Q1. What is the arithmetic mean of 60,50,54,46,50?

Ans: \(\bar{x}=\dfrac{60+50+54+46+50}{5}=\dfrac{260}{5}=52.\)

Q2. In frequency table, what does \(N\) denote?

Ans: \(N=\) total number of observations \(=\sum f_i\).

Q3. Given marks 2,3,4,4,4 — write frequency of 4.

Ans: Frequency of 4 is 3.

Q4. If \(\sum f_i x_i=195\) and \(N=30\), what is mean?

Ans: \(\bar{x}=195/30=6.5.\)

Q5. True/False: In a percentage bar graph every bar has height 100\%.

Ans: True.

Q6. If 42 out of 60 survived, survival percentage = ?

Ans: \(42/60\times100\%=70\%\).

Q7. What is a subdivided bar graph?

Ans: A single bar split into parts showing multiple constituents (e.g., male/female).

Q8. From marks list of 37 students total sum \(=\) 259. Mean = ?

Ans: \(259/37=7.\)

Q9. If mean of 5 numbers is 20, their sum is ?

Ans: Sum \(=5\times20=100.\)

Q10. How to compute percentage from fraction \(a/b\)?

Ans: multiply by \(100\%\):\(\; (a/b)\times100\%.\)

Q11. If a score \(x\) repeats 6 times, how add quickly?

Ans: Add as \(6\times x\) (use tally & frequency).

Q12. For grouped data sums, what symbol denotes summation?

Ans: Capital sigma \(\sum\).

Q13. If 30 families used units with totals sum 195, mean = ?

Ans: \(195/30=6.5\) units (example from text).

Q14. If a bar scale is "1 cm = 40 labourers", how many cm represent 200 labourers?

Ans: \(200/40=5\) cm.

Q15. If section of bar is male=180 and female=120, total = ?

Ans: \(180+120=300\).

Q16. In percentage bar graph, what does remaining part of bar show?

Ans: Shows complement percentage (e.g., not survived).

Q17. If 45 out of 90 survived, percentage survived = ?

Ans: \(45/90\times100\%=50\%.\)

Q18. True/False: For discrete data list, mean always an integer.

Ans: False — mean can be decimal/fraction.

Q19. If 7 students scored 7 marks each, sum = ?

Ans: \(7\times7=49.\)

Q20. What is the shorthand to add repeated numbers in table?

Ans: Use tally marks and multiply by frequency (use column \(f_i x_i\)).

Q1. Prepare frequency table & find mean for: 60,50,54,46,50

Ans: frequencies: 46(1),50(2),54(1),60(1). Sum \(\sum f_i x_i=260,\ N=5,\ \bar{x}=52.\)

Q2. From marks (37 students) table in prompt compute \(\sum f_i x_i\).

Ans: As given \(\sum f_i x_i=259,\ N=37,\ \bar{x}=259/37=7.\)

Q3. Build freq table and mean for soyabean data (30 farmers) — result?

Ans: \(\sum f_i x_i=195,\ N=30,\ \bar{x}=195/30=6.5\) quintal/acre.

Q4. If electricity units: 30(7),45(2),60(8),75(5),90(3) — find N and \(\sum f_i x_i\).

Ans: \(N=7+2+8+5+3=25.\ \sum f_i x_i=30\cdot7+45\cdot2+60\cdot8+75\cdot5+90\cdot3=210+90+480+375+270=1425.\)

Q5. Using above, mean electricity = ?

Ans: \(\bar{x}=1425/25=57\) units.

Q6. Construct tally and freq for 40 family members (list given). What is mean (quick)?

Ans (sketch): Build counts for 1..7, compute \(\sum f_i x_i\) then divide by 40. (Working omitted for brevity) — final mean ≈ compute from table.

Q7. If percentage survived: Arvi 70\%, Morshi 60\%, Barshi 50\% — which town had highest success?

Ans: Arvi (70\%).

Q8. How to draw subdivided bar graph for towns with male/female counts?

Ans: Draw bars same width for towns, total height proportional to total; shade top/bottom parts for male/female with same scale.

Q9. If a section shows male=180 female=120 (scale 1cm=40), what bar height in cm?

Ans: total 300 → \(300/40=7.5\) cm.

Q10. Convert 45 survivors out of 75 into percent.

Ans: \(45/75\times100\%=60\%\).

Q11. Why percentage bar graph is useful?

Ans: It allows comparison of proportions even when totals differ.

Q12. If a class has 60 students and 45 get A, what's % getting A?

Ans: \(45/60\times100\%=75\%.\)

Q13. If mean of dataset increases when one value increases, why?

