Mizoram Police Constable /Quantitative Aptitude

Bar & pie charts

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Bar & Pie Charts – Quantitative Aptitude Study Notes

(For the Mizoram Police Constable Examination)

1. Simple Explanation

Chart What It Shows When to Use Key Feature
Bar Chart Quantitative comparison of different categories (e.g., number of cases in each district). When data are discrete and you want to see which category is larger or smaller. Bars’ lengths (or heights) are proportional to the values.
Pie Chart Share or proportion of a whole (e.g., percentage of crimes by type). When data represent parts of a whole and you want to see the relative size of each part. Slices’ angles are proportional to their percentages.

Both charts are visual tools that help you convert numbers into a quick mental picture.

2. Key Points

2.1 Bar Charts

Aspect Details
Axes Horizontal axis (X) lists categories; vertical axis (Y) gives quantitative values.
Bar Orientation Can be vertical or horizontal.
Bar Width Should be uniform; gaps between bars indicate separation.
Reading Values - Exact: read the Y‑axis value that the bar reaches.
- Approximate: use a ruler or a reference line.
Missing Values If total is known, compute missing bar height: Missing = Total – Sum(known bars).
Comparisons Look at bar lengths; a taller bar = larger value.
Cumulative Bar Charts Bars represent cumulative totals; the last bar’s height = overall total.

2.2 Pie Charts

Aspect Details
Whole 100 % of the circle.
Slices Each slice’s angle ∝ its percentage.
Reading Percentages - Exact: read the percentage labels.
- Approximate: use a ruler or compare to a 60° (1/6) or 90° (1/4) reference.
Missing Percentage If total % = 100 %, then Missing = 100 – Sum(known percentages).
Proportionality A slice that is 1/4 of the circle is 90° and 25 % of the whole.
Converting to Numbers If you know the total (e.g., 200 crimes) and a slice is 25 %, then the slice’s value = Total × Percentage / 100.
Comparing Slices Larger angles = larger percentages.

2.3 General Tips

  • Always check the scale on axes or the sum of percentages.
  • Use a ruler or a straight edge to read bar heights accurately.
  • Round to nearest integer only when the question asks for “nearest whole number.”
  • Remember that bars are linear (height ∝ value), while pie slices are angular (angle ∝ value).
  • Avoid over‑interpretation: a bar that looks slightly higher may not be significantly different.

3. Worked Example

3.1 Bar Chart – Crime Distribution by District

District Murder Cases
A 18
B 12
C 24
D 6
Total 60

Question:

  1. Which district has the highest number of murder cases?
  2. What is the ratio of cases in District C to District B?
  3. If the total number of murder cases is 70, how many cases were omitted from the chart?

Solution

  1. Highest Cases – Compare bar heights: District C (24) > District A (18) > District B (12) > District D (6).
    Answer: District C.

  2. Ratio C : B – 24 ÷ 12 = 2.
    Answer: 2 : 1.

  3. Missing Cases – Missing = Total – (18+12+24+6) = 70 – 60 = 10.
    Answer: 10 cases were omitted.

3.2 Pie Chart – Types of Crimes (Total 200 Cases)

Crime Type Percentage
Theft 35 %
Assault 25 %
Fraud 15 %
Others ?

Question:

  1. What is the percentage of “Others”?
  2. How many cases fall under “Others”?
  3. If “Theft” cases increased by 10 % of the total, what would be the new percentage for “Theft”?

Solution

  1. Missing Percentage – Missing = 100 – (35+25+15) = 100 – 75 = 25 %.
    Answer: 25 %.

  2. Number of “Others” Cases – 200 × 25 / 100 = 50.
    Answer: 50 cases.

  3. New Theft Percentage – Increase by 10 % of total = 200 × 10 / 100 = 20 cases.
    New Theft cases = 35 % of 200 = 70 cases + 20 = 90 cases.
    New percentage = 90 ÷ 200 × 100 = 45 %.
    Answer: 45 %.

4. Quick Revision Summary

  • Bar Chart
    • Read

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