Median Definition

Median Concept

Median is a point which divides the ordered data in two equal points. It is fundamental for median calculation that data is in order i.e. data is arranged from lower value to high value. Median can also be defined as point below which 50% order data lies.

Median Formula

Median has two different formulas for two different cases i.e. n/2 integer and non integer.

1)    [{n/2}+1]th observation ( where n/2 is integer

2)    [n+1]/2 th observation  (where n/2 is not integer)

Median & Quin tiles

Median as well as quin-tile may be calculated for large data, typically there are three types of quintiles calculated Q1, Q2, and Q3 which divided the ordered data into 25%, 50% and 75% respectively.

Q1 = [n/4+1] th

Q3 = [3n/4] th observation

Mode Concept

Mode Concept

Mode means most frequent observation or observation occurring more frequently. There may be more than one mode; there may also be no mode for a data. In simple term observation with most number of frequencies is known as mode.

Mode for un grouped & Grouped Data

Mode for ungrouped data can be found by simpler observation. While mode for grouped data is found by a formula given below;

Mode for Grouped Data = l+       [fm-  f1]             x h

                                                   [fm-f1]+[fm-f2]

l=lower class boundary

h=class interval

fm = highest frequency

f1= previous class frequency

f2= nex class frequency

Mode Empirical Relationship Formula

Mode can be calculated by the following formula, it is important to remember that this formula will not work for the highly skewed or u shaped frequency distribution.

Mode = 3 median – 2 mean

Arithmetic Mean Concept

Arithmetic Mean Concept

Arithmetic mean can be calculated by a simple equation i.e. sum of all observation is divided by the number of observation.

Arithmetic Mean Formula

Arithmetic mean = Sum of all observation/Number of observation

Arithmetic Mean Example

There are five students in a class who obtained 56, 68, 72, 83, 49 in statistic paper, what is average mark of the class?

Arithmetic mean = Sum of all observation/Number of observation

= 56+68+72+83+49/5

=328/5

=65.6 (arithmetic mean or average marks)

Arithmetic Mean Types

Arithmetic mean can be broadly classified into two type i.e. simple arithmetic mean and weighted arithmetic mean. In case of weighted arithmetic mean weights (importance) is assigned to observation and then average is calculated.

Arithmetic mean (weighted) = ∑xw/∑w

Subject	Marks (x)	Weight (w)	xw
maths	40	10	400
English	34	8	272
		18	672

= 672/18

=37.33

Arithmetic mean of Grouped Data

Arithmetic mean of Group data may be calculated with the help of midpoint i.e. midpoint is multiplied with frequency and total is divided by the sum of frequency.

Class	Frequency (f)	Mid Point (x)	(f)*(x)
25-44	40	34.5	1380
45-64	33	54.5	1798
	73		3178

=3178/73

=43.53

Arithmetic Mean Short Cut Method

Arithmetic mean can be calculated by a short cut method by following formula

Arirthmetic mean = a+hu

Where

a-midpoint of largest frequenc

h- class width

u – ∑f*u/∑f

Types of Simple Price Index

Types of Simple Price Index

1.    Simple Aggregative Price Index

Simple aggregative price index may be calculated by the following formula

Price Index = ∑Pn / ∑Po x 100

Pn= current aggregative Price

Po= Base aggregative price

2.    Simple Price Relative Index

Simple price relative index may be calculated by the following formula

Simple price index = 1/k x ∑[pn/po]

Types of weighted Price Index

Weighted price index is calculated by assigning weight (importance) to prices , famous weighted price index includes lasper price index & Paasche Price Index

1.    Lasper Price Index

Lasper price index is calculated by the following formula

Price index = [∑Pnqo/∑Poqo] x 100

Prices are weighted by the base quantity of the commodities.

2.    Paasche Price Index

Paasche price index is calculated with following formula

Price index = [∑Pn x qn/∑Po x qn] x 100

Prices are weighted with the current quantity i.e. both current prices & base prices are weighted with the base quantity.

Frequency Distribution Concept

Frequency Distribution Concept

Frequency distribution is division of data into different classes, and number observation fall in each class is represented by frequency. As data is divided into different groups, therefore frequency distribution is also called grouped data.

