4. Data Handling and Presentation

Make a table with the names of the games. Put a tally mark for each student’s choice. Then count the tally marks for each game.

The most popular game is Hockey (8 students).

Ask each classmate their favourite game. Record the answers with tally marks in a table. The game with the most tally marks is the most popular.

(a) Most popular TV show among her classmates — ✓

(b) When did India get independence? — ✗ (it is a known fact)

(c) How much water is wasted in her locality? — ✓

(d) What is the capital of India? — ✗ (it is a known fact)

(a) Jalebi: 6 students   (b) Barfi: 3 students   (c) Gujiya: 13 students   (d) Rasgulla: 7 students   (e) Gulab jamun: 9 students

No. The table tells only how many students chose each sweet. It does not tell which student chose which sweet.

Alternative: Write the name of each student along with the sweet they chose.

(a) The largest shoe size in the class is 7

(b) The smallest shoe size in the class is 3

(c) There are 10 students who wear shoe size 5.

(d) There are 15 students who wear shoe sizes larger than 4 (10 + 4 + 1).

The smallest size comes first and the largest comes last. The same sizes come together, so they are easy to count.

Yes. We can arrange the data in descending order, or make a frequency table with tally marks.

Make a table of tree names and their numbers using tally marks. The tree with the largest number is found the most. Answers will differ for each student.

In English words, the letter ‘e’ is used the most and ‘x’ is used very rarely. So in any news item, the order of frequency is almost the same: x, c, r, i, e.

Process: Read the news item word by word. Put a tally mark in the table each time one of these letters appears. Count the tally marks.

Most students: School bus (11 students).

Least students: Cycle (3 students).

They would need to draw 30 or 35 symbols in a row. This takes a lot of time and space.

One symbol is 10 students and half a symbol is 5 students. It is not possible to show 3 or 7 students correctly with these symbols.

Monday 5, Tuesday 4, Wednesday 2, Thursday 0, Friday 5, Saturday 8

(a) Minimum books were borrowed on Thursday (none).

(b) Total books borrowed = 5 + 4 + 2 + 0 + 5 + 8 = 24

(c) Maximum books were borrowed on Saturday. Reason: Sunday is a holiday, so students borrow books to read at home.

(a) Rani: 3 symbols

(b) Poonam Ben purchased the maximum number of kites.

(c) Jasmeet purchased more kites than Chaman (450 > 250).

(d) Yes, Rukhsana is correct. Double of Rani’s kites = 2 × 300 = 600. Poonam Ben purchased 700, which is more than 600.

1. In Class 2, 5 students were absent that day.

2. The maximum number of students were absent in Class 8 (7 students).

3. Class 5 had full attendance that day.

150 + 1200 + 1000 + 800 + 700 + 600 = 4450 vehicles

It is very early in the morning. Most people have not yet left home for school, office or work.

This is the time when most students go to school and many people leave for their offices and work.

Most people had already reached school or office. Fewer people travel in the late morning.

Increase over 50 years = 102 − 36 = 66 crores

Each decade: 1951–61: 8 crores; 1961–71: 10 crores; 1971–81: 14 crores; 1981–91: 16 crores; 1991–2001: 18 crores.

1. Most on food (₹3400) and second most on house rent (₹3000).

2. Yes. Electricity ₹400 is half of education ₹800.

3. Yes. One-fourth of ₹3400 is ₹850. Education (₹800) is less than ₹850.

(a) Vidisha: 24

(b) Jabalpur: 20

(c) 6 units = 24 tickets, so 1 unit = 24 ÷ 6 = 4. Scale: 1 unit length = 4 tickets

(d) Sagar: 16 ÷ 4 = 4 units. Draw a bar of 4 unit lengths.

(e) Mark the vertical axis as 0, 4, 8, 12, 16, 20, 24, 28.

(f) The bar for Seoni (4 units = 16) is correct. The bar for Indore is wrong. It should be 28 ÷ 4 = 7 units tall.

