NCERT Solutions Ganita Prakash Chapter 4 – 79Section 4.1 Arranging Data in Order — Figure it Out
Book page 77 Updated on2026-09-05
Q1.
Help her to figure out the following: a. The largest shoe size in the class is ______. b. The smallest shoe size in the class is ______. c. There are ______ students who wear shoe size 5. d. There are ______ students who wear shoe sizes larger than 4.
Answer
Sushri Sandhya has already written the sizes in ascending order:
a. 7 — the last number in the ordered list. b. 3 — the first number in the ordered list. c. 10 students wear size 5. d. 15 students wear a size larger than 4.
The shoe-size data as a bar graph. Size 5 is the most common; only one student wears size 7.
Check it yourself: 3 + 9 + 10 + 4 + 1 = 27, and the board has 3 rows of 9 numbers = 27 readings. The counting is correct.
Q2.
How did arranging the data in ascending order help to answer these questions?
Answer
Ordering does three things at once:
The smallest and the largest jump out. In an ordered list they are simply the first and the last number — 3 and 7. In the jumbled board you would have to scan all 27 numbers, twice.
Equal values come together. All the 5's stand side by side, so counting them is one quick sweep instead of hunting all over the board.
“More than” questions become easy. Everything larger than 4 lies to the right of the last 4 — you just count the tail of the list.
Why it works: ordering does not change the data at all — the same 27 readings are there. It only changes the arrangement, and a good arrangement makes the answer visible instead of hidden.
Math Talk: Ask your friend to find the largest number in a jumbled list of 27 numbers, and time it. Then give the same list in order. Discuss why the second is so much faster.
Q3.
Are there other ways to arrange the data?
Answer
Yes — many. Each way suits a different question:
Descending order — 7, 6, 6, 6, 6, 5, 5, … Useful when you want the biggest values first.
Frequency table with tally marks — the shortest form of all: five rows instead of 27 numbers (the table in question 1 above).
Pictograph — one symbol for each student (or for every 2 students) against each size.
Bar graph — a bar for each size, its height showing how many students wear it.
Grouped table — “small sizes (3–4)”, “large sizes (5–7)”, if only the broad picture is needed.
Which one to pick: the frequency table is best for exact counts, the bar graph for comparing at a glance, and the ordered list for finding the smallest, the largest or the middle value. The data never changes — only the way we look at it.
Q4.
Write the names of a few trees you see around you. When you observe a tree on the way from your home to school (or while walking from one place to another place), record the data and fill in the following table: a. Which tree was found in the greatest number? b. Which tree was found in the smallest number? c. Were there any two trees found in the same numbers?
Answer
This is a survey you do outside the classroom. Carry a small notebook, and put one tally mark every time you pass a tree of that kind.
Tree
Tally marks
No. of Trees
Peepal
|||| |||
8
Neem
|||||||| ||
12
Banyan
||||
4
Mango
|||| ||
7
Gulmohar
||||
4
Total
—
35
For this sample walk:
a. The neem was found in the greatest number — 12 trees.
b. The banyan and the gulmohar were found in the smallest number — 4 trees each.
c. Yes — banyan and gulmohar have the same count, 4 each.
Your own table will have different trees and different numbers, and that is perfectly correct — the answer belongs to your route.
Tip: fix the route and the day before you start, and count only trees on one side of the road. If the plan keeps changing, the data cannot be compared with a friend's data.
Q5.
Take a blank piece of paper and paste any small news item from a newspaper. Each student may use a different article. Now, prepare a table on the piece of paper as given below. Count the number of each of the letters ‘c’, ‘e’, ‘i’, ‘r’, and ‘x’ in the words of the news article, and fill in the table. a. The letter found the most number of times is ______. b. The letter found the least number of times is ______. c. List the five letters ‘c’, ‘e’, ‘i’, ‘r’, ‘x’ in ascending order of frequency. Now, compare the order of your list with that of your classmates. Is your order the same or nearly the same as theirs? (Almost everyone is likely to get the order ‘x, c, r, i, e’.) Why do you think this is the case? d. Write the process you followed to complete this task. e. Discuss with your friends the processes they followed. f. If you do this task with another news item, what process would you follow?
Answer
Here is a filled table for one short news item of about 120 words:
Letter
c
e
i
r
x
Any other letter (a)
Number of times found in the news item
18
72
46
40
1
55
a. Among the five given letters, e was found the most number of times.
b.x was found the least number of times.
c. Ascending order of frequency: x, c, r, i, e (1, 18, 40, 46, 72).
Why everybody gets nearly the same order: the order does not depend on which news item you pick. It depends on the English language itself. e is the commonest letter in English — it sits in the, he, be, she, and in almost every ending like -ed, -es, -ment. x is the rarest — very few words use it at all. So any piece of ordinary English, long enough, will show the same pattern. This is a real and useful fact: it is exactly how secret codes are cracked, and how the letters were arranged on old typewriters and keyboards.
d. The process I followed:
Pasted the news item and read it once to see how long it was.
Drew the table with one column for each letter.
Read the article one word at a time, and put a tally mark in the right column for each letter found — bundling the marks in fives.
Counted both capital and small forms of a letter together (E and e), and did not count the headline separately from the text.
Counted the tally marks, wrote the frequencies, and arranged them in ascending order.
e. Different friends work differently — some go letter by letter (reading the whole article once for ‘c’, once for ‘e’, and so on), some strike off each letter with a pencil as they count, and some cut the article into lines and count line by line. Going through the article once with all five columns open is the fastest and makes fewer mistakes.
f. For another news item I would follow the same process — that is the whole point of writing the steps down. Only then can the two results be compared fairly. I would also note the number of words in each article, because a longer article naturally gives bigger counts.