Understanding Data

Given: Various services that require data maintenance.

Concept: Data is a collection of facts, numbers, characters and symbols needed to perform a specific task or service.

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a) Declare exam results and print e-certificates:

Data required:
- Student's full name, roll number, date of birth
- Subject names and marks obtained in each subject
- Maximum marks per subject
- Pass/fail criteria (minimum passing marks)
- School/Board name, exam year
- Student's photograph (for e-certificate)
- Unique certificate ID / serial number
- Digital signature or QR code data for verification

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b) Register participants in an exhibition and issue biometric ID cards:

Data required:
- Participant's full name, age, gender
- Contact details (phone number, email address)
- Organisation/Institution name
- Category of participation (visitor, exhibitor, judge, etc.)
- Biometric data: fingerprint scan and/or iris scan
- Photograph of the participant
- Unique participant ID / registration number
- Date and duration of participation

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c) To search for an image by a search engine:

Data required:
- Image file (pixel data, colour values, resolution)
- Metadata of the image: file name, file size, format (JPEG, PNG, etc.)
- Tags, labels, or keywords associated with the image
- URL / source location of the image
- Alt text or caption associated with the image on the web page
- Date of upload/indexing
- Image features extracted by AI (shapes, colours, objects detected)

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d) To book an OPD appointment with a hospital in a specific department:

Data required:
- Patient's full name, age, gender, contact number
- Patient ID / Aadhar number (for existing patients: medical history)
- Department name (e.g., Cardiology, Orthopaedics)
- Name of the preferred doctor
- Available appointment slots (date and time)
- Reason for visit / symptoms
- Insurance details (if applicable)
- Appointment confirmation number

Given:
- Total students = 500
- Scholarship criteria:
- Marks > 75% in two consecutive years, AND
- Family income < ₹5,00,000 per annum

Concept: Data Processing Cycle — Input → Storage → Processing → Output

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Step 1 — Data Collection (Input):
- Collect academic records of all 500 students for the last two consecutive years (marks/percentage obtained).
- Collect family income certificates or income declaration forms from all students.
- Collect basic student details: name, roll number, class, section.

Step 2 — Data Storage:
- Store all collected data in a structured format (e.g., a database or spreadsheet) with fields such as:
- Student Name, Roll No., Class
- Percentage in Year 1, Percentage in Year 2
- Annual Family Income

Step 3 — Data Validation:
- Verify that the income certificates are authentic (issued by a competent authority).
- Check that marks/percentage data is correctly entered and matches official records.

Step 4 — Data Processing (Filtering/Querying):
- Apply the first filter: Select students where Percentage in Year 1 > 75% AND Percentage in Year 2 > 75%.
- Apply the second filter on the result: Select students where Annual Family Income < ₹5,00,000.
- Students satisfying both conditions are the eligible beneficiaries.

This can be done using a database query such as:
\text{SELECT * FROM Students WHERE (Year1\_Percent &gt; 75) AND (Year2\_Percent &gt; 75) AND (Family\_Income &lt; 500000)}

Step 5 — Output Generation:
- Generate the final list of eligible students with their names, roll numbers, percentages, and family income.
- The list can be printed or published as the official scholarship beneficiary list.

Step 6 — Review:
- The list is reviewed by the school administration for final approval before announcing the scholarship.

Given:
- Bank: XYZ
- City: ABC
- Parameters: Number of bank accounts per family, Average monthly account balance per person

Concept: Data collection → Processing → Analysis to derive meaningful information.

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Steps for Data Collection:

1. Define the target population: Identify all families/residents of city ABC who are existing or potential customers.

2. Choose a data collection method:
- Primary data: Conduct surveys (online or door-to-door questionnaires) asking residents about the number of accounts they hold with Bank XYZ and their approximate monthly balance.
- Secondary data: Use the bank's internal database of existing account holders in city ABC.

3. Design the data collection form/questionnaire with fields such as:
- Family ID / Respondent Name
- Number of accounts held in Bank XYZ
- Number of accounts held in other banks
- Average monthly balance maintained in Bank XYZ
- Type of accounts (Savings, Current, FD, etc.)

4. Sample selection: If surveying all residents is not feasible, select a representative random sample from different localities of city ABC.

