SSC CGL Maths · Data Interpretation

Averages from Data

An average from a table is a total divided by the number of entries, and two averages over the same number of entries can be compared through their totals alone.

All Data Interpretation notes

Why this matters

Forty-two questions in the bank, the largest share of the chapter after pie charts, and thirty-eight of them are EASY. Four come from 2025. Most need one total and one division; the time is saved by not dividing when the question only compares.

Concept 1 of 4: Average of a row or a column

An average shares a total out equally. Add the entries the question names, count them, and divide. When the numbers sit close together, guess a round value in the middle and only average how far each entry sits from it.

Definition

Full method: average $=$ total $\div$ number of entries.
Count carefully: "from 2010 to 2013" is four years, "the first five months" is five.
Fast route (assumed average): pick a round value $A$ near the middle, add the gaps $x - A$ (with signs), divide that small sum by the count and add it to $A$ . This is exact, not an estimate, so it is always safe.
Average speed from a distance table is total distance $\div$ total time.
Mean of the highest and lowest is just those two values added and halved.
Keep the table's unit: an average of values "in thousands" is in thousands.

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}

nnumber of entries
Aany round value you choose

Worked example

The table shows a shop's monthly sales (in ₹ thousand).

Month	Jan	Feb	Mar	Apr	May
Sales	142	155	138	161	149

Find the average monthly sales.

Practice this conceptself-check · 4 quick reps

The same idea in a real exam question:

SSC CGL · 2025 · Tier I, 15 Sep 2025, Shift 1 · Q58Easy

Example 1 · Data Interpretation · Averages from Data

Table - Monthly Sales (in ₹000)

Salesperson	Jan	Feb	Mar	Apr
P	50	60	70	55
Q	65	68	62	64

What are the average monthly sales of Q?

Dividing by the wrong count

Years from 2010 to 2013 are four entries, not three. Count the entries you added, not the gap between the first and last year.

Rounding the entries before adding

Add the entries exactly, divide, and only then compare with the options. Rounding each entry first can shift the average onto a neighbouring option when the options sit close together.

Drill 19 more on average of a row or a column

Concept 2 of 4: Comparing or subtracting two averages

If two lists have the same number of entries, the one with the bigger total has the bigger average, because both are divided by the same number. And the gap between their averages is the gap between their totals, divided once.

Definition

Same count: compare totals; there is no need to divide at all.
Difference of two averages over the same count $=$ difference of totals $\div n$ . You can also add the pair-by-pair gaps and divide once.
Different counts: each average must be worked out on its own before you compare.
If one row beats another in every column, its average is higher with no arithmetic at all.

Difference of averages over the same count

\bar{x} - \bar{y} = \frac{\sum x_i - \sum y_i}{n}

nthe common number of entries

Worked example

The table shows the output of two plants (in thousand units).

Year	2019	2020	2021	2022
Plant A	36	41	39	44
Plant B	30	38	42	34

Find the difference between the average yearly outputs of the two plants.

Practice this conceptself-check · 4 quick reps

The same idea in a real exam question:

SSC CGL · 2025 · Tier I, 14 Sep 2025, Shift 1 · Q56Easy

Example 2 · Data Interpretation · Averages from Data

Table – Units Sold of 3 Products

Product	Jan	Feb	Mar
A	100	120	110
B	90	85	95
C	150	160	155

Q: Which product had the highest average units sold?

Comparing totals when the counts differ

A total of 300 over 4 years is a larger average than a total of 360 over 6 years. Totals stand in for averages only when the number of entries is the same.

Drill 12 more on comparing or subtracting two averages

Concept 3 of 4: Values above, below or closest to the average

Once the average is known, each entry is either above it, below it or on it. Questions ask you to count one side, or to find the entry with the smallest gap from it.

Definition

Find the average first, then compare each entry with it.
Above or below are strict: an entry equal to the average is neither.
Closest to the average: the entry with the smallest gap $|x - \bar{x}|$ . Two entries can tie, and the options may say "both".
The entries above and below always balance: their gaps add to zero, which is a quick check on the average.

Gap from the average

d_i = x_i - \bar{x} \qquad \sum d_i = 0

Worked example

The table shows a machine's output on seven days.

Day	Mon	Tue	Wed	Thu	Fri	Sat	Sun
Output	62	48	75	55	70	58	66

On how many days was the output above the average?

Practice this conceptself-check · 4 quick reps

The same idea in a real exam question:

SSC CGL · 2024 · Tier I, 10 Sep 2024, Shift 2 · Q72Easy

Example 3 · Data Interpretation · Averages from Data

The given bar graph shows the production of bikes by a company (in thousands) over the years. In how many of the given years was the production of bikes more than the average production of bikes over the years?.

Counting the entry that equals the average

An entry equal to the average is not more than it and not less than it. Leave it out of both counts unless the question says "at least" or "at most".

Drill 5 more on values above, below or closest to the average

Concept 4 of 4: Combined average of two or more groups

Putting two groups together means putting their totals together and their counts together. The combined average is the new total over the new count. It is the plain mean of the two averages only when both groups are the same size.

Definition

Combined average $=$ (sum of all entries) $\div$ (number of all entries).
From averages: multiply each average by its count to get totals, add, divide by the total count.
Equal group sizes: the combined average is the mean of the group averages. Unequal sizes: never take the plain mean.
A score table (how many students got each mark) is a combined average: $\sum (\text{count} \times \text{mark}) \div$ number of students.

Combined average

\bar{x}_{\text{combined}} = \frac{n_1 \bar{x}_1 + n_2 \bar{x}_2}{n_1 + n_2}

n_1, n_2sizes of the two groups
$\bar{x}_1$ , $\bar{x}_2$ their averages

Worked example

The table shows the daily output of two machines.

Machine	Day 1	Day 2	Day 3
M1	31	35	33
M2	41	38	44

What is the overall average output per machine per day?

Practice this conceptself-check · 4 quick reps

The same idea in a real exam question:

SSC CGL · 2025 · Tier I, 16 Sep 2025, Shift 1 · Q58Easy

Example 4 · Data Interpretation · Averages from Data

Table – Weekly Fuel Usage (litres)

Vehicle	Mon	Tue	Wed	Thu	Fri
Truck1	18	20	22	21	19
Truck 2	25	24	26	23	24

Q: What is the overall average daily fuel usage for both trucks?

Taking the plain mean of two averages

A group of 10 averaging 30 and a group of 30 averaging 40 do not combine to 35. The larger group pulls harder: the combined average is 37.5.

Drill 2 more on combined average of two or more groups

Summary — formulas & gotchas at a glance

A revision cheat-sheet for the formulas and gotchas above. Click any concept name to jump back to its full explanation.

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

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