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Given:

Cumulative frequency distribution of marks:

Below 40 = 50

Below 50 = 125

Below 60 = 210

Below 70 = 315

Below 80 = 350

Formula used:

Number of students in a class = Cumulative frequency of upper limit - Cumulative frequency of lower limit

Calculations:

Students between 60 and 70 = 315 - 210 = 105

∴ The number of students who scored between 60 and 70 marks is 105.

Given:

Cumulative frequency distribution of marks:

Below 40 = 50

Below 50 = 125

Below 60 = 210

Below 70 = 315

Below 80 = 350

Formula used:

Number of students scoring more than a mark = Total students - Cumulative frequency of that mark

Calculations:

Total students = 350 (Below 80)

Students scoring more than 50 = 350 - 125 = 225

∴ The number of students who scored more than 50 marks is 225.

Calculations:

Sum of D = 8 + 12 + 14 + 15 + 16 = 65 (thousands)

Average of D = 65 ÷ 5 = 13 (thousands)

Differences from average:

2019: |8 − 13| = 5

2020: |12 − 13| = 1

2021: |14 − 13| = 1

2022: |15 − 13| = 2

2023: |16 − 13| = 3

∴ The circulation of D was closest to its average (13 thousands) in the years 2020 and 2021 (difference = 1 thousand).

Given:

Circulation figures (in thousands) for newspapers A, B, C, D, E from 2019 to 2022

Formula used:

Average circulation = (A + B + C + D + E) ÷ 5

Calculations:

2019: Total = 20 + 10 + 15 + 8 + 20 = 73

Average = 73 ÷ 5 = 14.6; D = 8 → Difference = 6.6

2020: Total = 12 + 12 + 18 + 12 + 12 = 66

Average = 66 ÷ 5 = 13.2; D = 12 → Difference = 1.2

2021: Total = 24 + 14 + 17 + 14 + 15 = 84

Average = 84 ÷ 5 = 16.8; D = 14 → Difference = 2.8

2022: Total = 26 + 10 + 16 + 15 + 9 = 76

Average = 76 ÷ 5 = 15.2; D = 15 → Difference = 0.2

∴ The circulation of newspaper D was closest to the average in 2022.

Given:

Circulation figures (in thousands) of newspapers A, B, C, D, E for years 2019–2023

Formula used:

Average for individual newspaper = Sum of its circulation ÷ 5

Average of all newspapers for all years = Total circulation of all newspapers ÷ (5 × 5)

Calculations:

Total circulation for each newspaper:

A = 20 + 12 + 24 + 26 + 22 = 104 → Average = 104 ÷ 5 = 20.8

B = 10 + 12 + 14 + 10 + 16 = 62 → Average = 62 ÷ 5 = 12.4

C = 15 + 18 + 17 + 16 + 14 = 80 → Average = 80 ÷ 5 = 16

D = 8 + 12 + 14 + 15 + 16 = 65 → Average = 65 ÷ 5 = 13

E = 20 + 12 + 15 + 9 + 11 = 67 → Average = 67 ÷ 5 = 13.4

Total circulation of all newspapers = 104 + 62 + 80 + 65 + 67 = 378

Average circulation of all newspapers = 378 ÷ 25 = 15.12

Compare individual averages with 15.12:

A = 20.8 > 15.12 ✅

B = 12.4 < 15.12 ❌

C = 16 > 15.12 ✅

D = 13 < 15.12 ❌

E = 13.4 < 15.12 ❌

∴ There are 2 newspapers (A and C) whose average circulation is more than the average of all newspapers.

Given:

From Chart-I: Number of houses = 1,20,000

Angle for Pucca houses = 110°

From Chart-II: Population = 21,00,000

Angle for population living in Pucca houses = 60°

Formula used:

Part of total = (Angle / 360) × Total Value

Average = Total Value / Number of units

Calculations:

Number of Pucca Houses = (110 / 360) × 1,20,000

⇒ Number of Pucca Houses = (11 / 36) × 1,20,000

⇒ Number of Pucca Houses = 11 × (120000 / 36)

⇒ Number of Pucca Houses = 110000 / 3

Population Living in Pucca Houses = (60 / 360) × 21,00,000

⇒ Population Living in Pucca Houses = (1 / 6) × 21,00,000

⇒ Population Living in Pucca Houses = 3,50,000

Average Persons per Pucca House = Population Living in Pucca Houses / Number of Pucca Houses

⇒ Average Persons per Pucca House = 350000 / (110000 / 3)

⇒ Average Persons per Pucca House = (350000 × 3) / 110000

⇒ Average Persons per Pucca House = (35 × 3) / 11

⇒ Average Persons per Pucca House = 105 / 11

⇒ Average Persons per Pucca House ≈ 9.5454...

