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Bar Graph DI
Quantitative Aptitude / DI · Core DI
Useful for: SSC CGL, IBPS Banking
Overview
Each chart type answers different questions; reading the scale, legend and class intervals correctly is the core skill.
Key points
- Bar graph: separate bars, equal width; used for discrete categories.
- Histogram: adjacent bars for continuous class intervals; area represents frequency when widths differ.
- Frequency polygon: join the mid-points of the tops of histogram bars.
- Pie chart: central angle = (value/total) × 360°.
- Line graph: shows trends over time; the slope shows the rate of change.
Explanation
- Class mark (mid-point) = (lower limit + upper limit)/2.
- Unequal class widths: adjust heights (frequency density) before comparing.
- For pie charts, 1% = 3.6°.
- Stacked bars: read the segment, not the full bar.
Step by step
- Identify the chart.
- Read values with the scale.
- Compute and check units.
Examples
- An item that is 25% of the total gets 25 × 3.6 = 90° in a pie chart.
- Class 10–20 has class mark (10 + 20)/2 = 15.
- A line rises from 200 to 260: growth = 60/200 × 100 = 30%.
Traps and advanced points
- Trap: Treating a histogram like a bar graph with gaps.
- Trap: Reading the full stacked bar instead of a segment.
- Trap: Using degrees as percentages directly.
Quick revision
- 1% = 3.6°.
- Class mark = average of limits.
- Histogram bars touch; bar graphs do not.
Practice MCQs
Values are 112, 84, 116, 114. Find the range (highest − lowest).
- 38.4
- 35.2
- 28.8
- 32
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Answer: (d) 32. Highest = 116, lowest = 84. Range = 116 − 84 = 32.
Values are 136, 100, 124, 146. Find the range (highest − lowest).
- 50.6
- 46
- 41.4
- 55.2
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Answer: (b) 46. Highest = 146, lowest = 100. Range = 146 − 100 = 46.
Values are 152, 114, 136, 144. Find the range (highest − lowest).
- 41.8
- 38
- 45.6
- 34.2
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Answer: (b) 38. Highest = 152, lowest = 114. Range = 152 − 114 = 38.
Values are 163, 118, 133, 182. Find the range (highest − lowest).
- 70.4
- 76.8
- 64
- 57.6
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Answer: (c) 64. Highest = 182, lowest = 118. Range = 182 − 118 = 64.
Values are 174, 132, 150, 150. Find the range (highest − lowest).
- 50.4
- 46.2
- 37.8
- 42
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Answer: (d) 42. Highest = 174, lowest = 132. Range = 174 − 132 = 42.
Deposits change from 163 crore to 129 crore. What is the percentage change?
- -18.77
- -16.69
- -22.94
- -20.86
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Answer: (d) -20.86. % change = (129 − 163) ÷ 163 × 100 = -34 ÷ 163 × 100 = -20.86%. The negative sign shows a fall of 20.86%.
Deposits change from 171 crore to 145 crore. What is the percentage change?
- -16.73
- -13.68
- -15.2
- -12.16
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Answer: (c) -15.2. % change = (145 − 171) ÷ 171 × 100 = -26 ÷ 171 × 100 = -15.2%. The negative sign shows a fall of 15.2%.
Deposits change from 179 crore to 141 crore. What is the percentage change?
- -19.11
- -21.23
- -16.98
- -23.35
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Answer: (b) -21.23. % change = (141 − 179) ÷ 179 × 100 = -38 ÷ 179 × 100 = -21.23%. The negative sign shows a fall of 21.23%.
Deposits change from 187 crore to 157 crore. What is the percentage change?
- -12.83
- -14.44
- -17.65
- -16.04
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Answer: (d) -16.04. % change = (157 − 187) ÷ 187 × 100 = -30 ÷ 187 × 100 = -16.04%. The negative sign shows a fall of 16.04%.
Deposits change from 194 crore to 146 crore. What is the percentage change?
- -22.27
- -27.22
- -19.79
- -24.74
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Answer: (d) -24.74. % change = (146 − 194) ÷ 194 × 100 = -48 ÷ 194 × 100 = -24.74%. The negative sign shows a fall of 24.74%.
Branch A processed 266 thousand transactions and Branch B 206 thousand. Find A:B as a decimal ratio (A/B).
- 0.29
- 1.29
- 2.29
- 3.29
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Answer: (b) 1.29. A/B = 266 ÷ 206 = 1.29. (Both are in thousands, so the unit cancels.)
Branch A processed 272 thousand transactions and Branch B 200 thousand. Find A:B as a decimal ratio (A/B).
- 3.36
- 0.36
- 2.36
- 1.36
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Answer: (d) 1.36. A/B = 272 ÷ 200 = 1.36. (Both are in thousands, so the unit cancels.)
Branch A processed 277 thousand transactions and Branch B 210 thousand. Find A:B as a decimal ratio (A/B).
- 3.32
- 0.32
- 1.32
- 2.32
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Answer: (c) 1.32. A/B = 277 ÷ 210 = 1.32. (Both are in thousands, so the unit cancels.)
Branch A processed 283 thousand transactions and Branch B 204 thousand. Find A:B as a decimal ratio (A/B).
- 0.39
- 2.39
- 3.39
- 1.39
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Answer: (d) 1.39. A/B = 283 ÷ 204 = 1.39. (Both are in thousands, so the unit cancels.)
Branch A processed 288 thousand transactions and Branch B 224 thousand. Find A:B as a decimal ratio (A/B).
- 0.29
- 1.29
- 2.29
- 3.29
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Answer: (b) 1.29. A/B = 288 ÷ 224 = 1.29. (Both are in thousands, so the unit cancels.)
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