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REET L1+L2 · Maths

Data Handling

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In REET Maths, the Data Handling topic asks simple but precise questions based on tables, reading a bar graph, and the definitions of mean-median-mode-range. Here are all the definitions, formulas and ways to read a graph, in one place.

  • 4 questions in REET 2024
  • Class 6-7 level
  • 8 min read
Verified 17 September 2026

How REET asks this topic

All four of REET 2024's questions were based on straight definitions and basic reading skills — what 'tabulation' means, the definition of 'range', identifying a point on the x-axis on the coordinate plane, and reading a value directly off a given bar graph. In other words, this topic tests vocabulary and the ability to read a graph or table correctly more than it tests calculation, so knowing the definitions well is enough to lock down almost all the marks here. For practice, always work with real data (class attendance, a marksheet, the weather) so that any new graph or table given in the exam can be read comfortably.

From raw data to a table

When information is collected without any order, it's called raw data. To organise it, tally marks are used — each value is shown as a vertical stroke, and on the fifth value, a diagonal stroke is drawn across the first four vertical strokes to complete a group of 5.

The process of arranging data neatly into columns and rows is called tabulation. The number of times a value occurs is called its frequency.

Measures of central tendency, and range

MeasureDefinition / formula
MeanSum of all observations ÷ number of observations
MedianThe middle value once the data is arranged in order (for an even count, the mean of the two middle values)
ModeThe value that occurs most often
RangeMaximum value − minimum value

Reading a bar graph

In a bar graph, all bars have the same width and the gap between bars is also kept equal — only the height or length of a bar changes in proportion to the value it represents. Usually one axis shows categories and the other shows the value/frequency.

When reading a graph, first check the scale marked on both axes, then identify the tallest and the shortest bars, and compare as needed.

The basics of the coordinate plane

The form of a point on the x-axis
(x, 0) — that is, the y-coordinate is always zero
The form of a point on the y-axis
(0, y) — that is, the x-coordinate is always zero
Origin
(0, 0)

The difference between pictographs, bar graphs and pie charts

A pictograph is the simplest way to represent data, where a picture or symbol of an object shows a fixed quantity (for example, one 🚗 symbol = 10 cars). A bar graph shows the same information using the height of equal-width rectangular bars, which is more precise to read.

A pie chart divides a circle into different parts to show each part's share of the whole — the full circle is 360°, and each category's angle is worked out based on its proportion. This topic is covered in more depth on the next page (Pie Chart and Histogram).

Finding the mean from a frequency distribution, with an example

When data is given as a frequency distribution, the mean = Σ(f × x) ÷ Σf, where f is the frequency and x is the value. The running total of all frequencies up to a certain class is called the cumulative frequency.

Example: in a class, 4 students scored 5 marks, 6 students scored 6 marks, and 5 students scored 7 marks. Σ(f × x) = (4×5) + (6×6) + (5×7) = 20 + 36 + 35 = 91, and Σf = 4 + 6 + 5 = 15. Mean = 91 ÷ 15 ≈ 6.07. This method finds the mean of large data sets quickly without adding up every single value separately — that's the main advantage of tabulation.

How to teach children

Classroom activity

Ask students their favourite fruit or sport and collect real data, have them build a table using tally marks, and then draw their own bar graph on graph paper. Afterward, have them find the mean, median, mode and range from the same data so the whole process connects together.

Teaching aids

Graph paper, and building physical bar graphs with coloured blocks/chart paper — for instance, each child standing in a line for a category can form a 'human bar graph'. A pictograph can also be built using coloured pebbles or seeds.

Common misconception

Students often treat mean and median as the same thing, and when finding the mode, mistake the largest number for the mode — when actually the mode is whichever value repeats the most, even if it's a small number. Some children, when there's an even count of values, pick just one middle value for the median instead of averaging the two.

Assessment idea

Give real data from the school's attendance register or a newspaper table, have students find the mean, range and mode, and ask which measure (mean/median/mode) would be the best representative in which situation.

