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Interpreting Sets of Data

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1. Jack borrows $3000 to buy a second-hand car on a flat rate loan at 12% p.a. interest over 4 years.

a. How much will he repay altogether?

b. What is his monthly repayment?

2. Tina has a credit card with an interest-free period of 45 days and an interest rate of 16% p.a. She makes the following purchases for the period 1 Nov to 30 Nov:

7 Nov Clothes $325.509 Nov Shoes $295.0017 NovClothes $570.5024 NovSinging lessons $146.0025 NovMakeup $54.0026 NovBeauty treatment $137.00a. What is the total amount of her purchases?

b. Tina pays her account in full on 15 Dec. How much interest does she pay?

I = PrnI = 3000 x 0.12 x 4

I = $1440

3000 + 1440 = $4440

4440 ÷ 48 = $92.50

$1528.00

Interest is charged on each purchase from the date of purchase until the date payment is received.Purchase amount No. of days interest Interest to 15 Dec ($)$325.50 9325.50 x 0.000438 x 9 = 1.28$295.00 7295.00 x 0.000438 x 7 = 0.90

Total interest - 1.28 + 0.90 = $2.18Tina's total payment - $1528.00 + $2.18 = $1530.18

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Collecting and Displaying DataTypes of Data

Data falls into one of the following categories:·Quantitative (numerical) data that is discrete, such as the number of computers in schools.·Quantitative (numerical) data that is continuous, such as the weights of gym members·Categorical (qualitative) data, such as the birthplaces of people living in Sydney.Random Sampling

If a population is too large or too difficult to survey, a sample of items can be taken from the population and analysed, and the results used to reflect population characteristics. ·A simple random sample is one where each member of the population is equally likely to be chosen - e.g. choosing the winning balls in Lotto.·A systematic sample is one where the first member is chosen at random and the others are chosen at regular intervals - e.g. every 8th toy on a production line. ·A stratified sample is one where a representative sample is taken from each stratum or layer of a population - e.g. a stratified sample from a population containing 70% adults and 30% children would contain 70% adults and 30% children.

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Example 1What type of data is each of these?a) the numbers of people attending the Olympic Games.b) the types of breakfast cereal in Cottonworths supermarket.c) the body temperature of a hospital patient taken over a 24-hour period.

a) Quantitative and discrete since the data are distinct whole numbers.b) Categorical since the data are brand names of cereals.c) Quantitative and continuous since the data can be measured along a continuous scale.

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$1 650 $4 650

Q.3a. $1 050b. $486c. $73.56

d. $188.37e. $1 659f. $96.39

g. $222.34h. $1 608.18i. $194.93j. $131 262

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Answers:1a) quantitative continuous; b) quantitative discrete; c) quantitative continuous; d) categorical; e) categorical; f) quantitative continuous; g) quantitative discrete; h) quantitative continuous; 2. population too large; population too difficult to survey; 3) Biased sample is not truly representative of the population. Unbiased sample is representative of the whole population; 4a) systematic; b) stratified; c) simple.

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9% p.a.

11% p.a.

12% p.a.

9.5% p.a.

$1 687.50 $6 187.50$171.88

$433.50$2 133.50$59.26

5a) i) column graph showing percentages of different drugs used by Australians; ii) qualitative (or categorical); iii) display gives clear comparison of drugs most/least used.b) i) clustered column graph showing the numbers of people in different age groups who get a Newstart Allowance; ii) quantitative (or numerical) and continuous; iii) display should have a title on each axis; shows a good comparison within age groups.c) i) line grph showing road fatalities from March 1995 to March 1999; ii) qualitative (or categorical) iii) display shows peaks, troughs and steady decline in deaths; exact values not easy to read off.

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3+5=8

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