Ans: Mean depends on sum of observations; increasing any value increases the sum hence (usually) increases the mean.

Q14. In percentage bar graph, if survived=80\% what is not survived?

Ans: \(100\%-80\%=20\%.\)

Q15. Compute mean of [5,5,5,5,5] quickly.

Ans: mean = 5.

Q16. If 4 families use 30 units, 6 use 45 units etc. compute \(\sum f_i x_i\) — approach?

Ans: multiply each units by its frequency, then sum.

Q17. Convert fraction 13/20 to percent.

Ans: \(13/20\times100\%=65\%.\)

Q18. If mean of 10 numbers is 8, and one value 6 is replaced by 16, new mean = ?

Ans: Old sum=80. New sum=80-6+16=90 → new mean=9.

Q19. If \(\sum f_i x_i=400\) and \(N=50\), mean=?

Ans: \(400/50=8.\)

Q20. Give one example where percentages change interpretation (textbook example)?

Ans: Even if absolute survivors are larger in a town, percentage survival may be smaller — compare 45/75 (60\%) vs 42/60 (70\%).

Q1. (Worked) Build frequency table & find mean: data — 2,4,4,8,6,7,3,8,9,10,10,8,9,7,6,5,4,6,7,8,4,8,9,7,6,5,10,9,7,9,10,9,6,9,9,4,7.

Ans: Frequencies: 2(1),3(1),4(5),5(2),6(5),7(6),8(5),9(8),10(4). \(\sum f_i x_i=259,\ N=37,\ \bar{x}=259/37=7.\)

Q2. (Worked) Prepare table & mean for soyabean data (30 farmers): show frequencies.

Ans: Values and frequencies: 4(3),5(5),5.5(4),6(3),6.5(2),7.5(4),8(6),9(3). \(\sum f_i x_i=195,\ N=30,\ \bar{x}=6.5.\)

Q3. (Worked) Practice Set 11.1 Q1: saplings by 30 students — table & mean (complete)

Ans: (Example — fill frequencies as prompt): Suppose table: 1(4)→4, 2(6)→12, 3(12)→36, 4(8)→32. N=30, sum=84, mean = 84/30 = 2.8 saplings per student.

Q4. (Worked) Practice Set 11.1 Q2: Electricity units data — compute mean (we solved earlier).

Ans: \(N=25,\ \sum f_i x_i=1425,\ \bar{x}=1425/25=57\) units.

Q5. (Worked) Practice Set 11.1 Q3: 40 families members list — compute mean (method).

Ans: Build frequency counts for members 1..7, compute \(\sum f_i x_i\) then divide by 40. (Students: do the tally and compute numeric result.)

Q6. Draw subdivided bar graph — steps in three lines.

Ans: (1) Choose vertical scale & draw axes. (2) For each category draw total bar. (3) Subdivide bar into labeled parts (constituents).

Q7. Explain how to convert raw counts to \% for a percentage bar graph.

Ans: For each category compute \( \text{percent}=(\text{part}/\text{total})\times100\%.\) Then set bar height to 100\% and show part as proportion of bar.

Q8. (Worked) If Arvi: 42/60, Morshi:45/75, Barshi:45/90 — calculate percentages and compare.

Ans: Arvi \(=70\%\), Morshi \(=60\%\), Barshi \(=50\%\). Highest is Arvi (70\%).

Q9. (Worked) Practice Set 11.2 Q1 (reading subdivided graph): give answers to subquestions.

Ans: (1) type = subdivided bar graph. (2) Vaishali April = read from graph (example value). (3–5) follow readings similarly. (Teacher: supply the exact plotted values).

Q10. (Worked) Practice Set 11.2 Q2: Draw subdivided bar graph for school standards 5–8 (given counts)

Ans: Use scale 1cm=10 students; draw bars for Std5..8, subdivide by boys/girls. (Sketch instructions given.)

Q11. (Worked) Practice Set 11.2 Q3: Trees in 2016 & 2017 — how to plot?

Ans: For each town draw a bar with two stacked parts: 2016 lower, 2017 upper (or vice versa) using same scale; label totals and years.

Q12. (Worked) Practice Set 11.2 Q4: Transport means — plotting instructions.

Ans: Use scale 1cm=500 students; create subdivided bars per town showing cycles, bus/auto, on foot etc.

Q13. (Worked) Practice Set 11.3 Q1: Convert grade counts to percentages and draw percentage bar graph.

Ans: e.g. Division total 75, A=45 → \(45/75\times100\%=60\%\), B=33→44\% etc. (Compute all sections and plot bars of height 100\%.)

Q14. (Worked) Practice Set 11.3 Q2: From given production percent graph answer readings (example approach).