(b) The bike was used the most (13 times).

(c) Steps:

1. Make a table with two columns: means of transport and tally marks.
2. Stand near the road from 9 a.m. to 10 a.m.
3. Put a tally mark against each vehicle as it passes.
4. At 10 a.m., count the tally marks for each vehicle.

This is an activity. Write 1 to 6 in a column. Put a tally mark for each roll. Count the tally marks to find the number that appeared the minimum times, the maximum times, and the numbers that appeared an equal number of times. Results will differ for each student.

(a) It tells in how many matches Bumrah took 0, 1, 2, … 7 wickets.

(b) Title: “Wickets taken by Jaspreet Bumrah in his last 30 matches”.

(c) He took 3 wickets in the most matches (8 matches). He took 7 wickets in only 1 match.

(d) Bumrah took 4 wickets in 3 matches.

(e) No. Adding 0 + 1 + 2 + … + 7 ignores the number of matches. For example, he took 3 wickets in 8 matches, which is 24 wickets, not 3.

(f) Multiply wickets by the number of matches and add:

0 × 2 + 1 × 4 + 2 × 6 + 3 × 8 + 4 × 3 + 5 × 5 + 6 × 1 + 7 × 1

= 0 + 4 + 12 + 24 + 12 + 25 + 6 + 7 = 90 wickets

Village A 6, Village B 5, Village C 8, Village D 3, Village E 6

(a) Village D has the smallest number of tractors.

(b) Village C has the most tractors.

(c) Village C has 8 − 5 = 3 more tractors than Village B.

(d) Yes, Komal is right. Village D has 3 and Village E has 6. 3 is half of 6.

(a) Class 8 has the least number of girls (1½ symbols = 6 girls).

(b) Class 5 = 2½ symbols = 10 girls; Class 6 = 4 symbols = 16 girls. Difference = 16 − 10 = 6.

(c) Class 2 has 4½ symbols = 18 girls. With 2 more girls, it will be 20 girls. The half symbol will become a full symbol (5 full symbols).

(d) Class 7 has 3 symbols = 3 × 4 = 12 girls.

(a) A useful key is 1 symbol = 6 dogs, because all the numbers are multiples of 6.

(b) Village B: 36 ÷ 6 = 6 symbols.

(c) Yes, Kamini is right. B + D = 36 + 48 = 84. Other villages = 18 + 12 + 18 + 24 = 72. 84 is more than 72.

Other than playing, reading story books is preferred by most students.

Monday 52 (about), Tuesday 40, Wednesday 30, Thursday 40, Friday 50, Saturday 60, Sunday 40

(a) Wednesday + Thursday = 30 + 40 = 70

(b) Whole week = 52 + 40 + 30 + 40 + 50 + 60 + 40 = 312 (about)

(c) The greatest number were planted on Saturday and the least on Wednesday.

Possible reasons: more students may be free on Saturday, or it may have rained on Wednesday. We can check by asking the teachers or looking at attendance and weather records.

The bar for 2022 (3700) is correct. The other bars are wrong:

• 2006: the bar shows about 800. It should be 1400.
• 2010: the bar shows about 1500. It should be 1700.
• 2014: the bar shows about 2900. It should be 2200.
• 2018: the bar shows about 2200. It should be 3000.

Redraw the bars for 2006, 2010, 2014 and 2018 to the correct lengths.

8848 m − 2228 m = 6620 m

Denali (6194 m) and Kilimanjaro (5895 m) differ by only 299 m. They are not very different.

5642 × 2 = 11,284. Everest is only 8848 m. So Everest is not twice as tall as Elbrus. The picture is misleading.

Vertical bars. Height is measured upwards from the ground, so vertical bars look like standing persons and are easy to compare.

Horizontal bars. A river flows along the ground, so its length is best shown by a horizontal bar.

Africa (Nile) and South America (Amazon) have the longest rivers.