5. Data entry and storage: Enter collected data into a structured database/spreadsheet for further processing.

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Results that can be checked through processing:

1. Total number of accounts held by residents of city ABC in Bank XYZ — indicates the bank's reach.

2. Average number of accounts per family — indicates how many families prefer Bank XYZ.

3. Average monthly balance across all account holders — indicates the financial engagement of customers.

4. Market share: Compare the number of Bank XYZ accounts with accounts in other banks to determine popularity.

5. Mode of account type — which type of account (Savings/Current/FD) is most popular among residents.

6. Growth trend: If historical data is available, compare year-on-year growth in accounts and balances.

7. Locality-wise analysis: Identify which areas of city ABC have the highest concentration of Bank XYZ customers.

These results help the bank understand its popularity and plan marketing strategies accordingly.

Concept:
- Structured data: Data that is organised in a predefined format (rows and columns), easy to search and process. Example: tables in a database.
- Unstructured data: Data that does not have a predefined format or organisation. Example: images, videos, text posts.

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a) Recording a video:
Type: Unstructured Data
Justification: A video is a combination of audio and visual frames. It does not follow any predefined row-column format and cannot be directly stored in a relational database table. It is multimedia data, which is unstructured.

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b) Marking attendance by teacher:
Type: Structured Data
Justification: Attendance is recorded in a tabular format with predefined fields such as Student Name, Roll Number, Date, and Present/Absent status. This follows a fixed schema and is easily stored in a database or spreadsheet.

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c) Writing tweets:
Type: Unstructured Data
Justification: Tweets are free-form text messages written by users. They do not follow a fixed format — the content, length, and language vary from tweet to tweet. Text data of this nature is considered unstructured (though metadata like timestamp and user ID associated with tweets can be structured).

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d) Filling an application form online:
Type: Structured Data
Justification: An online application form has predefined fields such as Name, Date of Birth, Address, Email, Phone Number, etc. The data entered follows a fixed format and is stored in a database in an organised manner, making it structured data.

Given data: 34, 34, 27, 28, 27, 34, 34
Number of values (n) = 7

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a) Average Temperature — Technique: MEAN

Mean is the appropriate technique to find the average value.

$$\bar{x} = \frac{\sum x_i}{n} = \frac{34 + 34 + 27 + 28 + 27 + 34 + 34}{7}$$

$$\bar{x} = \frac{218}{7} = 31.14^\circ\text{C}$$

Average temperature of the week = 31.14°C

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b) Temperature Range — Technique: RANGE

Range is the appropriate technique to find the spread between the highest and lowest values.

$$\text{Range} = \text{Maximum value} - \text{Minimum value}$$

$$\text{Maximum temperature} = 34^\circ\text{C}$$
$$\text{Minimum temperature} = 27^\circ\text{C}$$

$$\text{Range} = 34 - 27 = 7^\circ\text{C}$$

Temperature Range of the week = 7°C

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c) Standard Deviation — Technique: STANDARD DEVIATION

Standard Deviation is the appropriate technique to measure how much the temperature values deviate from the mean.

$$\bar{x} = 31.14^\circ\text{C}$$

Calculate $(x_i - \bar{x})^2$ for each value:

| $x_i$ | $x_i - \bar{x}$ | $(x_i - \bar{x})^2$ |
|--------|-----------------|---------------------|
| 34 | 2.86 | 8.18 |
| 34 | 2.86 | 8.18 |
| 27 | −4.14 | 17.14 |
| 28 | −3.14 | 9.86 |
| 27 | −4.14 | 17.14 |
| 34 | 2.86 | 8.18 |
| 34 | 2.86 | 8.18 |

$$\sum(x_i - \bar{x})^2 = 8.18 + 8.18 + 17.14 + 9.86 + 17.14 + 8.18 + 8.18 = 76.86$$

$$\sigma = \sqrt{\frac{\sum(x_i - \bar{x})^2}{n}} = \sqrt{\frac{76.86}{7}} = \sqrt{10.98} \approx 3.31^\circ\text{C}$$

Standard Deviation of temperature = 3.31°C

Concept: Different statistical techniques are used for different types of analysis:
- Mode — to find the most frequently occurring value
- Mean — to find the average
- Range / Standard Deviation — to compare spread/variation

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a) Comparing performance in terms of division secured:

Appropriate Technique: MODE

Justification:
Division secured (First Division, Second Division, Third Division, Pass) is a categorical value, not a numerical one. The teacher wants to know which division appears most frequently in each class. Mode gives the most frequently occurring value in a dataset. By finding the mode of divisions in Class XII A and Class XII B separately, the teacher can compare which division is most common in each class and thus compare overall performance.

