Presentation of Data (Tables, Diagrams, Graphs) — Practice

Question 1

India's budget allocation (in ₹ crore): Defence = 6,00,000; Education = 1,10,000; Health = 86,000; Agriculture = 1,25,000; Others = 2,79,000. Calculate the angle for each sector in a pie chart.

Accepted Answer

Total = 6,00,000 + 1,10,000 + 86,000 + 1,25,000 + 2,79,000 = 12,00,000. Angles: Defence = (6,00,000/12,00,000) × 360 = 0.5 × 360 = 180°. Education = (1,10,000/12,00,000) × 360 = 33°. Health = (86,000/12,00,000) × 360 = 25.8° ≈ 26°. Agriculture = (1,25,000/12,00,000) × 360 = 37.5°. Others = (2,79,000/12,00,000) × 360 = 83.7° ≈ 84°. Verification: 180 + 33 + 26 + 37.5 + 83.5 = 360° ✓

Question 2

Distinguish between a bar diagram and a histogram. When would you use each? Draw a labelled sketch of each for the following data: (a) Sale of cars by brand (Maruti: 40, Hyundai: 30, Tata: 20, Honda: 10). (b) Heights of 50 students grouped as 140–150: 8, 150–160: 15, 160–170: 19, 170–180: 8.

Accepted Answer

Differences: Bar Diagram: Used for DISCRETE categories or qualitative data; bars are separated by gaps; width of bar has no meaning; length (height) = value. Histogram: Used for CONTINUOUS frequency distributions; bars touch (no gaps); width = class interval; area = frequency (not just height); height = frequency (or frequency density for unequal classes). (a) Bar diagram for car brands: X-axis labels = Maruti, Hyundai, Tata, Honda (with gaps between bars); Y-axis = number of cars; heights = 40, 30, 20, 10. (b) Histogram for heights: X-axis = height (continuous, 140–150, 150–160, 160–170, 170–180) with NO GAPS; Y-axis = frequency; heights = 8, 15, 19, 8. Bars must be contiguous because height is a continuous variable.

Question 3

Draw a less-than ogive for the following frequency distribution and find the median graphically. Marks: 0–20: 5, 20–40: 10, 40–60: 20, 60–80: 10, 80–100: 5. Total N = 50.

Accepted Answer

Step 1: Construct cumulative frequency table. Less-than ogive plots upper boundary against cumulative frequency: Less than 20: CF = 5; Less than 40: CF = 15; Less than 60: CF = 35; Less than 80: CF = 45; Less than 100: CF = 50. Step 2: Plot points: (20, 5), (40, 15), (60, 35), (80, 45), (100, 50). Also plot starting point (0, 0). Step 3: Connect points with a smooth curve — this is the less-than ogive. Step 4: Finding median graphically: N = 50, so N/2 = 25. Draw a horizontal line from CF = 25 to the ogive. Drop a perpendicular to the X-axis. Reading: the perpendicular meets X-axis at approximately 53–54 marks. Verification by formula: Median = L + [(N/2 − CF) / f] × h = 40 + [(25 − 15) / 20] × 20 = 40 + 10 = 50 marks. (The graphical method gives an approximate reading; the formula gives the exact value.)

Practice — Presentation of Data (Tables, Diagrams, Graphs)

Sign in to save attempts to your dashboard and track your accuracy over time

Find a verified tutor

Join a live course

Browse coaching centres

About

Categories

Support

Documentation

Get Study Tips & Updates

Download Our App

Download for iOS

Download for Android

Popular Cities