Frequency Distribution Purposes

Frequency distribution main purposes are to arrange the data in a meaningful manner.  Other important purpose of frequency distribution is to manage huge volume of data.

Frequency Distribution Class limits

Frequency distribution class limits are consisting of lower class limit and upper class limit; these limits identify the data limit for that class. Class limits are inclusive in nature.

Frequency Distribution Class boundary

Frequency distribution class boundary defines the class limits more clearly and any difficult for defining class for a value may be overcome with frequency distribution class boundary. Therefore class boundary used one more decimal than class limits.

Frequency Distribution class boundary is midway point between higher class limit of a class and lower class limits of next class.

Frequency Distribution Class Mark

Frequency distribution class mark is middle or midpoint of a class i.e. divides each class into two equal parts. Class mark can be calculated with very easy formula i.e. summing up the upper and lower class limits and dividing the result (sum) with 2.

Graph Concept

Graph Concept

Graph is used to represent time series (continuous data change over the period of time).  example variation of weather during the day etc.

Graph Advantages

1.    Series Comparison

Graph facilitates comparison of two or more series, for example the score card of a cricket match effectively presents the progress of both team.

2.    Prediction

Graph facilitates future prediction & forecast. Graph basically shows a trend of performance of variable and such trend can be used to predict future value.

Graph Types

Graph can be broadly classified into two types i.e. Time series Graph & Frequency Distribution Graph.

1.    Time Series Graph

Graph in the form of curve which shows the changes in a variable over the period of time is known as time series. Time is shown over the x-axis while the other dependant variable is shown on y-axis.

2.    Frequency Distribution Graph

Frequency distribution graph can be further classified into histogram, frequency polygon, and frequency curve.

i.        Histogram

Graph of adjacent rectangle with marked bases with class boundaries. Area of rectangle shows the frequency, if class interval is same, then width will be same of all rectangles and length will show the frequency position, otherwise width & length both will be changed. Length presents the number of observation (frequency).

ii.        Frequency polygon

Graph constructed with help of class mark and related frequency is known as frequency poly gone. Class marks are shown on x-axis while the frequency is shown on y axis, the connecting the points (class mark & related frequency) will result in frequency polygon.

iii.        Frequency Curve

Graph with small class interval and large observation result in frequency curve and therefore effectively Frequency curve is extension of histogram & frequency polygon.

Types of Frequency Curves

Types of frequency curves include symmetrical curve, moderately skewed (asymmetrical), and extremely skewed (J shape) and U shaped distribution.

1       .    Symmetrical Curve

Curve which has equal distance from the central maximum point is known as symmetrical curve, for example a normal curve.

2       .    Asymmetrical Curve

Curve which both end tail are of different length is known as asymmetrical.

3       .    Extremely Skewed

    Extremely skewed curve where most of frequency fall at one end of the curve. This curve         also known as J curve.

4        .    U Shaped curve

U shaped curve frequency at both end goes to maximum, these types of curves are rarely found.

Diagram Concept

Diagram Concept

Diagrams are used to present the data in pictorial form. Diagram are used , where same type of data is presented in pictorial form over period of time.

Diagrams Advantages

Diagram are used for number of advantages

1.    Attractive

Diagrams are more attractive than table, and therefore widely used for presentation.

2.    User Friendly

Diagrams are easier to understand than figures and therefore have long lasting effect on user.

3.    Comparison

Diagram facilitates the comparison between two periods.

Diagram Disadvantages

1.    Complex Data

Diagram cannot be used for complex data presentation; these are only suitable for limited and simple data.

2.    Additional Job

Diagram is time consuming job because diagram is prepared from the classified data. Therefore first data is collected & classified, and then diagrams are prepared from classified data.

Diagram Types

1.    Linear Diagram

Diagram which has one dimension is known as linear diagrams. Examples of linear Diagrams are simple bars, multiple bars. Bars will have equal width but different length, where length presents the value, while width has no significance.

Single diagram used to describe single characteristics of a variable for example production of cotton over period.  Multiple bars are used to describe two characteristics of variable. for example cotton production & area used.

