Data Handling — Making Sense of Information
"Data is everywhere — from cricket scores to rainfall records. Data handling helps us FIND PATTERNS and make DECISIONS based on numbers."
1. What Is Data?
Data is a collection of facts and information (numbers, words, measurements) gathered for analysis. Raw data is unorganised — we need to ARRANGE it to make sense. 'A list of 50 students' heights in random order is raw data. Arrange it in ascending order — NOW it tells a story.'
Types of Data
| Type | Description | Example |
|---|---|---|
| Quantitative | Numerical data | Heights, marks, weights |
| Qualitative | Descriptive data | Colours, opinions, types |
| Discrete | Countable values | Number of students in a class |
| Continuous | Measurable values | Temperature, time, length |
2. Measures of Central Tendency
'These are SINGLE values that represent the CENTRE of a data set — they tell us what is "typical" or "average."'
Mean (Arithmetic Average)
Formula: Mean = (Sum of all observations) ÷ (Total number of observations). Notation: x̄ = Σx/n.
Worked Example: Marks scored by 7 students in a test: 45, 50, 32, 48, 55, 42, 38. Sum = 45 + 50 + 32 + 48 + 55 + 42 + 38 = 310. Mean = 310 ÷ 7 = 44.29 (approximately).
AP Context: 'Mean monthly rainfall of Visakhapatnam: Jan (10 mm), Feb (8 mm), Mar (5 mm), Apr (15 mm), May (50 mm), Jun (120 mm), Jul (140 mm), Aug (130 mm), Sep (110 mm), Oct (80 mm), Nov (35 mm), Dec (12 mm). Sum = 715 mm. Mean = 715 ÷ 12 ≈ 59.6 mm per month.'
Median — The Middle Value
Steps: 1. Arrange data in ASCENDING order. 2. If n is ODD → middle term. 3. If n is EVEN → average of two middle terms.
Worked Example (Odd n): Heights (cm) of 9 students: 145, 152, 148, 160, 155, 158, 142, 150, 156. Arrange: 142, 145, 148, 150, 152, 155, 156, 158, 160. Middle (5th) value = 152 cm. Median = 152.
Worked Example (Even n): Marks of 8 students: 32, 45, 48, 50, 55, 58, 60, 65. Two middle values = 50 and 55. Median = (50 + 55)/2 = 52.5.
'Median is BETTER than mean when data has EXTREME values. Example: Salaries in a company: 20, 30, 25, 35, 500 (lakhs). Mean = 122 — misleading! Median = 30 — more representative.'
Mode — The Most Frequent Value
Mode is the observation that occurs the MOST number of times.
| Data Set | Mode | Reason |
|---|---|---|
| 2, 3, 3, 5, 7, 3, 8, 3 | 3 | Appears 4 times |
| 5, 5, 7, 8, 8, 8, 10 | 8 | Appears 3 times |
| 1, 2, 3, 4, 5 | No mode | All values appear once |
| 2, 2, 4, 4, 5, 6 | 2 and 4 (Bimodal) | Both appear twice |
Real-world use: 'Shoe manufacturers produce more shoes of the MODAL size because that is what MOST people wear.'
3. Bar Graphs
Types of Bar Graphs
| Type | Description | Example Use |
|---|---|---|
| Simple Bar Graph | One set of data | Rainfall per month |
| Double Bar Graph | Two sets for comparison | Rainfall of two cities per month |
| Multiple Bar Graph | More than two sets | Crop yield across years |
Drawing a Bar Graph
Step 1: Choose a SUITABLE SCALE (e.g., 1 cm = 10 units). Step 2: Draw X-axis (categories) and Y-axis (values). Step 3: Draw bars of EQUAL WIDTH with EQUAL GAPS between them. Step 4: Height = value according to scale.
Double Bar Graph — Worked Example
'Compare AP and Telangana rice production (in lakh tonnes): 2019 (75, 68), 2020 (80, 72), 2021 (85, 70), 2022 (82, 74).' Draw bars side by side for each year — two colours to distinguish. 'Double bar graphs help VISUALISE comparisons instantly.'
4. Basics of Probability
Probability measures the CHANCE of an event happening. Scale: 0 (impossible) to 1 (certain).
Formula: P(Event) = Number of favourable outcomes / Total number of possible outcomes.
Examples
- 'Tossing a fair coin. P(Head) = 1/2. P(Tail) = 1/2.'
- 'Rolling a die. P(3) = 1/6. P(even number) = 3/6 = 1/2. P(number > 4) = 2/6 = 1/3.'
- 'Drawing a red card from a standard deck of 52 cards: 26 red cards. P(red) = 26/52 = 1/2.'
Range of Probability
| Probability | Meaning |
|---|---|
| 0 | The event is IMPOSSIBLE |
| 0.25 | Not very likely |
| 0.5 | Equally likely |
| 0.75 | Very likely |
| 1 | The event is CERTAIN |
Common Misconception
'Probability does NOT guarantee outcomes. P(Head) = 1/2 does NOT mean you will get exactly 5 heads in 10 tosses — it means the LONG-TERM average is half.'
5. Common Mistakes and Fixes
| Mistake | Why It Is Wrong | Correct Approach |
|---|---|---|
| Mean = sum of all terms / 2 | Wrong formula | Mean = sum ÷ number of terms |
| Median = middle term without sorting | Must sort first | Always arrange in ascending order |
| Mode = first number in the list | Mode is about FREQUENCY | Count how many times each value appears |
| Probability > 1 | P(E) can never exceed 1 | P(E) ranges from 0 to 1 inclusive |
6. AP SSC Exam Focus
| Topic | Marks | Question Type |
|---|---|---|
| Mean, median, mode | 4-5 | Compute from given data |
| Bar graphs (including double) | 3-4 | Draw and interpret |
| Probability basics | 2-3 | Simple problems |
| Data interpretation | 2-3 | Analyse table/graph |
Quick Self-Test
Q1. Find the mean of: 12, 15, 18, 22, 25, 28. A1. Sum = 120. n = 6. Mean = 120/6 = 20.
Q2. Find the median of: 45, 32, 67, 28, 54, 39, 61. A2. Arrange: 28, 32, 39, 45, 54, 61, 67. Median (4th) = 45.
Q3. Find the mode of: 5, 7, 5, 9, 5, 7, 11, 5, 7, 7. A3. 5 appears 4 times, 7 appears 4 times. Bimodal: 5 and 7.
Q4. A bag has 3 red, 5 blue, and 2 green marbles. What is the probability of drawing a blue marble? A4. Total = 10. Blue = 5. P(blue) = 5/10 = 1/2.
Q5. What is the probability of getting a sum of 7 when rolling two dice? A5. Favourable pairs: (1,6), (2,5), (3,4), (4,3), (5,2), (6,1) = 6. Total outcomes = 36. P = 6/36 = 1/6.
