NCERT Solutions: Class 6 Maths Chapter 4 - Data Handling and Presentation

The game occurring the greatest number of times in the organised table is the most popular game.

Counting the list gives Hockey a frequency of $8$, which is greater than the frequency of any other game.

Ask each classmate for one favourite game, make a frequency table, and identify the game with the highest frequency.

Questions a and c ask about a group or locality and need fresh data collection. Questions b and d are fixed factual questions and can be answered without collecting new data.

Read the tally marks in the table. Jalebi has $6$, Barfi has $3$, Gujiya has $13$, Rasgulla has $7$, and Gulab jamun has $9$ students.

The table gives only how many students chose each sweet. It does not tell which student chose which sweet. An alternative is to group or list students according to their sweet preference.

From the ordered data, the smallest value is $3$ and the largest value is $7$. Shoe size $5$ appears $10$ times. Sizes larger than $4$ are the ten $5$s, four $6$s, and one $7$, giving $10+4+1=15$ students.

When equal sizes are placed together, we can count repetitions quickly and use the data without searching through an unordered list.

A frequency table lists each shoe size once and records how many students have that size.

If one symbol represents $10$ students and a half-symbol represents $5$ students, then totals such as $33$ or $27$ require parts representing $3$ or $7$ students, which are not easy to show accurately.

Reading the pictograph, Thursday has the fewest symbols and Saturday has the most. Adding the daily counts gives a total of $24$ books. A possible reason for the maximum on Saturday is that Sunday is a holiday, so students can read the books then.

Since one symbol represents $100$ kites, Rani's $300$ kites require $3$ symbols. Poonam Ben purchased $700$ kites, the maximum. Jasmeet purchased $450$ kites and Chaman purchased $250$, so Jasmeet purchased more. Double Rani's purchase is $2\times300=600$; Poonam Ben purchased $700$, which is more than double.

The bar graph and table show $5$ absent students for Class 2.

Class 8 has the tallest bar, representing $7$ absent students, which is the greatest value.

Full attendance means zero absences. The graph shows $0$ absent students for Class 5.

The hourly values are about $150, 1200, 1000, 800, 700,$ and $600$. Their sum is $150+1200+1000+800+700+600=4450$ cars.

Traffic generally increases when offices, schools and markets begin. The 6-7 a.m. interval is earlier than those peak travel times.

The bar for 7-8 a.m. is the longest. This interval commonly matches morning commute time, so traffic is expected to be high.

The bars become shorter after 8 a.m. This suggests that fewer vehicles pass the crossing once the peak travel period is over.

The expenses are Food $= Rs\ 3400$ and House rent $= Rs\ 3000$. These are the two largest amounts in the table.

Education costs $Rs\ 800$ and electricity costs $Rs\ 400$. Since $400=\frac{1}{2}\times800$, electricity is one-half of education.

Food costs $Rs\ 3400$, so one-fourth is $3400\div4=Rs\ 850$. Education costs $Rs\ 800$, and $800<850$.

Use the insects as categories on one axis and the number seen on the other axis. A convenient scale is $1$ unit length $=1$ insect, giving bar heights $6,10,5,3,$ and $2$.

The table gives Vidisha $24$, Jabalpur $20$, Seoni $16$, Indore $28$, and Sagar $16$. Since Vidisha has $24$ tickets and a bar of $6$ unit lengths, the scale is $24\div6=4$ tickets per unit. Sagar's $16$ tickets need $16\div4=4$ unit lengths, and Indore's $28$ tickets need $28\div4=7$ unit lengths.

Counting each vehicle type in the list gives the frequency table. The largest frequency is Bike with $13$, so it was used the most. For data collection, prepare a two-column table, list each vehicle type as it passes, mark tallies, and convert tallies into frequencies.

Make a table with die faces $1$ to $6$. For each roll, add one tally mark in the corresponding row. Count the tallies to find the least frequent face, the most frequent face, and any faces with equal frequencies.

To get total wickets, multiply each wicket count by the number of matches: $0\times2+1\times4+2\times6+3\times8+4\times3+5\times5+6\times1+7\times1=0+4+12+24+12+25+6+7=90$. Adding only $0+1+2+\cdots+7$ ignores how many matches had each wicket count.

Read the pictograph with one symbol representing one tractor. Village C has the largest count, Village D the smallest count, and Village C has $3$ more tractors than Village B. Village D's count is half of Village E's count.

The key is one full symbol $=4$ girls. Reading the pictograph, Class 8 has the least number of girls. The difference between Classes 5 and 6 is $6$. Adding $2$ girls to Class 2 converts its half-symbol into a full symbol. Class 7 has $12$ girls.

All the numbers are multiples of $6$, so one symbol can represent $6$ dogs. Village B has $36$ dogs, so it needs $36\div6=6$ symbols. Villages B and D together have $36+48=84$ dogs. The other four villages have $18+12+18+24=72$ dogs. Since $84>72$, Kamini is right.

With scale $1$ unit length $=5$ students, the bar heights are Playing $45\div5=9$, Reading story books $30\div5=6$, Watching TV $20\div5=4$, Listening to music $10\div5=2$, and Painting $15\div5=3$ units. Excluding Playing, Reading story books has the greatest count.

Reading the bar graph gives Wednesday plus Thursday as $70$ saplings and the whole-week total as $310$ saplings. The tallest bar is Saturday and the shortest bar is Wednesday. Possible reasons include rainy weather or different numbers of students being present on different days; these can be checked by comparing with attendance and weather records.

The table lists 2006: $1400$, 2010: $1700$, 2014: $2200$, 2018: $3000$, and 2022: $3700$. The bars should be redrawn to these values on the given scale.

Heights are measured upward from the ground, so vertical bars make the comparison of heights intuitive. A horizontal bar graph could also be used, but vertical bars are more natural for height data.

River length is a horizontal feature, so horizontal bars make it easy to compare lengths visually. The exact table depends on the river-length data collected for each continent.