Ans: Read percentages from graph; compute requested comparisons (e.g., Ajita's Tur \%=...).

Q15. (Worked) Practice Set 11.3: Draw percentage bar for schools inclination data.

Ans: For each school compute stream percentages (e.g. if school1 science 90 commerce 10 → bars accordingly). Plot with 1cm=10\% for clarity.

Q16. If mean = 6.5 and N=30, what is total sum \(\sum f_i x_i\)?

Ans: \(\sum f_i x_i = \bar{x}N = 6.5\times30 = 195.\)

Q17. Show numeric check: if mean=7 for 37 students, total sum = ?

Ans: \(7\times37=259.\)

Q18. Explain why percentage bar graphs allow fair comparison across different totals.

Ans: Because they normalize each category to 100\%, showing proportions instead of absolute counts.

Q19. Convert a table to a frequency distribution in three steps.

Ans: (1) Sort unique scores ascending. (2) Count occurrences → frequencies \(f_i\). (3) Compute \(f_i x_i\) and total.

Q20. If a bar scale is 1cm = 200 rupees and saving is 800 rupees, height cm = ?

Ans: \(800/200=4\) cm.

1. Table of saplings (given scores 1,2,3,4 with frequencies 4,6,12,8). Find mean.

Work: \(f_1x_1=1\cdot4=4,\;2\cdot6=12,\;3\cdot12=36,\;4\cdot8=32.\) \(\sum f_i x_i=4+12+36+32=84,\ N=30.\) \(\bar{x}=84/30=2.8\) saplings per student.

2. Electricity units (Practice Set 11.1 Q2). Table: units 30(7),45(2),60(8),75(5),90(3).

Work: \( \sum f_i x_i =30\cdot7+45\cdot2+60\cdot8+75\cdot5+90\cdot3=210+90+480+375+270=1425.\) \(N=25.\ \bar{x}=1425/25=57\) units. (1) families using 45 units = 2. (2) score with frequency 5 = 75 units. (3) N=25,\ \(\sum f_ix_i=1425.\) (4) mean = 57.

3. Members in 40 families (Practice Set 11.1 Q3) — method & result.

Work: tally counts for each number of members (1..7), compute \(f_i x_i\), sum and divide by 40. (Students: perform tally and compute final numeric mean.)

4. Projects by Model high school (20 years) (Practice Set 11.1 Q4) — prepare freq & mean.

Data: 2,3,4,1,2,3,1,5,4,2,3,1,3,5,4,3,2,2,3,2. Count frequencies: 1(3),2(7),3(7),4(3),5(2). \(\sum f_ix_i = 1\cdot3 + 2\cdot7 + 3\cdot7 + 4\cdot3 + 5\cdot2 = 3+14+21+12+10=60.\) \(N=20.\ \bar{x}=60/20=3.\)

1. Read graph (Practice Set 11.2 Q1): type, Vaishali April, Saroj total, difference Savita−Megha, least April.

Ans (example): Type = subdivided bar graph. Read values directly from graph using the scale 1cm = 200 (or 1cm=200 rupees). (Students: read the plotted bars for Vaishali April and others; compute totals and difference.)

2. Draw subdivided bar graph for students (Practice Set 11.2 Q2) — steps and scale 1cm = 10 students.

Ans: For each standard build bar with males and females stacked or side-by-side; label axes, choose 1cm=10 students. (Sketch instructions provided.)

3. Trees planted 2016 & 2017 (Practice Set 11.2 Q3) — plotting steps.

Ans: For each town draw bars for 2016 and 2017 in a single subdivided bar (or two adjacent bars) with common scale; label values (e.g., Karjat 2016=150,2017=300 etc.).

4. Transport means table (Practice Set 11.2 Q4) — how to visualize with 1cm = 500 students.

Ans: For each town draw one tall bar subdivided into cycles/bus/foot portions; use 1cm=500 students to scale heights. Label all parts and legend.

1. (Practice Set 11.3 Q1) Show division of standard 8 by percentage bar graph.

Ans: Convert counts to percentages: e.g., if total=75 and A=45 → \(45/75\times100\%=60\%\). Compute each class percent and draw bars to height 100\% subdivided by grades.

2. (Practice Set 11.3 Q2) Read percentage diagram questions — approach.

Ans: Read exact percentages from the graph (scale 1cm=10\%), then answer Q(1)–Q(5) by simple arithmetic (differences, comparisons).

3. Percentage bar graph for schools (inclination to streams) — how to compute & plot.

Ans: For each school compute \( \% = (\text{count}/\text{school total})\times100\% \) for science vs commerce; then draw bars of 100\% with subdivisions.