DISTINTOS NIVELES ABCD Compulsory Secondary Education, 1 st and 2 nd years Compulsory Secondary...

DISTINTOS NIVELES

A B C DCompulsor

y Secondary Education, 1st and 2nd

years

Compulsory

Secondary Education,

3rd and 4th years

Non-Compulsor

y Secondary Education

University

12 to 14

14 to 16

16 to 18

From 18

onwards

GOODSFinland

KiuruvesiSpain

Granada Italy FolignoItaly

Bussero

price/€ price/€ price/€ price/€

Milk (1.5% fat) 0,78 0,85 0,78 1,33

Danone Activia (yoghurt) 1,23 1,38 2,83 2,2

Philadeplhia (cream cheese) 2,09 1,39 1,7 1,77

Butter 3,89 2,9 1,9 4,39

Mozzarella cheese 1,8 1,5 1,18 1,83

ESTADÍSTICA DESCRIPTIVA

1.- Display by means of a bar chart

the prices of goods.

1 → Milk 2 → Danone Activia (yoghurt) 3 → Philadeplhia (cream cheese) 4 →Butter 5 → Mozzarella cheese

2.- Display by means of a bar chart a comparison of the prices of mozzarella cheese in the different cities.

1 → Kiuruvesi 2 → Granada 3 → Foligno 4 → Bussero

3.- Carry out a pictograph in order to compare the prices of one milk good in different countries.

1,83 € 1,8 €

1,5 € 1,18 €

The chosen good will be Mozzarella cheese:

Bussero Kiuruvesi Granada Foligno

4.- What is the average price in each country?

the arithmetic

mean

Kiuruvesi

9,79/5

1,958

Granada

8,02/5

1,604

Foligno

8,39/5

1,678

Bussero

11,52/5

2,304

5.- What is the median in the case of milk?

All the observations are arranged from lowest value to highest value and then we look for the price which is a 50% higher than all the rest:

GOODSFinland

Kiuruvesi Italy Foligno Spain GranadaItaly

Bussero


Milk (1.5% fat) 0,78 0,78 0,85 1,33

Me = = 0,815 €.

6.- ¿What is the data variation in relation to the atithmetic mean in each good?

GOODThe

arithmetic mean

The variance

The standar

d deviatio

n

Milk (1.5% fat) 0,935 0,052825 0,2298

Danone Activia 1,91 0,41845 0,6469

Philadeplhia (cream cheese)

1,7375 0,06187 0,2487

Butter3,27 0,91315 0,9556

Mozzarella cheese 1,5775 0,06932 0,2633

7.- Which good has more homogeneous data?

Milk (1.5% fat) 25,58 %Danone Activia

(yoghurt)33,87 %

Philadeplhia (cream cheese)

14,31 %Butter 29,22 %

Mozzarella cheese 16,69 %Therefore, the good whose data are more homogeneous is “Philadeplhia (cream cheese)”.

CV

CV

CV

CV

CV

8.- Carry out a graphic representation where all the milk goods are compared, in relation to all the countries

1. Milk (1.5% fat) 12. Coca cola 23. French fries1. Danone Activia 13. Red Bull energy drink 24. Carte d'or ice cream1. Philadeplhia 14. Ristorante pizza sal. 25. Coca Cola Zero1. Chiquita bananas 15. Heinz tomato ketchup 26. Twix chocolate bar1. Apples (Jonagold) 16. Granini juice 27. Pringles Original 1. McVites Digestive 17. Wheat flour 28. Nestle Fitness cereal 1. Coffee filters 18. Pasta 29. Nestle Nesquik cereals1. Salt 19. Twinings tea 30. Sugar1. Nescafe G. coffee 20. Ham 31. Mozzarella cheese1. LU TUC crackers 21. Oranges 32. Butter1. Kellogg's corn flake 22. Knorr lasagnette 33. Bread

