Statistics

Question 1

Descriptive and Inferential Statistics

Answer 1

`Statistics is the science of making decisions under uncertainty and variability .
Its a group of methods used to collect , analyze , present and interpret data to make decisions .

Question 2

Terminology

Answer 2

Data ; Measurements or facts that are effected from a statistical unit / entity of interest .

Population ; Set of all elements in the universe of interest to the researcher .

Sample ; Subset or a portion of the population of interest . Sample must be representative of the population .

Elements / Units ; Entities or objects which the data are collected from .

Variable ; Characteristic or an attribute that can assume different values .

Census ; Gather data from the whole population for a given measurement .

Sampling ; Collecting data on only a sample of a population.

Sampling Error ; Error in a statistical analysis arising from the unrepresentativeness of the sample taken .

Question 3

Branches Of Statistics

Answer 3

Descriptive ; use graphical / numerical methods to summarize data .

Inferential ; used to reach interferences about populations from which the samples have been derived .

Question 4

Raw data table

Answer 4

Consists of all the individual values measured during a study .

Question 5

Frequency Table

Answer 5

Shows how many times “x” occurred in the data set

Question 6

Tally Marks

Answer 6

When the observation are large we can use tally marks which consist of slashes similar to that of “/” , Once 4 of these marks are present its cut by a diagonal slash .

Question 7

Cumulative Frequency Table

Answer 7

Shows the total number of values that fall below the upper boundary of each variable .

Question 8

Measures of Central Tendency

Answer 8

Central tendency , a descriptive statistic , calculates the average . It will point out the repeated and/or centralized number .

Question 9

Mean (Arithmetic Average)

Answer 9

This is the average out of numerical values .
It can only be applied to quantitative data and is found through adding all the numbers and then dividing the answer by the amount of numbers added .

Equation to calculate Mean ; = x-Bar ( Σ x) / n

Question 10

Median

Answer 10

Is the central value of a set of numbers , it can be calculated through two methods ;

Method 1 ; If its an odd number then add “1” to the number and divide it by 2 - (n=1)/2
If its an even number [(n/2) + value of (n/2) + 1] /2

Method 2 ; First divide by 2 , then if n/2 is a whole number find the mid point .
If n/2 isn’t a whole number , round the number up and pick the corresponding term .

Question 11

Mode

Answer 11

This is the most frequently occurring number .

At times there may be no mode or there may be multiple modes ; when there are two modes its called bi mode .

If there are more than 2 modes then this data becomes less reliable .

Mode is usually made up of nominal data .

Question 12

Measures of Dispersion

Answer 12

This describes how spread out the data is within a dataset .

This the degree to which numerical data tends to spread about an average value .

Without knowing the variation between numbers then the central tendency can be misleading .

Question 13

Range

Answer 13

This is the difference between the largest and smallest number .

Question 14

Variance

Answer 14

This is the average between the squared differences from the mean .

Variance can be found out by :
Working out the mean .
Subtracting each number from the dataset with the mean , then square the result .
Finally working out the average of the squared differences .

Question 15

Decimals , Fractions and Percentages

Answer 15

`Percent to Decimal - Divide by 100 .

Decimal to Percent - Multiply decimal by 100 .

Fraction to Decimal - Divide numerator by denominator .

Decimal to Fraction - Multiply both numerator and denominator by 100 , then simplify .

Fraction To Percentage - Multiply fraction by 100 .

Percentage to Fraction - Write the percentage in fraction form , then simplify .

Question 16

Group Frequency Distribution

Answer 16

Obtained by constructing classes/intervals for the data and then listing the corresponding number of values in each interval .

Classes are mutually exclusive , which means a particular observation can only fit in one category .

Question 17

Class Intervals And Class Intervals

Answer 17

The total range of the observations are divided into a number of classes , which are known as class intervals

Class limits are the smallest and largest possible values that can fall into a given class .

The frequency in a class interval refers to the amount of values present within a specific interval .

Question 18

Class Boundaries

Answer 18

In a frequency distribution , class boundaries are the values that separate the classes .

Obtained by adding the upper limit and lower limit class limit of the next higher class interval and divided by two .

Question 19

Class Width

Answer 19

The difference between the lower and upper class boundaries .

Width = (Largest Value - Smallest Value) / Number of Classes .

Question 20

Class Mark

Answer 20

Mid point of the class ; (Lower Limit + Upper Limit) / 2

The mid point value is taken as the representative of the class .

Question 21

Bar Graphs

Answer 21

A Bar Graph or Bar Chart is a graphical display of data using bars of different height .

Bar graphs are more efficient to use when we have data that can be categorised .

Question 22

Histogram

Answer 22

Useful for presenting distributions of observations of continuous variables .
The area of one block is proportional to its frequency .
Much of the original data is destroyed through the grouping process .
The importance of histograms is that the overall picture of a set of data can be obtained .

The frequency of an individual bar can be found via the equation ;
Frequency Density = Frequency / Class Width