2.    Areal or Two Dimension Diagram

Diagram which has two dimensions are known as two dimension Diagrams. Rectangles and sub divided rectangles are example of two dimension diagram. Rectangles use both length and width to represent the variable value.

3.    Cubical or Three Dimensional Diagram

Diagram which have more than two dimensions are known as Cubical or three dimension diagram.

4.    Pie-Diagram

Diagram which present data in the form of circles or sector is known as pie gram. Size of sector is proportional to the value.

5.    Pictograph

Diagram which uses small pictures or symbols are known as pictograph

Statistical Population Concept

Statistical Population Concept

Population is set of all possible observation. For example all students in a school is population. Statistical population is not necessarily required to represent a whole population of area; rather it is a group of people which is being studied.

Statistical Population Size

Statistical population size means the number of possible outcome or observation of finite population. For example we studying height of 9^th class student, then population size is would be total number of student in the 9th class.

Statistical Population Parameter

Statistical population mean the numeric value assigned to population. For example the average height of 9^th class student is 5 feet that was calculated from the population of 50 student of 9^th class. Height of 5 feet is parameter (represent population).

Statistical Population Types

Population can be broadly classified as under

1.    Finite Statistical population

Population which represents or consists of a fixed number of values is known as finite population. For example number of student in school, number of student in class, number of flights from Karachi airport.

2.    Infinite Statistical population

Population which size is not exactly known is regarded as infinite population. Infinite population size is so large that no one can exactly tell about size. For example, Particles of sand in a desert, number of point on a line.

3.    Real Statistical Population

Population that represents real values is known real population i.e. age, height, weight, length.

4.    Hypothetical Statistical population

Population may comprise of hypothetical events or observation i.e. possible outcome of coin toss, possible outcome of a cricket match, etc.

Secondary Data Concept

Secondary Data Concept

Secondary data is a data which is not originally collected for a purpose, such data collected by someone else for some purpose. Secondary data has already gone through a statistical process / technique.

Secondary Data Sources

Secondary data sources include Government, Semi Government, Trade union, research & educational institution, professional magazine and news paper.

Secondary Data Advantages

1.    Low Cost

Secondary data first advantage is its low cost. There is very little cost involved in collected such data. For example you need to buy a professional magazine from the market and this is the total cost for your data collection.

2.    Time Saved

Secondary data second advantage is saving of time because data is readily available and therefore can immediately be used for the research or other purposes.

Secondary Data Disadvantages

1.    Not updated

Secondary first disadvantage is its non update ion issue because it is originally collected by the current user.

2.    Difficult to use

Secondary data second disadvantage is difficulty faced by the user for using the data because it may be available in a form and format which may be difficult to manipulate by current user.

Primary Data Concept

Primary Data Concept

Primary Data is a kind of data which is originally collected for a purpose. Such data is then processed by using different statistical technique for decision making, prediction etc.

Primary Data Collection Methods

Primary data Collection methods includes direct interview, indirect interview or investigation, questionnaires,

1.    Direct investigation

Interested person collect the data personally. Data collected under this method is regard to be accurate and relevant to the need of interested person.

2.    Indirect Investigation

Under this method interested person hire some person for data collection. Primary reason to hire other person is difficult to get data. For example male researcher cannot get information about pregnancy related disease.

3.    Questionnaire

Under this method data is collected by designing a questionnaire. This methods cheap and provides exact question. However, this method is effective if questionnaire has been well designed, questions are well structure, and data is properly recorded in the forms.

4.    Enumerator

Under this method questionnaire is filled by the trained enumerator , there are number of advantages for using trained enumerator for form /questionnaire filling i.e. low rate of mistakes, high response, efficiency etc.

Primary Data Advantages

Primary data advantages includes more relevant, update (current data)

1.    Relevance of Data

Primary data is regarded as more relevant to purpose and therefore more useful for decision making and analyses.

2.    Current Data

Primary data main advantage includes its updated form. Therefore primary data is regarded as more reliable for statistical analyses. Secondary data on other side may not be current and therefore not useful.