Data Interpretation: SSC CGL Quantitative Aptitude

Formulas (2)

• Totals and differences of totals from a table · Difference of two totals
  $$\sum a_i - \sum b_i = \sum (a_i - b_i)$$
• Reading a cumulative and-above table · Bands from a cumulative table
  $$N_{a \le x < b} = N_{\ge a} - N_{\ge b} \qquad N_{< a} = N_{\text{total}} - N_{\ge a}$$

Watch out for (6)

• Dropping the unit line
  → Totals and differences of totals from a table
• Adding a printed Total row again
  → Totals and differences of totals from a table
• Counting the row that equals the limit
  → Picking out the rows that meet a condition
• Reading second highest as the second row
  → Picking out the rows that meet a condition
• Reading a cumulative column as a band
  → Reading a cumulative and-above table
• Looking up the percentage instead of the marks
  → Reading a cumulative and-above table

Formulas (4)

• Average of a row or a column · Average and the assumed average
  $$\bar{x} = \frac{x_1 + x_2 + \cdots + x_n}{n} \qquad \bar{x} = A + \frac{\sum (x_i - A)}{n}$$
• Comparing or subtracting two averages · Difference of averages over the same count
  $$\bar{x} - \bar{y} = \frac{\sum x_i - \sum y_i}{n}$$
• Values above, below or closest to the average · Gap from the average
  $$d_i = x_i - \bar{x} \qquad \sum d_i = 0$$
• Combined average of two or more groups · Combined average
  $$\bar{x}_{\text{combined}} = \frac{n_1 \bar{x}_1 + n_2 \bar{x}_2}{n_1 + n_2}$$

Watch out for (5)

• Dividing by the wrong count
  → Average of a row or a column
• Rounding the entries before adding
  → Average of a row or a column
• Comparing totals when the counts differ
  → Comparing or subtracting two averages
• Counting the entry that equals the average
  → Values above, below or closest to the average
• Taking the plain mean of two averages
  → Combined average of two or more groups

Formulas (3)

• Ratio of two totals in lowest terms · Ratio in lowest terms
  $$a : b = \frac{a}{h} : \frac{b}{h}, \quad h = \text{HCF}(a, b)$$
• How many times, and ratios of averages · Ratio of averages over the same count
  $$\frac{\bar{x}}{\bar{y}} = \frac{\sum x_i \div n}{\sum y_i \div n} = \frac{\sum x_i}{\sum y_i}$$
• Finding each part before taking the ratio · Recovering a value from a ratio
  $$E : I = p : q \;\Rightarrow\; I = E \times \frac{q}{p}$$

Watch out for (4)

• Writing the ratio the wrong way round
  → Ratio of two totals in lowest terms
• Stopping before lowest terms
  → Ratio of two totals in lowest terms
• Dividing averages that cover different counts
  → How many times, and ratios of averages
• Counting only the "only" row
  → Finding each part before taking the ratio

Formulas (3)

• One value as a percentage of another · A as a percentage of B
  $$\frac{A}{B} \times 100\%$$
• A part as a percentage of the whole · Share of the whole
  $$\text{Share} = \frac{\text{part}}{\text{whole}} \times 100\% \qquad \%\,\text{rest} = 100\% - \%\,\text{share}$$
• Aggregate percentage of marks · Aggregate percentage
  $$\text{Aggregate} = \frac{\sum \frac{p_i}{100} M_i}{\sum M_i} \times 100\%$$

Reference tables (1)

Watch out for (5)

• Dividing by the wrong base
  → One value as a percentage of another
• Mixing up one-sixth and one-seventh
  → Fractions and their percentage values
• Comparing parts instead of rates
  → A part as a percentage of the whole
• Averaging percentages from papers of different sizes
  → Aggregate percentage of marks
• Judging the best subject by raw marks
  → Aggregate percentage of marks

Formulas (3)

• Percentage increase or decrease between two values · Percentage change
  $$\%\,\text{change} = \frac{\text{new} - \text{old}}{\text{old}} \times 100$$
• Percent more than and percent less than · Percent more or less
  $$\frac{A - B}{B} \times 100 \qquad A = B\left(1 + \frac{r}{100}\right) \Rightarrow B \text{ is } \frac{r}{100 + r} \times 100\% \text{ less than } A$$
• Applying a percentage change to find a value · Applying a percentage change
  $$\text{New} = \text{Old} \times \left(1 + \frac{r}{100}\right) \qquad \text{Old} = \frac{\text{New}}{1 + \frac{r}{100}}$$

Watch out for (5)

• Dividing by the new value
  → Percentage increase or decrease between two values
• Taking the biggest jump as the biggest percentage
  → Percentage increase or decrease between two values
• Using the same percentage both ways
  → Percent more than and percent less than
• Picking the size before the direction
  → Percent more than and percent less than
• Taking the percentage off the new value
  → Applying a percentage change to find a value

Formulas (4)

• From a percentage share to a value · Value of a share
  $$\text{Value} = \frac{p}{100} \times \text{Total}$$
• Degrees and central angles in a pie chart · Pie chart angles
  $$\text{Value} = \frac{\theta}{360^\circ} \times \text{Total} \qquad \theta = \frac{p}{100} \times 360^\circ = 3.6p^\circ$$
• From one known share to the total or another share · From a known share
  $$\text{Total} = \frac{V}{p} \times 100 \qquad \text{Other share} = V \times \frac{q}{p}$$
• Comparing sectors without working out the total · Comparing sectors of one chart
  $$\frac{\text{Sector } A}{\text{Sector } B} = \frac{p_A}{p_B} = \frac{\theta_A}{\theta_B}$$

Watch out for (6)

• Comparing percentages across different totals
  → From a percentage share to a value
• Rounding each share before adding
  → From a percentage share to a value
• Reading degrees as percentages
  → Degrees and central angles in a pie chart
• Using 100 where 360 belongs
  → Degrees and central angles in a pie chart
• Dividing by the wanted share instead of the known one
  → From one known share to the total or another share
• Comparing sectors of charts with different totals directly
  → Comparing sectors without working out the total

Formulas (2)

• A ratio or a percentage inside a share · A part inside a share
  $$\text{Part} = \text{Total} \times \frac{p}{100} \times \frac{b}{a + b}$$
• Working back to a missing total · Back to the total
  $$\text{Total} = \frac{\text{known part}}{\frac{p}{100} \times \frac{b}{a + b}}$$

Watch out for (4)

• Adding ratios from different groups
  → A ratio or a percentage inside a share
• Applying the second percentage to the whole total
  → A ratio or a percentage inside a share
• Undoing only one step of the chain
  → Working back to a missing total
• Reading 20% less as 20% of
  → Working back to a missing total