CLASS 6 · GANITA PRAKASH · CHAPTER 4
Student-friendly answers on collecting, organising, picturing and interpreting data.
76 worked answers · short steps first, explanations when you need them
Textbook pages 75–100
Question 1(a)
Write each game name once in a table.
Go through the responses one by one and add a tally beside that student’s chosen game.
Count each set of tallies to get its frequency.
A frequency table groups matching answers and shows how often each answer occurred.
Question 1(b)
Compare the frequencies in the game table.
The largest frequency is 8 for Hockey.
The mode is the category with the greatest frequency.
Question 1(c)
Ask each student the same question.
Record one choice per student.
Make a tally table and compare the totals.
A fair comparison needs the same question for everyone and a complete count.
Question 1(d)
A class preference and a local observation are not known in advance.
The independence year and national capital are established facts.
Collect data when the answer depends on people’s current choices or a local condition. Established facts can be checked in a reliable reference.
Question 2
Count each group of tally marks.
The totals are jalebi 6, gulab jamun 9, gujiya 13, barfi 3 and rasgulla 7.
Each tally stands for one student, so count the marks in each row.
Question 2(a)
A frequency tells how many chose each sweet.
It does not identify which individual student made each choice.
To distribute the correct sweet to each person, we need the link between a student and their choice, not just category totals.
Question 3(a)
Compare the recorded sizes.
The values range from 3 to 7.
The extremes are the greatest and least values in the raw list.
Question 3(b)
Count every 5 in the list, or read the frequency table.
The size-5 frequency is 10.
Frequency counts the number of times a value occurs.
Question 3(c)
Sizes greater than 4 are 5, 6 and 7.
Add their frequencies: 10 + 4 + 1 = 15.
“Greater than 4” excludes size 4, so add the counts for 5, 6 and 7.
Question 4(a)
Walk around a defined area with a teacher.
Record each tree once, identifying its type carefully.
Tally the types and compare counts.
A clear boundary and one count per tree prevent missing or double-counting trees.
Question 6(a-b)
Choose one article and count each letter in its text.
Compare the letter frequencies.
Unlike a fixed fact, the answer changes with the text selected.
Question 4.2 travel (most)
Compare the number of symbols in each row.
The longest row is for school buses.
School bus is used by the most students.
Question 4.2 travel (least)
Compare the number of symbols in each row.
The shortest row is for cycles.
Cycle is used by the fewest students.
Question 4.2 books (a)
Compare the number of book symbols in each day’s row.
Thursday has no symbols.
Thursday had the fewest books borrowed: 0.
Question 4.2 books (b)
Count the symbols: Monday 5, Tuesday 4, Wednesday 2, Thursday 0, Friday 5 and Saturday 8.
Add: 5 + 4 + 2 + 0 + 5 + 8 = 24.
24 books were borrowed during the week.
Question 4.2 books (c)
Find the row with the greatest number of symbols.
Saturday has 8 book symbols.
Saturday had the most books borrowed. One possible reason is that students borrowed books before Sunday, when they had more time to read.
Question 4.2 kites (a-d)
Use half-symbols for 50 kites.
Chaman 2½; Rani 3; Rukhsana 1; Jasmeet 4½; Jetha Lal 2½; Poonam Ben 7 symbols.
Double Rani’s 300 is 600; Poonam Ben bought 700.
Pictograph rows: Chaman 2½, Rani 3, Rukhsana 1, Jasmeet 4½, Jetha Lal 2½, Poonam Ben 7 symbols. Rani: 3 symbols; most: Poonam Ben; Jasmeet bought more than Chaman; yes, 700 is greater than 2 × 300 = 600.
Question 4.2 key challenge
Subtract the complete groups of 10 and 5 from each total.
The remaining 3 or 7 students cannot be shown by a whole 10-symbol or 5-symbol.
The leftover 3 or 7 students do not match a whole symbol worth 10 or 5. A smaller key or a clearly explained fraction of a symbol is needed.
Question 5(a-c) trees
Compare the counts in your completed table.
The greatest count is the most common; the least count is the least common; equal counts indicate a tie.
Answers depend on the route you observed. Name the tree with the greatest count, the tree with the smallest count, and any tree types with equal counts.
Question Letter order (6c)
Arrange the five letters from the smallest count to the largest in your article.
Different articles in the same language often use common letters more and x less, though the exact order can change.
Order the letters by your article’s counts. Many classmates may get a similar order because English text uses some letters, such as e, more often than others, such as x; the result depends on the article.
Question 6(d)
Choose and mark one article.
Decide whether spaces, headings and punctuation are ignored.
Count c, e, i, r, x and one chosen extra letter consistently.
Record each total in the table.
Describe the article you chose, the counting rule, how you tallied each letter, and how you checked the totals.
