Prerequisites:
ex: The following pie chart represents the number of questions came in a test paper from different subjects. Find the;
- Percentage and Ratio applications
- Familiarity with different sets of data presentation techniques
Key Points:
Know your tables, approximation techniques and calculation techniques specific to the data sets.
Revision:
How to compare small fractions?
Let's say you want to check which one is bigger: 9/13 or 11/17
9 11
13 17
Cross multiply numerator of the 1st fraction with the denominator of 2nd fraction and denominator of 1st with the numerator of 2nd fraction
= 9 * 17 = 153
= 11 * 13 = 143
Since 153 is greater than 143; so 1st fraction (9/13 ~ 0.69) is greater than 2nd fraction (11/17 ~ 0.65).
Here we compare numerators, so 153 is associated with 9. So 9/13 is bigger.
Exercise: compare 12/27 with 17/39
How to add numbers faster?
Most of the time you need to sum 5-6 numbers to find the average or compare their sum with some other. So it's crucial how you add numbers quickly.
Case 1: close range number
Let's say we want to find the avg of this sum:
[ 187 + 193 + 168 + 205 + 182 + 185]/6
One thing you can do is keep a base number aside like 180. Now with respect to 180 we can see other numbers as sum or difference of 180.
= 180 + [7 + 13 - 12 + 25 + 2 + 5]/6
= 180 + [7 + (13 -12) + (25 + 5) + 2]/6
= 180 + [(7 + 1 + 2) + (30)]/6
= 180 + 40/6
= 186.66
This may look like a lot of steps but all these will be mental calculations for you in some time. Just make sure to pair numbers as if you want to make multiple of 10 everywhere.
Case 2: Number are far apart:
Find the avg of
[181 + 307 + 413 + 729 + 995]/5
Step 1: Separate the hundredth place value:
100 + 300 + 400 + 700 + 900
= (100 + 900) + (300 + 700) + 400
= 2400
Step 2: Repeat the step 1 for the tenth place value:
80 + 0 + 10 + 20 + 90
= 200
Step 3: Repeat the step 1 for the unit place value:
1 + 7 + 3 + 9 + 5
= (1 + 9) + (7 + 3) + 5
= 25
Total = 2400 + 200 + 25 = 2625
Avg = 525
with little practice you can do this in a single step.
Pie Charts
Pie charts are useful to compare different parts of a whole amount. A pie chart is a circular chart in which the circle is divided into sectors. Each sector visually represents an item in a data set to match the amount of the item as a percentage or fraction of the total data set.
There are two main things to remember:
- Know how to convert the % sector into equivalent fraction or angle.
- Know how to convert an angle into equivalent fraction or % sector.
Whole circle = 360°
ex: The following pie chart represents the number of questions came in a test paper from different subjects. Find the;
- Percentage of questions that came from English.
- What's the percentage difference between no of questions from Biology and Polity.
- Angle made by no of History Questions
Solution:
Ans 1: Total Sum = 92
%English = (12/92) * 100 = 13.04%
Ans 2: Percentage difference = (34 - 23)/92 * 100 = 11.96%
Ans 3: Angle = (23/92)*360° = 90°
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