# Important formulas for Data Interpretation

### Data Interpretation Formulas

We use some aptitude formulas in solving DI questions. Most Common questions are asking in this format from Percentages

1) X is what % of y that means x/y * 100.

Eg: 72 is what % of 360 = [72/360]×100 =20%

2) What percentage is x of y? I.e. x/y * 100.

3) X is what percent more than y = x-y/y * 100

4) X is what percent less than y = y-x/y * 100

5) Percentage change between two particular values = [final – initial/ initial] * 100

Memorize some fractional values and percentage values.

• 1/2 = 50%
• 1/3 = 33.33%
• ¼ = 25%
• 1/5 = 20%
• 1/6 =16.66%
• 1/7 = 14.28%
• 1/8 = 12.5%
• 1/9 = 11.11%
• 1/10 = 10%
• 1/11 =9.09 %
• 1/12 = 8.33%
• 1/13 = 7.69%
• 1/14 = 7%
• 1/15 = 6.66%
• 1/16 = 6.25%
• 1/17 = 5.88%
• 1/18 =5.55%
• 1/19 = 5.26%
• 1/20= 5%
• 5%= 1/20 = 0.05
• 10% =1/10 =0.1
• 15% =3/20
• 20% = 1/5
• 25% = ¼
• 30% =3/10
• 40% =2/5
• 50% =1/2
• 55%=11/20
• 60% = 3/5
• 70% = 7/10
• 75% = 3/4
• 80% = 4/5
• 90% = 9/10
• 100%=1
• 6 ¼ % = 1/6
• 12 ½ % = 1/8
• 16 2/3 % = 1/6
• 33 1/3 % = 1/3
• 66 2/3 % =2/3
• 125% =5/4
• 150% = 3/2

Comparison of two fractions:

Eg: Compare, 3/4, and 1/4.

By seeing itself, we can say 3/4 is big. Implement here our logic of cross multiplication of two fractions.

¾ ¼ we get, 12 and 4 we know 12 > 4 so we can say ¾ >1/4

Apply the same logic big fractions it’s very simple and takes less time.

#### Formulas on Averages:

• Average = sum of elements/ no. of elements  (or) (a1 + a2 + a3 + a4 +………… an)/n
• Sum of first n odd numbers:   1 + 3 + 5 + ………… + (2n-1)= n2
• Sum of first n even numbers:  2 + 4 + 6 + …………+ 2n = n (n+1).
• Sum of first n natural numbers: 1+2+3 +4 + ……..+n = n(n+1)/2.
• Sum of squares of first n natural numbers: 12 + 22 + 32 + 42 + 52 + 62 + …………+n[n (n+1)(2n+1)]/6.
• Sum of cubes of first n natural numbers:  13 + 23+33 + 43 + …… + n3  [n(n+1)/2]2