Question 6(e)
Check that you used the same article and counting rules.
Compare the tally method and recount any different totals.
Explain your steps to each other. If you used the same article but got different counts, check that you treated capital letters and headings consistently.
Question 6(f)
Choose a new article and apply the same counting rules.
Make a fresh tally table and recount the selected letters.
Compare the new frequencies with the first article.
Use the same counting rules on the new article, record fresh tallies, and compare the results. The counts may change because the text is different.
Question 4.5 (1)
Heights are measured upward from the ground.
Vertical bars make that direction easy to picture.
Vertical bars (a column graph) are an intuitive choice because height is an upward measurement. Horizontal bars can also show the same data correctly.
Question 4.5 (2)
A river’s length extends along the ground, so horizontal bars are intuitive.
Find reliable length data, make a labelled table and use one scale for every bar.
Horizontal bars are a natural choice for comparing lengths, though vertical bars also work. Use a consistent source and units, label each river and continent, and draw bars to the chosen scale. The longest-river answers depend on the data source and definitions used.
Question 5(a)
Multiply the number of pictures by the key value: 5 × 10.
Each symbol represents 10 children, so five symbols represent five groups of ten.
Question 5(b)
Two full pictures represent 20.
Half a picture represents 5.
Add 20 + 5.
A half-symbol represents half of the key value.
Question 5(c)
Multiply 4 by 10.
Use the key for every symbol in the pictograph.
Question 6(a)
Read the height of the Class 2 bar against the vertical scale.
The bar height gives the number of absent students.
Question 6(b)
Compare all bar heights.
The tallest bar is for Class 8.
The tallest bar represents the greatest frequency.
Question 6(c)
Full attendance means zero students absent.
Find the class whose bar has height zero.
A zero-height bar means nobody was absent.
Question 7(a)
Read the six hourly bars: 150, 1200, 1000, 800, 700 and 600.
Add them: 150 + 1200 + 1000 + 800 + 700 + 600 = 4450.
The total across intervals is the sum of the bar values; the graph values are approximate.
Question 7(b)
Think of how many people usually travel early in the morning.
Treat this as a possible explanation, not a fact proved by the graph.
A graph shows what happened, but it does not by itself explain why.
Question 7(c)
The time may overlap with people travelling to work or school.
Later, the morning rush may finish.
Other days or locations could show a different pattern.
An explanation is a hypothesis; the recorded counts alone do not establish its cause.
Question 8(a)
Read 36 crore in 1951 and 102 crore in 2001.
Subtract: 102 − 36 = 66.
An increase is found by subtracting the earlier value from the later value.
Question 8(b)
Subtract consecutive values: 44−36, 54−44, 68−54, 84−68 and 102−84.
For each interval, subtract the earlier decade’s population from the later one.
Question Population graph discussion
Ask about individual decade values, the greatest or smallest increase, and comparisons between decades.
Use the labelled years and population scale to answer.
Questions could include “Which decade had the largest increase?” or “How much did the population grow from 1951 to 2001?”
Question 9
Put the five sweets on one axis and number of students on the other.
Choose a scale of one unit per student.
Draw equal-width bars with heights 6, 9, 13, 3 and 7.
A bar graph needs categories, a numerical scale, labelled axes, equal-width bars and heights matching the frequencies.
Question 10(a)
The scores reach 100.
Use marks at intervals of 10 runs so the graph fits clearly.
A scale groups the values into equal steps and should cover the greatest score.
Question 10(b)
Compare the amounts: food ₹3,400, rent ₹3,000, miscellaneous ₹1,200, education ₹800, transport ₹600, electricity ₹400.
Ordering the amounts from greatest to least identifies the top two categories.
Question 10(c)
Half of ₹800 is ₹400.
Electricity costs ₹400.
To test “half”, divide the larger amount by 2 and compare.
Question 10(d)
One-fourth of ₹3,400 is ₹850.
Compare education, ₹800, with ₹850.
Find one-fourth by dividing by four, then compare the education amount.
Question 11(a)
Use one category for each insect type.
Draw bars of heights 6, 10, 5, 3 and 2 in the given order.
Each bar height equals the frequency for that category.
Question 11(b)
Read their values from the data table.
The original table supplies the values even though part of the graph is erased.
Question 11(c)
Divide 24 tickets by 6 units.
The scale is the number of tickets represented by one unit of bar length.
Question 11(d)
Sagar has 16 tickets.
At 4 tickets per unit, calculate 16 ÷ 4.
Convert the count to graph units by dividing by the scale.
Question 11(e)
Compare the bars with their counts using 4 tickets per unit.
Seoni 16 tickets needs 4 units; Indore 28 tickets needs 7 units.
A bar is correct only when its height matches the value and scale.
Question 12(a)
Tally each appearance of each type in the list.
A frequency table groups identical observations and counts each group.