Memory trick / exam tip

Never make the mistake of thinking the mode is the maximum value (the largest number) — the mode is whichever value repeats most often in the data, no matter how small that number is. Likewise, when building a table, always write a clear title, column headings and source, so the data is understandable without needing any extra explanation.

Questions asked in REET 2024 (with solutions)

Question 96

The system of presenting data in a systematic form in columns and rows is called

  1. Aसारणीयन
  2. Bमध्यमान
  3. Cदण्ड आरेख
  4. Dमाध्यिका

Explanation

आँकड़ों को स्तम्भों (columns) और पंक्तियों (rows) में क्रमबद्ध रूप से प्रस्तुत करना सारणीयन (Tabulation) कहलाता है। मध्यमान और माध्यिका केंद्रीय प्रवृत्ति के माप हैं, तथा दण्ड आरेख आँकड़ों का चित्रात्मक (graphical) प्रस्तुतीकरण है, सारणी नहीं।

Question 101

The difference between the maximum value and minimum value at data in a given group is called :

  1. Aपरिसर
  2. Bमाध्य
  3. Cबारम्बारता
  4. Dमाध्यिका

Explanation

आँकड़ों के सबसे बड़े (महत्तम) और सबसे छोटे (न्यूनतम) मान के अन्तर को परिसर (Range) कहते हैं: परिसर = महत्तम मान − न्यूनतम मान। माध्य और माध्यिका केन्द्रीय प्रवृत्ति के माप हैं तथा बारम्बारता किसी मान के आने की संख्या है।

Question 109

The point on x-axis is :

  1. A(2, 3)
  2. B(2, 0)
  3. C(0, 2)
  4. D(2, 2)

Explanation

x-अक्ष पर स्थित प्रत्येक बिन्दु का y-निर्देशांक शून्य होता है, अर्थात् वह (x, 0) के रूप में होता है। अतः (2, 0) x-अक्ष पर है। (0, 2) का x-निर्देशांक शून्य है, इसलिए वह y-अक्ष पर है।

Question 94

Using the given Bar diagram answer that which domestic animal is the most popular after cows

Figure: Bar chart of pet animals: Dogs 8, Cows 10, Goats 6, Rabbits 4, Cats 5. Diagram added with the exact values from the official figure note.

  1. Aबिल्लियाँ
  2. Bखरगोश
  3. Cबकरियाँ
  4. Dकुत्ते

Explanation

दंड आरेख में गायें सबसे अधिक (10) हैं। उसके बाद कुत्ते 8, बकरियाँ 6, बिल्लियाँ 5 और खरगोश 4 हैं। अतः गाय के बाद सबसे लोकप्रिय पालतू जानवर कुत्ते हैं।

Practice questions

Question 1

Find the mean of the data: 4, 8, 6, 10, 12.

  1. A7
  2. B8
  3. C9
  4. D10

Explanation

Sum = 4+8+6+10+12 = 40. Mean = 40 ÷ 5 = 8.

Question 2

Find the range of the data: 12, 45, 7, 89, 34.

  1. A77
  2. B82
  3. C89
  4. D7

Explanation

Maximum value = 89, minimum value = 7. Range = 89 − 7 = 82.

Question 3

Find the median of the data: 5, 3, 9, 1, 7.

  1. A3
  2. B5
  3. C7
  4. D9

Explanation

Arranging the data in ascending order: 1, 3, 5, 7, 9. The middle value (the median) = 5.

Question 4

Find the median of the data: 4, 8, 2, 10.

  1. A4
  2. B6
  3. C8
  4. D5

Explanation

Ascending order: 2, 4, 8, 10. Since the count (4) is even, the median = the mean of the two middle values (4 and 8) = (4+8)/2 = 6.

Question 5

Find the mode of the data: 2, 3, 3, 5, 3, 7, 5.

