Solutions to ‘making a lawn’

Learning from the marking of the previous questions, write out a good solution to the following problem.

Example 18: Making a lawn

Suppose you have some friends who are planning to put a new lawn in their garden. The lawn is to be 12 m by 14 m and they have a choice of either laying turf or sow
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6.3 Solving the riddle of St Ives

Write out your own solution to the following problem.

Example 17: St Ives

As I was going to St Ives

I met a man with seven wives.

Each wife had seven sacks.

Each sack had seven cats.

Each cat had seven kits.

Kits,
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6.2 Another ‘billions’ solution

Pretend that you are the marker of another solution to the same problem. How would you mark Solution B?

Example 16 Billions

You may think that you know what the word billion means but do you really have a feel for its size?

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4.4 ‘Show that ’ questions

In this type of question you are given the answer! All the marks are allocated for correct reasoning and justification.

Example 15

Suppose you now decide to place your new bath (length 1.7 m, height 0.8 m) against this wall as shown in the diagram below.

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4.3 ‘Find’ questions

Example 14

Suppose you have decided to tile the wall using square tiles of side 10 cm. You are proposing to use the tiles across the full 5 metre width of the wall up to a height of 1.8 m.

Find the number of boxes of tiles that you will require to cover the wall if the tiles are sold in boxes o
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3.2.1 Try some yourself

1 You are planning to paint three rooms with total wall areas of 56, 38 and 40 square metres, using paint that comes in tins which claim to cover 15 square metres per tin. How many tins will you need for each room? And how many in total?

<
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3.2 Using formulas

Formulas are important because they describe general relationships, rather than specific numerical ones. For example, the tins of paint formula applies to every wall. To use such a formula you need to substitute specific values for the general terms, as the following examples show.

Example 8

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1.3.4 Guidelines for graphics

  1. Data in the form of counts of individual entities (for example, people, animals, power stations) in a small set of discrete categories can be presented in bar charts or pie charts. For most purposes, bar charts are preferable. Pie charts draw particular attention to the proportions in which the entities are split between the different categories. However, they do so by representing the proportions by angles, and even when the main interest lies in the propo
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2.5 Position vectors

Finally, we relate the method of specifying points in the plane as an ordered pair of real numbers (that is, via the Cartesian coordinate system) to vectors.

In order to do this, we use those vectors whose starting point is the origin; such vectors are called position vectors. For example, the position vector (2, −1) is the vector shown below.

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3.5 More examples of percentages

In lots of everyday situations percentages are used to make predictions and comparisons.

Example 14

The number of casualties handled by the outpatients department of a hospital increases by approximately 8% per year. The number of casualties this year was 1920. Make a prediction for the number
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3.4 Decreasing by a percentage

Discount can be calculated in the same way as an increase by a percentage. For example, £8 with 15% discount means you actually pay

  £8 less (15% of £8)

  15% of 8 = × 8 = Author(s): The Open University

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Real Brazilian Conversations #36 – Avisos Importantes e Carnaval
Hello guys, Guilherme here. After a little break, we’re back again! Today I talk about an important cultural event in Brazil, the Carnival! Thre is something I need you to know about RLP, listen to...

Check out our website, reallylearnportuguese.com and find out more how we can help you to improve your Portuguese language skills!

A Factor Analysis of the Speech of Children with Cleft Palate
Original source: ; ; ; ; This electronic text file was created by Optical Character Recognition (OCR). No corrections have been made to the OCR-ed text and no editing has been done to the content of the original document. Encoding has been done through an automa ted process using the recommendations for Level 2 of the TEI in Libraries Guidelines. Digital page images are linked to the text file.
Author(s): Duane R. Van Demark

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2.1.3 Concept cards

Another way to tackle unfamiliar words is to start a ‘concept card’ system, using index cards. When you meet a word which seems important, take a new card and write the word at the top, followed by any useful information you have found. File the cards alphabetically and add details as you come across new information. (It is worth getting an index card box anyway, then you can try out various ways of using it to organise your studies.)


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