For example:
- If Mode of Class XII A = First Division and Mode of Class XII B = Second Division, it indicates Class XII A performed better overall.

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b) Comparing class performance over five unit tests (July to November):

Appropriate Technique: MEAN

Justification:
The teacher wants to compare the overall/average performance of the class in each of the five months. Mean (average marks) of the class in each unit test gives a single representative value for that month's performance. By comparing the mean scores of July, August, September, October, and November, the teacher can easily identify in which month the class performed best or worst, and track the trend of improvement or decline over time.

For example:
- Mean score in July = 65, August = 70, September = 68, October = 75, November = 78 → shows an improving trend.

Given: School annual day — parents who are alumni of the same school are to be felicitated. Students are from Classes XI and XII.

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a) Finding the number of students whose both parents are alumni:

Appropriate Technique: MODE

Justification:
The data collected will be categorical in nature — for each student, the response will be one of: "Both parents are alumni", "Only father is alumni", "Only mother is alumni", or "Neither parent is alumni". Mode identifies the most frequently occurring category. However, to specifically count the number of students whose both parents are alumni, the teacher needs to count the frequency of the category "Both parents are alumni".

Thus, frequency count (a part of Mode analysis) is the most appropriate technique here. The school can collect data through a survey/form and count how many students fall in the "both parents are alumni" category.

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b) How varied are the ages of parents:

Appropriate Technique: RANGE or STANDARD DEVIATION

Justification:
To measure the variation or spread in the ages of parents, Range or Standard Deviation is appropriate.

- Range = Maximum age − Minimum age → gives the overall spread of ages.
- Standard Deviation gives a more precise measure of how much individual ages deviate from the average age of parents.

If the standard deviation is large, it means the ages of parents are widely spread (highly varied). If it is small, the ages are clustered close to the mean (less variation).

For a quick comparison, Range can be used; for a more detailed statistical analysis, Standard Deviation is preferred.

Given:
- Class strength = 42 students
- Selection criteria: Singing skill, Writing skill, Monitoring skill

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a) Mode of Data Collection:

Appropriate Method: Primary Data Collection through Observation and Practical Assessment (Audition/Test)

Justification:
Since the skills to be evaluated are practical in nature (singing, writing, monitoring), the most appropriate mode of data collection is direct observation and practical assessment:

- Singing skill: Conduct an audition where each student sings, and the teacher (or a panel) rates them.
- Writing skill: Give a short writing task (e.g., write a script or paragraph) and evaluate it.
- Monitoring skill: Observe students in a group activity or assign a small task to assess their ability to manage/coordinate.

Alternatively, a structured rating form/questionnaire can be used where the teacher assigns scores to each student on each skill during the assessment.

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b) Representing the skill of students as data:

The skills can be represented as numerical scores on a defined scale, stored in a structured tabular format.

For example, each skill can be rated on a scale of 1 to 10:

| Student Name | Roll No. | Singing Skill (1–10) | Writing Skill (1–10) | Monitoring Skill (1–10) | Total Score |
|---|---|---|---|---|---|
| Student 1 | 1 | 8 | 7 | 9 | 24 |
| Student 2 | 2 | 6 | 9 | 7 | 22 |
| ... | ... | ... | ... | ... | ... |

- Each skill is assigned a numerical rating (quantitative data).
- The total score or weighted average of the three skills can be calculated.
- The student with the highest total score is selected as the anchor.
- This is structured data stored in a tabular format, easy to process and compare.

Concept: Data can be classified as structured or unstructured based on its organisation and format.

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| Basis | Structured Data | Unstructured Data |
|---|---|---|
| Definition | Data that is organised in a predefined format, typically in rows and columns. | Data that does not have a predefined format or organisation. |
| Storage | Stored in relational databases (tables). | Stored as files — text files, images, videos, audio, etc. |
| Ease of processing | Easy to search, query, and process using SQL or spreadsheet tools. | Difficult to process directly; requires special tools (AI, NLP, etc.). |
| Format | Fixed schema with defined data types for each field. | No fixed schema; format varies widely. |
| Example | A student database table with fields: Roll No., Name, Class, Marks. | A video recording of a lecture, a social media post, or an email. |

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Example of Structured Data:
A school's student record stored in a spreadsheet:

| Roll No. | Name | Class | Marks |
|---|---|---|---|
| 101 | Aman | XII | 85 |
| 102 | Priya | XII | 90 |

Example of Unstructured Data:
A photograph clicked during the school annual day function — it is an image file with no predefined rows/columns and cannot be directly stored in a relational database table.