  1. A5
  2. B7
  3. C3
  4. D2

Explanation

3 appears most often (three times), so the mode = 3.

Question 6

How is the fifth tally mark drawn in tally marks?

  1. Aपहले चार खड़ी रेखाओं पर एक तिरछी रेखा खींचकर
  2. Bपाँचवीं खड़ी रेखा अलग से बनाकर
  3. Cएक गोला बनाकर
  4. Dपाँच बिंदु बनाकर

Explanation

In tally marks, the first four values are shown as vertical strokes, and the fifth is shown by drawing a diagonal stroke across them, completing a group of 5.

Question 7

If the y-coordinate of a point is zero, the point lies on the:

  1. Ay-अक्ष पर
  2. Bx-अक्ष पर
  3. Cमूलबिंदु पर
  4. Dप्रथम चतुर्थांश में

Explanation

Every point on the x-axis has a y-coordinate of zero, i.e. it is of the form (x, 0).

Question 8

If all the bars in a bar graph have unequal widths, then the graph:

  1. Aसही तरीके से आँकड़े दर्शाएगा
  2. Bआँकड़ों की सही तुलना संभव नहीं होगी, क्योंकि दंड आलेख में सभी दंडों की चौड़ाई समान होनी चाहिए
  3. Cकोई फर्क नहीं पड़ता
  4. Dमाध्य अपने आप बदल जाएगा

Explanation

For a bar graph to be read and compared fairly, all bars must have the same width and the same gap between them — only then can comparing heights alone be valid.

Question 9

The mean of five numbers is 15. If another number 27 is added to them, find the new mean.

  1. A17
  2. B18
  3. C16
  4. D20

Explanation

Sum of the five numbers = 15 × 5 = 75. Adding 27 gives a new sum of 102, over 6 numbers. New mean = 102 ÷ 6 = 17.

Question 10

Which is the most effective way to teach data handling in Class 7?

  1. Aसीधे सूत्र देकर अभ्यास कराना
  2. Bविद्यार्थियों से स्वयं वास्तविक आँकड़े एकत्र कर सारणी व आलेख बनवाना
  3. Cकेवल पाठ्यपुस्तक की परिभाषाएँ रटवाना
  4. Dविषय को परीक्षा के लिए छोड़ देना

Explanation

Having students collect real data themselves and build tables and graphs from it gives them a much deeper, experience-based understanding of tabulation and graphing than either formulas alone or rote definitions.

Frequently asked questions

How many questions come from data handling in REET?+

REET 2024 had 4 questions from this topic — most based on definitions and directly reading a graph/table, so these marks can be won quickly and easily.

What's the difference between mean, median and mode?+

Mean is the average of all the values, median is the middle value once arranged in order, and mode is the most frequently occurring value — all three are different measures of central tendency, useful in different situations.

What is range?+

The difference between the maximum and minimum values in the data is called the range: range = maximum value − minimum value. It's the simplest measure of how spread out the data is.

In what groups are tally marks made?+

Tally marks are made in groups of five — the first four are vertical strokes, and the fifth is shown by drawing a diagonal stroke across them, which makes even large amounts of data easy to count.

What's the difference between a pictograph and a bar graph?+

In a pictograph, data is represented by pictures/symbols where each symbol stands for a fixed quantity, while a bar graph shows values through the height of equal-width rectangular bars — a bar graph is considered more precise and easier to read. This also strengthens the foundation for the more advanced statistics topics that come up in higher classes.

Read next

Surface Area and Volume

Previous topic — revise the formulas for solid shapes.

Pie Chart and Histogram

The next ways to represent data — pie charts and histograms.

REET Syllabus

See the complete REET Level 1 and Level 2 syllabus in one place.

REET 2024 Solved Papers

Read all of REET 2024's solved questions, subject by subject.

Change Log

  • 17 September 2026 — English page published — mirrors the fact-checked Hindi page, independently bilingual-accuracy checked