Data Handling and Presentation · Lesson 1 of 7
Collecting and Organising Data
“Turn a question and a collection of observations into an organised table that can answer it.”
• Recognise data and decide when a question needs fresh observations. • Collect responses while keeping track of what each response means. • Sort data or use tally marks to count each category accurately. • Read frequencies and distinguish a category count from other information. • Use a frequency table to answer and investigate questions.
Start with a question
Suppose two friends disagree about which game is most popular in their class. Their own favourites cannot settle the matter. They could ask every classmate the same question, record each answer once, and then compare the numbers who chose each game. This is the purpose of data handling: gathering information to answer a clear question.
A collection of facts, numbers, measurements, observations, or descriptions that tells us something about what we are investigating.
A list of favourite games is data, and so is a list of students’ shoe sizes. “Which television show is most popular in our class?” calls for collecting classmates’ answers. “What is the capital of India?” can be answered from an existing reliable source; surveying classmates would measure what they believe, which is a different question. For “How much water is wasted in our locality?”, decide what counts as waste, where and when to observe it, and which measurements to record.
Problem
How could Navya and Naresh find their class’s favourite game?
- 1.Ask each student to name one favourite game, so every response is comparable.
- 2.Record the responses without skipping or counting a student twice.
- 3.Group identical answers and count them. The game with the greatest count is most popular among the students surveyed; this does not prove it is most popular everywhere.
From a raw list to useful counts
The friends initially have names paired with games. Such a raw list preserves who chose what, but the most common game is hard to spot. We can group the answers into categories and count how often each category occurs. If we care about delivering each student the sweet they chose, we must also keep the name-and-choice list: a table of totals alone cannot identify the recipients.
The number of times a particular value or category occurs in a set of data.
One vertical tally stroke records one observation. For the fifth observation, draw a crossing stroke through the previous four: a complete group then means five. Groups of five are quick to count because six is five plus one, while thirteen is five plus five plus three. Write the resulting frequency beside each category.
| Sweet | Tally in groups of five | Number of students |
|---|---|---|
| Jalebi | 5 + 1 | 6 |
| Gulab jamun | 5 + 4 | 9 |
| Gujiya | 5 + 5 + 3 | 13 |
| Barfi | 3 | 3 |
| Rasgulla | 5 + 2 | 7 |
The table answers how many of each sweet to buy: 6 jalebis, 9 gulab jamuns, 13 gujiyas, 3 barfis, and 7 rasgullas. Its frequencies add to 38, a useful check against the number of students who answered. The totals do not tell the teacher which particular student chose a gujiya.
Problem
There are two groups of five tally marks and three more beside gujiya. How many students chose it?
- 1.Two complete groups represent 5 + 5 = 10 students.
- 2.Add the three separate marks: 10 + 3 = 13.
- 3.Record 13 as the frequency for gujiya; do not mistake the number of tally groups for the number of children.
Order numerical data and look for patterns
Shoe sizes can be arranged from smallest to largest. Once ordered, the smallest and largest sizes appear at the ends and equal sizes sit together, making their counts easier to check. A frequency table is another useful arrangement: one row for each shoe size and one count beside it. Ordering keeps individual values visible; a frequency table is more compact when we mainly need category counts.
| Shoe size | 3 | 4 | 5 | 6 | 7 |
|---|---|---|---|---|---|
| Number of students | 3 | 9 | 10 | 4 | 1 |
Problem
The shoe-size list has frequencies 3, 9, 10, 4, and 1 for sizes 3 through 7. How many students wear a size larger than 4?
- 1.Only sizes 5, 6, and 7 are larger than 4.
- 2.Add their frequencies: 10 + 4 + 1 = 15 students.
- 3.The largest size is 7, but that answer is different from the number of students above size 4.
You can carry out the same process yourself. Record the tree types seen along a chosen route, then count each type and compare most, least, and equal frequencies. Or select a news item and tally the letters c, e, i, r, and x. Compare your ordering with classmates’ results and ask why some letters appear more often. Describe how you recorded observations so someone else can repeat the investigation.
Read a frequency table carefully
A frequency distribution table pairs each possible value with the number of times it occurred. It helps us see the most common value and check the total number of observations. But its two columns may have different meanings: in a cricket table, “wickets in one match” is a value, while “number of matches” is its frequency.
| Wickets in one match | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 |
|---|---|---|---|---|---|---|---|---|
| Number of matches | 2 | 4 | 6 | 8 | 3 | 5 | 1 | 1 |
Problem
How many wickets are represented by this table of 30 matches?
- 1.Multiply each wickets value by its number of matches: 0×2, 1×4, 2×6, 3×8, 4×3, 5×5, 6×1, 7×1.
- 2.Add the contributions: 0 + 4 + 12 + 24 + 12 + 25 + 6 + 7 = 90 wickets.
- 3.Check the separate total of frequencies: 2 + 4 + 6 + 8 + 3 + 5 + 1 + 1 = 30 matches. Thirty counts matches; ninety counts wickets.
A frequency of 9 for gulab jamun tells us how many students chose it, not which students. Adding the distinct wicket labels 0 through 7 gives neither the number of matches nor the total wickets; each label must be counted as many times as its frequency.
Try a roadside survey by making a category list for bikes, cars, cycles, scooters, buses, auto rickshaws, and other vehicles. Add a tally whenever one passes, and later turn the tallies into a frequency table. Alternatively, roll a die 30 times, tally the six outcomes, and make sure their frequencies add to 30. Different classes may obtain different results; the method of checking remains the same.
Quiz
Which question calls for collecting fresh data from classmates?
A category has two complete groups of five tally marks and two extra marks. Its frequency is…
A sweets table gives 9 students for gulab jamun. What can it tell us?
Shoe-size frequencies for sizes 5, 6, and 7 are 10, 4, and 1. How many students have a size above 4?
A player took 3 wickets in each of 8 matches. What is this row’s contribution to total wickets?
You roll a die 30 times and make a frequency table. What should its six frequencies total?
Practice Problems
- Survey one favourite activity per classmate. Explain how you will avoid counting anyone twice, then make a tally and frequency table.
- For sweet frequencies 6, 9, 13, 3, and 7, find the total responses and explain whether the table identifies any particular child’s choice.
- A sorted shoe-size list has sizes 3, 4, 5, 6, 7 with frequencies 3, 9, 10, 4, 1. Find the most common size and the number with sizes below 5.
- Observe trees on one route, tally each kind, and state the route and time of observation. Could another route give a different most common tree?
- Roll a die 30 times. Give the least and most frequent outcomes and check that all six counts add to 30.
- Use the wickets table to explain, in words and calculations, why the number of matches and the number of wickets have different totals.
Key Takeaways
• Collect data for a clearly stated question and record every observation consistently. • Tallies and ordered lists help turn raw observations into trustworthy frequencies. • A frequency is a count of occurrences; it may not identify the people or objects behind that count. • Check category frequencies against the number of observations, and multiply value by frequency when finding a total of values.
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Reading and Making Pictographs