Data Handling & Probability (VI–VIII) • Topic 1 of 4

Organising & Representing Data

Raw data is just a jumble of numbers until it is organised — and CTET expects you to know the NCERT progression. The first tool children meet (Class 6) is the tally mark: every fifth tally is drawn as a cross-stroke (the 'gate' or 'four-and-a-cross' grouping) so totals are read in fives. Tally marks feed a frequency distribution table, where each value (or class) is paired with how many times it occurs (its frequency). The same idea scales up: when data spreads over a wide range, we group it into class intervals (e.g. marks 0–10, 10–20) to get a grouped frequency table. CTET's pedagogy angle here is about purpose — why we organise data (to spot patterns, compare, and summarise), and the common child errors: miscounting tallies, forgetting that the crossing tally is the fifth (not sixth) mark, and the boundary confusion of whether a mark of exactly 20 goes in 10–20 or 20–30 (the convention is the upper limit is excluded, so 20 goes into 20–30). Questions often hand you a tally table and ask for a frequency, a total, the most frequent value, or which interval a reading falls in.

✅ Solved examples

1. In a tally table the marks for 'cricket' are drawn as one full 'gate' (a group of four with a crossing stroke) followed by three single strokes. How many children chose cricket?
A crossed group of tallies stands for 5, and there are 3 extra single marks. So 5 + 3 = 8 children chose cricket.
2. A frequency table shows shoe sizes: size 4 → 6 pupils, size 5 → 11 pupils, size 6 → 9 pupils, size 7 → 4 pupils. How many pupils were surveyed, and which size is most common?
Total = 6 + 11 + 9 + 4 = 30 pupils. The highest frequency is 11, at size 5, so size 5 is the most common (the mode of the data).
3. Marks are grouped into class intervals 0–10, 10–20, 20–30 (upper limit excluded). In which interval does a student scoring exactly 20 belong?
By the standard 'continuous' convention the upper limit is not counted in its own interval, so 20 is excluded from 10–20 and falls in the interval 20–30.
4. Why does NCERT introduce tally marks before bar graphs in the data-handling chapter?
Tally marks let children count and record frequencies quickly and concretely while collecting data, building the idea of frequency first; the bar graph then pictures those frequencies. It follows concrete-to-pictorial sequencing — count and tabulate before you represent.

✏️ Practice — try these, take hints as needed

1. In a tally chart, how many items does one completed 'gate' (a group of four strokes with a fifth crossing stroke) represent?
Tallies are grouped in fives.
The crossing stroke is the fifth mark, not the sixth.
5
2. A frequency table records: red → 7, blue → 5, green → 7, yellow → 3 marbles. What is the total number of marbles?
Add all the frequencies.
7 + 5 + 7 + 3.
22 marbles
3. A child counting tallies treats the crossing (fifth) stroke as a sixth mark. Each completed group will be miscounted as how many?
A correct group is 5.
They add one extra.
6 (instead of the correct 5)
4. Grouping data such as test scores into intervals like 0–10, 10–20, 20–30 produces what kind of table?
Data is bundled into classes.
Each class has a frequency.
A grouped frequency distribution table

📝 Topic test — 8 questions

Auto-graded with full solutions; saved to your dashboard. Use the calculator and formula sheet (top-right) any time.

Loading questions…
Bar Graphs, Pie Charts & Histograms →