GOODS QuantityFinland

KiuruvesiSpain


Bussero


Milk (1.5% fat) 1 l 0,78 0,85 0,78 1,33

Philadeplhia (cream cheese) 200g 2,09 1,39 1,7 1,77

Chiquita bananas 1 kg 1,79 1,8 1,7 1,87

Apples (Jonagold) 1 kg 1,49 1 1,68 1,61

McVites Digestive bisquits 400 g 1,52 1,49 2,84 2,09

Coffee filters 100 kpl 1,39 0,8 3 3,34

Salt 1 kg 0,85 0,17 0,3 0,53

Nescafe Golden coffee 0,5 kg 5,69 4,65 5,38 17,26

Kellogg's corn flakes 500 g 2,29 1,99 2,46 2,91

Coca cola 1,5 l 2,39 1,38 1,49 1,36

Red Bull energy drink 0,25 l 1,55 1,19 1,43 1

Ristorante pizza salame 320 g 2,79 2,49 2,6 2,59

Granini juice 1 l 1,71 1,57 1,65 1,5

Wheat flour 1 kg 0,76 0,71 0,6 0,57

Pasta 1 kg 1,13 0,7 0,82 1,61

Twinings tea 200 g 4,3 2 3,5 6,75

Ham 1 kg 16,06 13,3 25 25,2

Oranges 1 kg 1,49 1,38 1,68 1,55

Knorr lasagnette 338 g 3,35 3,12 3,2 2,84

French fries 450 g 0,76 1,75 2,5 1,36

Carte d'or ice cream 0,9 l 4,39 3,8 3,85 3,58

Coca Cola Zero 1 l 1,21 1,52 1,54 1,4

Pringles Potato chips 165 g 1,96 1,89 1,89 1,91

Sugar 1 kg 0,89 0,71 1,15 0,89

Mozzarella cheese 150 g 1,8 1,5 1,18 1,83

Butter 500 g 3,89 2,9 1,9 4,39

Bread 500 g 2,19 2,39 1,9 1,4

ESTADÍSTICA DESCRIPTIVAMás ampliado

1.- What is the average Price of the shopping basket in each city?

n = 27

Kiuruvesi 70,51 2,611 €

Granada 58,44 2,164 €

Foligno 77,72 2,879 €

Bussero 94,44 3,498 €

2.- Once we work out how much prices differ in Granada and Foligno, what is the arithmetic mean of that quantity?

GOODS GOODSMilk 0,07 Pasta -0,12Philadeplhia (cream cheese) -0,31 Twinings tea -1,5Chiquita bananas 0,1 Ham -11,7Apples (Jonagold) -0,68 Oranges -0,3McVites Digestive bisquits -1,35 Knorr lasagnette -0,08Coffee filters -2,2 French fries -0,75Salt -0,13 Carte d'or ice cream -0,05Nescafe Golden coffee -0,73 Coca Cola Zero -0,02Kellogg's corn flakes -0,47 Pringles Potato chips 0Coca cola -0,11 Sugar -0,44Red Bull energy drink -0,24 Mozzarella cheese 0,32Ristorante pizza salame -0,11 Butter 1Granini juice -0,08 Bread 0,49Wheat flour 0,11

-19,28

3- Make a graphic representation displaying the differences of prices between Kiuruvesi and Bussero.

4.- Which city has a cheaper shopping basket on the average?

Kiuruvesi70,51 2,611 €

412,6351 8,465 2,9095 € 111,434%

Granada58,44 2,164 €

281,1358 5,7295 2,3936 € 110,612%

Foligno77,72 2,879 €

763,4058 19,9856 4,4705 € 155,28%

Bussero94,44 3,498 €

1084,614 27,9349 5,2853 € 151,096%

The city where the shopping basket is cheaper in relation to the average is: Granada.

5.- Which differences are less dispersed, those of Granada in relation to Foligno or those of Kiuruvesi in relation to Bussero?

KiuruvesiBussero -23,93 -0,886 € 149,4592 4,7505 2.1796 € 246%

GranadaFoligno -19,28 -0,714 € 232,3543 8,0959 2,8453 € 398,51%

The differences of the prices of the goods are less dispersed between Kiuruvesi and Bussero.


KiuruvesiSpain


Bussero


Milk (1.5% fat) 1 l 0,78 0,85 0,78 1,33

Philadeplhia (cream cheese) 200g 2,09 1,39 1,7 1,77

Chiquita bananas 1 kg 1,79 1,8 1,7 1,87




Salt 1 kg 0,85 0,17 0,3 0,53

Kellogg's corn flakes 500 g 2,29 1,99 2,46 2,91

Coca cola 1,5 l 2,39 1,38 1,49 1,36


Granini juice 1 l 1,71 1,57 1,65 1,5

Wheat flour 1 kg 0,76 0,71 0,6 0,57

Pasta 1 kg 1,13 0,7 0,82 1,61

Ham 1 kg 16,06 13,3 25 25,2

Oranges 1 kg 1,49 1,38 1,68 1,55



Sugar 1 kg 0,89 0,71 1,15 0,89


Butter 500 g 3,89 2,9 1,9 4,39

Bread 500 g 2,19 2,39 1,9 1,4

1.- Make the punctual and interval estimation of the average difference of prices between the cities of Granada and Kiuruvesi. Given a normality of prices.