Question 12(b)
Compare the frequencies in the table.
The highest frequency identifies the most common observation.
Question 12(c)
Choose a fixed place and one-hour time period.
Make a category list and tally one vehicle as it passes.
Avoid counting the same vehicle twice.
A defined time, place and counting rule make the observations interpretable and reduce double-counting.
Question 13
Record all 30 outcomes with tally marks.
Count the tally marks for faces 1 to 6.
Compare the six frequencies.
Random outcomes are not fixed in advance; the method gives a correct answer for the results actually observed.
Question 14(a)
Each row pairs a wicket count with the number of matches in which that count occurred.
The first column is the value being counted; the second is its frequency.
Question 14(b)
Name the player and the measured quantity.
Include the 30-match period.
A useful title says what the data describe and the group or period covered.
Question 14(c)
Look for an unusually large wicket count or a very high frequency.
Seven wickets occurred once; three wickets occurred most often, eight times.
A notable feature can be the most frequent row or an unusual extreme.
Question 14(d)
Read the frequency beside 4 wickets.
The frequency column tells how many matches had that wicket count.
Question 14(e)
Those numbers are possible wickets-per-match values, not the observed total.
Each value occurred in a different number of matches.
A frequency table repeats a value according to its frequency. A weighted total must account for those repetitions.
Question 14(f)
Multiply each count by its frequency: 0×2, 1×4, 2×6, 3×8, 4×3, 5×5, 6×1, 7×1.
Add the products: 0 + 4 + 12 + 24 + 12 + 25 + 6 + 7.
For each row, multiply wickets per match by the number of matches. Add these row totals.
Question 15(a)
Compare the number of symbols in the village rows.
The fewest symbols represent the smallest count when the key is the same.
Question 15(b)
Compare the symbol counts.
The most symbols represent the greatest count.
Question 15(c)
Count their symbols using the one-tractor key.
Subtract the Village B count from the Village C count.
A difference is found by subtracting the smaller count from the larger count.
Question 15(d)
Compare the symbol counts: D has half as many symbols as E.
With a common key, halving the number of symbols also halves the quantity.
Question 16(a)
Compare the symbols, remembering that each full symbol is 4 girls.
A common key lets us compare symbol counts directly.
Question 16(b)
Count the difference in symbols, including any half symbol.
Convert that difference using 4 girls per full symbol.
The key converts pictograph symbols into actual students.
Question 16(c)
One full picture represents 4 girls.
Two girls are half of the key value.
A partial symbol represents a fraction of the key value.
Question 16(d)
Count the Class 7 symbols and multiply by 4.
The key says each full symbol represents four girls.
Question 17(a)
The counts 18, 36, 12, 48, 18 and 24 are all multiples of 6.
Let each symbol represent 6 dogs.
A useful key divides every count into a whole number of symbols.
Question 17(b)
Divide 36 dogs by 6 dogs per symbol.
Number of symbols equals quantity divided by the key.
Question 17(c)
B and D: 36 + 48 = 84.
Other villages: 18 + 12 + 18 + 24 = 72.
Compare 84 and 72.
Add the two groups separately and compare their totals.
Question 18(a)
Divide each count by 5.
The values are 45, 30, 20, 10 and 15.
Convert each frequency into graph units by dividing by the scale value.
Question 18(b)
Compare the remaining counts: 30, 20, 10 and 15.
Exclude playing as requested, then select the greatest remaining frequency.
Question 19(a)
Read the Wednesday and Thursday bars.
Add their values: 30 + 40.
The combined amount is the sum of the two daily counts.
Question 19(b)
Add the seven daily values from the graph.
The total is 310.
A weekly total is found by adding each day once.
Question 19(c)
Find the tallest and shortest bars.
The graph shows Saturday highest and Wednesday lowest.
Possible causes such as weather or attendance need separate evidence.
The graph identifies when counts differ, but further data are needed to test a cause.
Question 20
Use the table values for each year.
Draw bars to 1,400; 1,700; 2,200; 3,000 and 3,700 for 2006, 2010, 2014, 2018 and 2022.
A graph must match its data table, use one numerical scale throughout and keep bars aligned to their year labels.
Question Infographic scale check
Double Elbrus’s height: 5,642 × 2 = 11,284 m.
Compare 11,284 m with Everest’s height, 8,848 m.
No. Twice 5,642 m is 11,284 m, greater than Everest’s 8,848 m. The infographic makes Everest look about twice as tall, but the values show that it is not.
Question Mountain height comparison
Everest minus Kosciuszko: 8,848 − 2,228 = 6,620 m.
Denali minus Kilimanjaro: 6,194 − 5,895 = 299 m.
Everest is 6,620 m taller than Kosciuszko. Denali is 299 m taller than Kilimanjaro, so their heights are fairly close.