Given: Canteen data for fruit juice, biscuits, and samosa — purchase price and sale price.

Step 1 — Create the Dataset:

Let us assume the following dataset (prices in ₹):

Table 1: Purchase Price and Sale Price of Canteen Items

| Item | Purchase Price (₹) | Sale Price (₹) |
|---|---|---|
| Fruit Juice (Company A, 200 ml) | 15 | 20 |
| Fruit Juice (Company B, 200 ml) | 18 | 25 |
| Fruit Juice (Company C, 200 ml) | 12 | 18 |
| Biscuits (Pack 1) | 5 | 8 |
| Biscuits (Pack 2) | 10 | 14 |
| Samosa (per piece) | 6 | 10 |

Table 2: Monthly Sales Quantity

| Item | Units Sold per Month |
|---|---|
| Fruit Juice | 150 |
| Biscuits | 200 |
| Samosa | 180 |

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a) Compare purchase and sale price of Fruit Juice and Biscuits — Technique: MEAN

Mean Purchase Price of Fruit Juice:
$$\bar{x}_{\text{purchase, juice}} = \frac{15 + 18 + 12}{3} = \frac{45}{3} = ₹15$$

Mean Sale Price of Fruit Juice:
$$\bar{x}_{\text{sale, juice}} = \frac{20 + 25 + 18}{3} = \frac{63}{3} = ₹21$$

Mean Purchase Price of Biscuits:
$$\bar{x}_{\text{purchase, biscuits}} = \frac{5 + 10}{2} = \frac{15}{2} = ₹7.5$$

Mean Sale Price of Biscuits:
$$\bar{x}_{\text{sale, biscuits}} = \frac{8 + 14}{2} = \frac{22}{2} = ₹11$$

Comparison:
- Fruit Juice: Average profit per unit = ₹21 − ₹15 = ₹6
- Biscuits: Average profit per unit = ₹11 − ₹7.5 = ₹3.5
- Fruit Juice gives a higher average profit margin than Biscuits.

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b) Compare sales of Fruit Juice, Biscuits and Samosa — Technique: MODE / Frequency Count / Mean

Using the monthly sales data:

| Item | Units Sold |
|---|---|
| Fruit Juice | 150 |
| Biscuits | 200 |
| Samosa | 180 |

- Maximum sales: Biscuits (200 units) — most popular item.
- Minimum sales: Fruit Juice (150 units) — least popular item.

The Mode (most frequently sold item) is Biscuits.

Total Revenue from Sales:
- Fruit Juice: $150 \times 21 = ₹3150$
- Biscuits: $200 \times 11 = ₹2200$
- Samosa: $180 \times 10 = ₹1800$

Conclusion: Biscuits have the highest number of units sold, but Fruit Juice generates the highest revenue.

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c) Variation in sale price of fruit juices of different companies — Technique: RANGE and STANDARD DEVIATION

Sale prices of fruit juice (200 ml) by three companies: 20, 25, 18

Range:
$$\text{Range} = 25 - 18 = ₹7$$

Mean Sale Price:
$$\bar{x} = \frac{20 + 25 + 18}{3} = \frac{63}{3} = ₹21$$

Standard Deviation:

| $x_i$ | $x_i - \bar{x}$ | $(x_i - \bar{x})^2$ |
|---|---|---|
| 20 | −1 | 1 |
| 25 | 4 | 16 |
| 18 | −3 | 9 |

$$\sum(x_i - \bar{x})^2 = 1 + 16 + 9 = 26$$

$$\sigma = \sqrt{\frac{26}{3}} = \sqrt{8.67} \approx ₹2.94$$

Conclusion: The sale price of fruit juice varies by a Range of ₹7 and a Standard Deviation of approximately ₹2.94 across the three companies, indicating moderate variation in pricing for the same quantity (200 ml).