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Lecture No. 3

Dated: 05-11-2024

graph TD
    A[Types of Data]
    A --> B[Qualitative]
    A --> C[Quantitative]

    B --> D[Univariate Frequency Table]
    B --> E[Bivariate Frequency Table]
    D --> F[Percentages]
    F --> G[Pie Chart]
    G --> H[Bar Chart]
    E --> I[Component Bar Chart]
    E --> J[Multiple Bar Chart]

    C --> K[Discrete]
    C --> L[Continuous]
    K --> M[Frequency Distribution]
    M --> N[Line Chart]

    L --> O[Frequency Distribution]
    O --> P[Histogram]
    P --> Q[Frequency Polygon]
    Q --> R[Frequency Curve]

Example

In a survey of 1200 first-year students in a co-ed college in Lahore, we aim to find the proportion from Urdu and English medium schools.
Interviews will gather data, resulting in an array of observations.

We will have an array of observations as follows:
U, U, E, U, E, E, E, U, …
Here U is for Urdu and E is for English.

Medium of institution No. of Students(f) % = \(\frac f t \times 100\)
Urdu 719 59.9% = 60%
English 481 40.1% = 40%
1200 (t)

Pie Chart

We created a univariate frequency table for qualitative data.
This can be represented using a pie chart, where the circle is divided into sectors based on the categories (Urdu and English medium schools).
To determine the angle for each sector,

\[\frac{\text{cell frequency}}{\text{Total Frequency}} \times 360^\circ\]
Medium of institution No. of Students(f) \(\theta = \frac f t \times 360\)
Urdu 719 \(215.7^\circ\)
English 481 \(144.3^\circ\)
1200 (t) 
pie
    "Urdu" : 719
    "English" : 481

Simple bar Chart

A simple bar chart uses horizontal or vertical bars of equal width, with lengths proportional to the values they represent.
The bar widths hold no mathematical significance but enhance visual appeal.
Let's consider an example.

Years 1965 1966 1967 1968 1969
Turnover (Rupees) 35,000 42,000 43,500 48,000 48,500 
%%{
    init: {
        "themeVariables": {
            "xyChart": {
                "backgroundColor": "#1e2129",
                "plotColorPalette": "#009485"
            }
        } 
    }
}%%
xychart-beta
    title "Turn over per year"
    x-axis[1965, 1966, 1967, 1968, 1969]
    y-axis 0 --> 50000
    bar [35000, 42000, 43500, 48000, 48500]

Previously, we examined univariate situations, focusing on a single variable like ‘medium of schooling’ or ‘turnover.’
Now, let’s consider a bivariate situation.
For instance, in the first-year students’ survey, we could record both the medium of schooling and the student's sex.

Student No. Medium Gender
1 U F
2 U M
3 E M
4 U F
5 E M
6 E F
7 U M
8 E M
… … …

To summarize this table

Med\Sex Male Female Total
Urdu 202 517 719
English 350 131 481
Total 552 648 1200

Component bar Chart

Pasted image 20241105145329.png

Each bar is divided into two parts: the first for male students, the second for female students.
The lower section of each bar represents English medium students, and the upper section represents Urdu medium students.
This diagram allows quick comparison of both gender and medium of schooling simultaneously.

Multiple bar Chart

Years Imports (Crores of Rs.) Exports (Crores of Rs.)
1970-71 370 200
1971-72 350 337
1972-73 840 855
1973-74 1438 1016
1974-75 2092 1029

Pasted image 20241105145659.png