FUZY MATH ACADEMY

Class 9 Maths Chapter 12 Statistics – Exercise 12.4 NCERT Solutions Introduction Exercise 12.4 focuses on median of grouped data. Students learn how to calculate the median using the median formula for frequency distributions. This exercise is important for understanding the central tendency of data and interpreting real‑life datasets. Key Formula For grouped data, median is calculated using: Median = l + ( n 2 − C f ) ⋅ h Where: l = lower limit of median class n = total frequency ( ∑ f i ) C = cumulative frequency before median class f = frequency of median class h = class size Common Mistakes Forgetting to calculate cumulative frequencies. Not identifying the correct median class. Arithmetic errors in numerator and denominator. Confusing median with mean or mode. NCERT Questions with Step‑by‑Step Solutions (10) Q1. Find median of data: Class intervals 0–10, 10–20, 20–30, 30–40; frequencies 5, 7, 10, 8. Total frequency n = 30 . Median class = 20–30 (since cumulative frequency ...

Class 9 Maths Chapter 12 Statistics – Exercise 12.3 NCERT Solutions Introduction Exercise 12.3 focuses on mode of grouped data. Students learn how to calculate the mode using the mode formula for frequency distributions. This exercise is essential for understanding the most frequent value in a dataset and applying it to real‑life problems. Key Formula For grouped data, mode is calculated using: Mode = l + ( f 1 − f 0 2 f 1 − f 0 − f 2 ) ⋅ h Where: l = lower limit of modal class h = class size f 1 = frequency of modal class f 0 = frequency of class before modal class f 2 = frequency of class after modal class Common Mistakes Not identifying the correct modal class (highest frequency). Forgetting to use class size h . Arithmetic errors in numerator and denominator. Confusing mode with mean or median. NCERT Questions with Step‑by‑Step Solutions (10) Q1. Find mode of data: Class intervals 0–10, 10–20, 20–30, 30–40; frequencies 5, 7, 10, 8. Modal class = 20–30, l = 20 , h = 10 , f ...

Class 9 Maths Chapter 12 Statistics – Exercise 12.2 NCERT Solutions Introduction Exercise 12.2 focuses on mean of grouped data using the direct method, assumed mean method, and step‑deviation method. Students learn how to calculate averages from frequency distributions and apply these techniques to real‑life data sets. This exercise builds analytical skills and prepares students for advanced statistics. Key Formulas Direct Method: x ˉ = ∑ f i x i ∑ f i where f i = frequency, x i = mid‑point of class interval. Assumed Mean Method: x ˉ = A + ∑ f i d i ∑ f i where d i = x i − A , A = assumed mean. Step‑Deviation Method: x ˉ = A + ∑ f i u i ∑ f i ⋅ h where u i = x i − A h , h = class size. Common Mistakes Forgetting to calculate mid‑points correctly. Mixing up direct and assumed mean methods. Arithmetic errors in summation of frequencies. Not multiplying frequency with mid‑point. NCERT Questions with Step‑by‑Step Solutions (10) Q1. Find mean of marks obtained by 10 students: 10, 20, 30...

Class 9 Maths Chapter 12 Statistics – Exercise 12.1 NCERT Solutions Introduction Exercise 12.1 introduces basic statistical concepts such as mean, median, and mode of ungrouped data. Students learn how to calculate measures of central tendency and interpret them in real‑life contexts. This exercise builds the foundation for data handling and probability. Key Concepts Mean (Average): Mean = Sum of observations Number of observations Median: Arrange data in ascending order. If n is odd: median = middle value. If n is even: median = average of two middle values. Mode: The observation occurring most frequently. Common Mistakes Forgetting to arrange data before finding median. Confusing mean with median. Ignoring frequency of values when finding mode. Arithmetic errors in calculating averages. NCERT Questions with Step‑by‑Step Solutions (10) Q1. Find mean of 5, 10, 15, 20, 25. Mean = 5 + 10 + 15 + 20 + 25 5 = 75 5 = 15 Q2. Find mean of 7, 14, 21, 28, 35. Mean = 7 + 1...

Class 9 Maths Chapter 11 Surface Areas and Volumes – Exercise 11.8 NCERT Solutions Introduction Exercise 11.8 focuses on problems involving conversion of one solid shape into another. Students learn how to apply the principle of conservation of volume when solids are melted and recast into different shapes such as spheres, cones, or cylinders. This exercise is highly practical and connects geometry with real‑life applications. Key Concept Volume Conservation Principle: When a solid is melted and recast, its volume remains unchanged. V original = V new Common Mistakes Forgetting to cube the radius in volume formulas. Using diameter instead of radius. Confusing surface area with volume. Not converting units consistently (cm 3 , m 3 , litres). NCERT Questions with Step‑by‑Step Solutions (10) Q1. A metallic sphere of radius 4.2 cm is melted and recast into smaller spheres of radius 2.1 cm. Find number of spheres formed. Number = ( 4.2 ) 3 ( 2.1 ) 3 = 74.088 9.261 = 8 Q2. A solid sphere o...

Class 9 Maths Chapter 11 Surface Areas and Volumes – Exercise 11.7 NCERT Solutions Introduction Exercise 11.7 focuses on conversion of solids from one shape to another. Students learn how to calculate the volume of a solid when it is melted and recast into a different shape, such as spheres, cones, or cylinders. This exercise is important for applying the principle of conservation of volume in practical problems. Key Concept Volume Conservation: When a solid is melted and recast, its volume remains constant. V 1 = V 2 where V 1 = volume of original solid, V 2 = volume of new solid. Common Mistakes Forgetting that volume remains constant during melting and recasting. Using diameter instead of radius in formulas. Confusing surface area with volume. Not converting units properly. NCERT Questions with Step‑by‑Step Solutions (10) Q1. A metallic sphere of radius 4.2 cm is melted and recast into smaller spheres of radius 2.1 cm. Find number of spheres formed. Number = ( 4.2 ) 3 ( 2.1 ) 3...

Class 9 Maths Chapter 11 Surface Areas and Volumes – Exercise 11.6 NCERT Solutions Introduction Exercise 11.6 focuses on surface areas and volumes of combinations of solids. Students learn how to calculate the surface area and volume of objects formed by combining two or more basic solids such as cylinders, cones, hemispheres, and spheres. This exercise is important for solving real‑life mensuration problems. Key Concepts Combination of Solids: Add volumes of individual solids to get total volume. Add curved surface areas and bases as required to get total surface area. Common Combinations: Cylinder + Hemisphere (e.g., water tanks). Cone + Hemisphere (e.g., ice‑cream cones). Cylinder + Cone (e.g., tent structures). Common Mistakes Forgetting to exclude hidden surfaces when calculating TSA. Using diameter instead of radius. Confusing CSA with TSA. Not converting units consistently. NCERT Questions with Step‑by‑Step Solutions (10) Q1. A toy is in the form of a hemisphere surmounted by a ...