INFERENCIA ESTADÍSTICA Intervalo de confianza

n = 21

KiuruvesiGranada

9,6 0,457 € 12,1268 0,3686 0,6071 €

Average prices of goods in Kiuruvesi are higher to those of Granada between 0,1973 and 0,7167 €, at a 95% of confidence.

2.- How big should the sample be in order to obtain an acuteness of 0,1 € in the difference of prices between the previous cities?

Since the target acuteness (0,1 €) is lower than the one obtained (0,2597 €) it is necessary to increase the size of the sample by means of the following expression:

The solution is of at least 142 goods.

3.- Make the confidence interval to estimate the average price of the goods of the shopping basket at Foligno.

Foligno 61,48 2,9276 € 707,9728 25,142 5,0142 €

Since normality of the difference of prices is supposed, the expression of the interval of

confidence is given by:

The average price of goods at Foligno is between 0,783 € and 5,0722 €, at a 95% of

confidence.

4.- Make a graphic representation of the initial data, by means of the arithmetic mean and standard deviation parameters.

n = 21

Kiuruvesi 55,04 2,9276 € 707,9728 25,142 5,0142 €

Granada 45,44 2,1638 € 245,1522 6,9912 2,6442 €

Foligno 61,48 2,9276 € 707,9728 25,142 5,0142 €

Bussero 64,76 3,0838 € 732,6858 25,38

5,0379 €

5- Make an estimation of the regression straight line of the differences of prices at Kiusuvesi and Bussero, in relation to the differences of prices of Kiuruvesi and Foligno

Y = “the differences between the prices at

Kiuruvesi and Bussero”

X = “the differences between the prices at Kiuruvesi and Foligno”

= = = = 88,6287 = = 87,2868 = = 83,6445 = The regression straight line Y over X is:


KiuruvesiSpain

GranadaItaly

FolignoItaly

Bussero


Milk (1.5% fat) 1 l 0,78 0,85 0,78 1,33

Philadeplia (cream cheese) 200g 2,09 1,39 1,7 1,77




Salt 1 kg 0,85 0,17 0,3 0,53

Coca cola 1,5 l 2,39 1,38 1,49 1,36


Wheat flour 1 kg 0,76 0,71 0,6 0,57

Pasta 1 kg 1,13 0,7 0,82 1,61

Ham 1 kg 16,06 13,3 25 25,2

Oranges 1 kg 1,49 1,38 1,68 1,55



Sugar 1 kg 0,89 0,71 1,15 0,89


Butter 500 g 3,89 2,9 1,9 4,39

Bread 500 g 2,19 2,39 1,9 1,4

1.- Are there relevant differences in the average prices of the shopping baskets between the cities of Kiuruvesi and Granada ? Given a normality of prices.

INFERENCIA ESTADÍSTICA Intervalo de confianza y Test de

hipótesis

The task is going to be carried out by University

students of 1st and 2nd year of Medicine and

Health Sciences.

“There is no difference in the average prices of the shopping basket of

Kiuruvesi and Granada”.

“There is difference in the average prices of the

shopping basket of Kiuruvesi and Granada”.

= 0,5094 = 0,4081

The experimental quantity is, subsequently, worked out:

It is compared to , , is rejected so there are relevant differences in the arithmetic

mean of the prices at Kiuruvesi and Granada, that is, generally speaking prices are lower at Granada.

2.- Work out the confidence interval of the difference of average prices at Kiuruvesi and Granada.

The average price of goods at Kiuruvesi is higher than the

average at Granada, between 0,1917 € and 0,8271 €, at a 95 %

of confidence.

3.- Are there relevant differences in the average prices of the shopping baskets between the cities of Bussero and Kiuruvesi? If so, count them.

“There is no difference in the average prices of the

shopping basket of Kiuruvesi and Bussero”.

“There is difference in the average prices of the shopping basket of

Kiuruvesi and Bussero”.

= 0,5094 = 0,4081

The experimental quantity is, subsequently, worked out:

It is compared to , , is

accepted so there are not evidences enough to state that there are differences in the arithmetic mean of the prices at

Kiuruvesi and Bussero.

The average price of goods at Kiuruvesi is higher than the

average at Bussero in some goods, up to 0,5782 € on the average; and lower up to , at a 95 % of

confidence.

DISTINTOS NIVELES ABCD Compulsory Secondary Education, 1 st and 2 nd years Compulsory Secondary...

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