∴ The correct answer is option 3.

Given:

From Chart-I: Initial total number of houses = 1,20,000

Initial angle for Kutcha houses = 40°

Increase in Kutcha houses = 5000

Formula used:

Number of houses for a category = (Angle for category / 360°) × Total number of houses

Angle for a category = (Number of houses for category / Total number of houses) × 360°

Calculations:

Initial number of Kutcha houses = (40 / 360) × 1,20,000

⇒ Initial number of Kutcha houses = (1 / 9) × 1,20,000

⇒ Initial number of Kutcha houses = 120000 / 9

New total number of houses = Initial total number of houses + 5000

⇒ New total number of houses = 1,20,000 + 5000

⇒ New total number of houses = 1,25,000

New number of Kutcha houses = Initial number of Kutcha houses + 5000

⇒ New number of Kutcha houses = (120000 / 9) + 5000

⇒ New number of Kutcha houses = (120000 + 45000) / 9

⇒ New number of Kutcha houses = 165000 / 9

New angle for Kutcha houses = (New number of Kutcha houses / New total number of houses) × 360°

⇒ New angle for Kutcha houses = ((165000 / 9) / 125000) × 360°

⇒ (165000 / (9 × 125000)) × 360°

⇒ (165 / (9 × 125)) × 360°

⇒ (11 / 75) × 360° = 11 × 4.8 = 52.8°

Change in angle = New angle for Kutcha houses - Initial angle for Kutcha houses

⇒ Change in angle = 52.8° - 40°

⇒ Change in angle = 12.8° ≈ 13° 

∴ The approximate change in angle for Kutcha houses in Pie Chart-I will be 12.8°.

Given:

From Chart-III: Total number of families = 3,60,000

Angle for families in "Houseless" category = 20°

Angle for families "Living in Kutcha houses" = 185°

Number of families from "Houseless" category shifting to Kutcha houses = 300

Formula used:

Number of families for a category = (Angle for category / 360°) × Total number of families

Average families per house = Total families in houses / Total number of houses of that type

Calculations:

Initial Families in Kutcha Houses = (185 / 360) × 3,60,000

⇒ Initial Families in Kutcha Houses = 185 × (3,60,000 / 360) = 1,85,000

Initial Houseless Families = (20 / 360) × 3,60,000

⇒ Initial Houseless Families = 20 × (3,60,000 / 360) = 20,000

New Families in Kutcha Houses = Initial Families in Kutcha Houses + 300

⇒ New Families in Kutcha Houses = 1,85,000 + 300 = 1,85,300

From previous calculations or Chart-I:

Number of Kutcha Houses = (40 / 360) × 1,20,000

⇒ Number of Kutcha Houses = 120000 / 9

Average families per Kutcha house = New Families in Kutcha Houses / Number of Kutcha Houses

⇒ Average families per Kutcha house = 1,85,300 / (120000 / 9)

⇒ Average families per Kutcha house = (1,85,300 × 9) / 120000

⇒ Average families per Kutcha house = 1667700 / 120000

⇒ Average families per Kutcha house = 16677 / 1200

⇒ Average families per Kutcha house ≈ 13.8975 ≈ 13.9

∴ The average number of families in every Kutcha house will be 13.90.

Given:

Total students = 60

Marks range considered = ≥ 60 and < 80

Calculations:

Number of students in the range = 16

Percentage = (16 ÷ 60) × 100

⇒ Percentage = 26.67% ≈ 26.7%

∴ Approximately 26.7% of students scored between 60 and 79 marks.

Given:

Initial arithmetic mean of 100 observations = 50

Misread observations = 82 and 6

Correct observations = 182 and 56

Formula used:

Mean = (Sum of all observations) ÷ (Number of observations)

Calculations:

Initial sum of observations = Mean × Number of observations = 50 × 100 = 5000

Difference in sum due to misread observations = (182 + 56) - (82 + 6) = 238 - 88 = 150

Corrected sum of observations = 5000 + 150 = 5150

Corrected mean = Corrected sum ÷ Number of observations = 5150 ÷ 100 = 51.5

∴ The corrected mean is 51.5