Statistic

STATISTIC

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Subject: Matematics                      

Level  : 2º ESO

In this unit we are going to study the basic concepts of statistical data. The students will learn how to collect information to use in a statistical study, and how organize and interpret statistical data. They have to learn the typical measures of statistic, too.

Learning outcomes

-To learn definition of statistic.

-To learn basic concepts of statitical data.

-To collect information to use in a statistical study.

-To organise statistical data into tables

-To do and interpret statistical data

-To learn the measures of central tendency, position and dispersion.

. Subject Content

-Statistics variable

-Frequency distribution

-Bar chart , pie chart and histogram

-Mode, median, arithmetic mean, quartiles, percentiles

-Standard deviation, average deviation and coefficient of variation.

 

Language Content / Communication

Vocabulary

Nouns: variable, diagram, population, simple, histogram, ba rchar, pie chart, distribution, table, mode, median, arithmetic mean, quartiles, percentiles, standar deviation, average deviation, coefficient of variation.

Verbs: Solve, organise, collect, calculate, find ,analyse...

Expressions: doing a statistic graphic, join the events, intersection of events, absolute frequency and relative frequency...

Structures

Simple Present and Present Continous, conditional ,modal verbs (can, could, may...)

Discourse type/ Language skills

Listening: the teacher will explain the concepts and the activities (some of them can be watching a video)

Reading: the students will read small text

Writing: fill in gaps

Speaking: the students will answer the teacher's question and some activities will be in groups.

Cognitive (thinking) processes

- To traduce data into graphics

- To analyse results

- To interpret statistical graphics

- To argue the results of exercises

Task(s)

This unit will take 10 sessions.

Each content will be explain in Spanish and English, and the students will have the specific vocabulary.

Statistics variable (2 sessions)

Activity 1: Reading a text with the description of concepts of statistic variable

Statistical Concepts

Population : A population is the set of all elements that are subjected to a statistical study.

Sample: : A sample is a representative set of the reference population. The number of individuals in a sample is less than the population.

Values: The values are the different results that can be obtained in a statistical study

A statistical study consists of the following phases:

       Data capture.

       Organization and representation of data.

       Data analysis.

       Obtaining conclusions.

statistical variable : A statistical variable is each of the characteristics or qualities that the individuals of a population possess.

Types :

a)    Categorical Variable

Nominal categorical variables are non-numerical forms that do not admit an order criterion.

For example: The sex status of the population with the following forms: male and female.

b)    Ordinal Variable

An ordinal qualitative variable represents non-numerical forms, in which there is an order.

For example: Sports Medals: gold, silver, bronze.

Quantitative Variable

A quantitative variable is expressed in numerical form, therefore arithmetic operations can be performed.

There are two types:

       Discrete Variable

A discrete variable does not admit intermediate values between two specific numbers. It is represented by whole integer values.

For example: The number of brothers of 3 friends: 1, 1, 3

       Continuous Variable

A continuous variable can take values between two numbers.

For example: The height of 3 friends measured in meters: 1.68, 1.75, 1.80

Activity 2: In pairs, solve some problems of statistic

Read the following text and complete the table:

Imagine that your friends gave yor these information in minutes about the time they spend having breakfast:

5, 0, 6,5,7,0,8,15,9,0,6, 8, 8, 5, 6,8,9,15,0,7

Questions:

a)           How many people go to school without having breakfast?

b)           How many people spend more than 7 minutes having breakfast?

c)            What's the most common answer?

Complete the table:

Values (in minutes)	Number of people
0
	3
6
	2
8
	2
15

 

In pairs, write a sentence related the information that you got.

Tell your partner how much time you spend having breakfast and compare the answer.

 

Activity 3: In pairs, propose a problem similar.

Frequency distribution  (2 sessions)

Activity 1: Reading a text with concepts of frequency distribution and fill gaps, watch videos...

Frequency distribution

The frequency distribution or frequency table is a tabular organization of statistical data, assigning to each piece of data its corresponding frequency.

Types of Frequencies

Absolute Frequency

The absolute frequency is the number of times that a certain value appears in a statistical study.

It is denoted by fi.

The sum of the absolute frequencies is equal to the total number of data, which is denoted by N.

This sum is commonly denoted by the Greek letter Σ (capital sigma) which represents 'sum'.

Relative Frequency

The relative frequency is the quotient between the absolute frequency of a certain value and the total number of data.

It can be expressed as a percentage and is denoted by ni.

The sum of the relative frequency is equal to 1.

Activity 2: In pairs make exercises about types of frequencies.

Activity 3: In pairs, construct a table of grouped frequency

 

 

Bar chart, pie chart and histogram  (2 sessions)

 

Activity 1: Make the different types of charts

 

Activity 2: In pairs, interpret the charts proposed by the teacher.

 

Measures of central tendency (2 sessions)

Activity 1: Watching a video about measures of central tendency.

Activity 2: Reading aloud and explain statements about this measures.

Activity 3: Solving exercises, individually

Average deviation, variance, standard deviation and coefficient variation  (2 sessions)

Activity 1: Rading a text with these concepts.

Average Deviation

The average deviation is the arithmetic mean of the absolute deviations.

The average deviation is represented by   

Variance

The variance is the arithmetic mean of the squared deviations from the mean of a statistical distribution.

The variance is denoted by  .

Properties of the Variance

                 The variance is always positive or in the event that the values are equal, the variance is zero.

                 If all values of the variable are added by the same number, the variance does not change.

                 If all values of the variable are multiplied by the same number, the variance is multiplied by the square of that number.

                 If there are multiple distributions with the same mean and their variances are known, the total variance can be calculated.

standard Deviation

The standard deviation is the square root of the variance. It is denoted by σ.

Properties of the Standard Deviation

                 The standard deviation is always positive or in the event that the values are equal, it is zero.

                 If all values of the variable are added by the same number the standard deviation does not change.

                 If all values of the variable are multiplied by the same number the standard deviation is multiplied by the square of that number.

                 If there are multiple distributions with the same mean and their standard deviations are known, the total standard deviation can be calculated.

The coefficient of variation

The coefficient of variation is the ratio between the standard deviation of a sample and its mean.

The coefficient of variation is usually expressed in percentages.

Activity 2: In pairs, solve problems about average deviation and standard deviation.

Activity 3: In pairs, solve problems about variance an coefficient variation.

Actividades interactivas

http://en.educaplay.com/en/learningresources/1901486/statistical_concepts.htm

http://en.educaplay.com/en/learningresources/1901536/statistical_words.htm

Resources / Materials

Sheets of specific vocabulary

Sheets of basic concepts

Scholar material.

Webpages

Videos.

Key Competences

-To understand and interpret statisctic data.

-To make different types of charts

-To acquire the specific vocabulary

-To be an independent learner

Evaluation (criteria and instruments)

- To prepare and interpret statistical tables

- To make and interpret statistical graphs.

- To use the most common statistical parameters for discrete distribution

- To use the most common statistical parameters for continuous distribution

Mª FRANCISCA ​HERNÁNDEZ CABALLO

 El enlace en google drive es: https://drive.google.com/file/d/0B9eKy5qs9KJrQ21xYjVYc2tVNms/view?usp=sharing