Complete step-by-step solutions for DAV Class 7 Secondary Mathematics Chapter 12: Data Handling (Brain Teasers, HOTS & Value Based Questions). Includes detailed calculations for Mean, Median, Mode, Range, frequency distributions, bar graphs, Higher Order Thinking Skills (HOTS), and Value-Based Questions (VBQs) aligned strictly with the DAV Education Board curriculum.
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Q.1. (A) Tick (✓) the correct option
(i) If the mean of 7, 4, x, and 10 is 8, the value of x is:
- (a) 13
- (b) 11
- (c) 12
- (d) 9
Mean = (Sum of observations) ÷ (Number of observations)
8 = (7 + 4 + x + 10)/4
8 = (21 + x)/4
⇒ 21 + x = 8 × 4 = 32
⇒ x = 32 − 21 = 11.
Correct Option: (b) 11
(ii) The observation that occurs maximum number of times in a data set is called:
- (a) Range
- (b) Median
- (c) Mode
- (d) Mean
Correct Option: (c) Mode
(iii) The heights (in cm) of 6 students in a class are 145, 152, 148, 150, 153, 146. The median height is:
- (a) 149 cm
- (b) 151 cm
- (c) 148 cm
- (d) 150 cm
1. Arrange data in ascending order: 145, 146, 148, 150, 152, 153.
2. Total observations n = 6 (even).
3. Median = Average of 3rd and 4th terms:
= (148 + 150)/2 = 298/2 = 149 cm.
Correct Option: (a) 149 cm
(iv) The difference between the highest and lowest observations in a data set is known as:
- (a) Frequency
- (b) Mean
- (c) Range
- (d) Class mark
Correct Option: (c) Range
(v) The mean of the first 5 natural numbers is:
- (a) 2.5
- (b) 3
- (c) 3.5
- (d) 5
First 5 natural numbers: 1, 2, 3, 4, 5.
Mean = (1 + 2 + 3 + 4 + 5)/5 = 15/5 = 3.
Correct Option: (b) 3
Q.1. (B) Short Answer Questions
(a) Find the mode of the following numbers: 12, 14, 12, 16, 15, 13, 14, 18, 14.
• 12 occurs 2 times.
• 13 occurs 1 time.
• 14 occurs 3 times.
• 15 occurs 1 time; 16 occurs 1 time; 18 occurs 1 time.
Since 14 has the highest frequency (3 times), Mode = 14.
Ans: 14
(b) If the mean of 5 observations is 20, what is the sum of these observations?
Ans: 100
(c) State the formula for finding the median when the number of observations (n) is odd.
Ans: Median = Value of the (n + 1)/2th observation when data is arranged in ascending or descending order.
(d) What is the range of the numbers: 23, 35, 12, 40, 56, 18, 29?
Range = 56 − 12 = 44.
Ans: 44
Q.2. Marks scored by 10 students in a mathematics test out of 50 are: 28, 35, 40, 35, 42, 38, 35, 45, 40, 32. Find the Mean, Median, and Mode
Sum = 28 + 35 + 40 + 35 + 42 + 38 + 35 + 45 + 40 + 32 = 370.
Total count = 10.
Mean = 370/10 = 37.
2. Calculation of Median:
Arranging marks in ascending order:
28, 32, 35, 35, 35, 38, 40, 40, 42, 45.
Since n = 10 (even), median is the average of 5th and 6th terms:
• 5th term = 35
• 6th term = 38
Median = (35 + 38)/2 = 73/2 = 36.5.
3. Calculation of Mode:
The mark 35 appears 3 times (highest frequency).
Mode = 35.
Ans: Mean = 37 | Median = 36.5 | Mode = 35
🔥 Higher Order Thinking Skills (HOTS)
HOTS Q1: The mean weight of a group of 20 students is 45 kg. If the weight of their teacher is included, the mean weight increases by 1 kg. Find the weight of the teacher.
Sumstudents = 20 × 45 = 900 kg.
Step 2: Total weight with teacher included (21 persons):
New Mean = 45 + 1 = 46 kg.
Total count = 21.
Sumtotal = 21 × 46 = 966 kg.
Step 3: Find teacher’s weight:
Weight of Teacher = 966 − 900 = 66 kg.
Ans: 66 kg
HOTS Q2: The mean of 10 observations is 25. If each observation is increased by 5, what will be the new mean? Prove mathematically.
When each of the 10 observations is increased by 5, total increase = 10 × 5 = 50.
New Sum = 250 + 50 = 300.
New Mean = 300/10 = 30.
Property Proved: If a constant ‘k’ is added to every observation, the mean also increases by ‘k’ (25 + 5 = 30).
Ans: 30
🌱 Value Based Questions (VBQ)
VBQ: A school environment club conducts a survey on water consumption in 5 residential blocks. The daily water wastage recorded (in litres) is: 120, 150, 100, 180, 200.
(a) Find the average (mean) daily water wastage across the blocks.
Mean = (120 + 150 + 100 + 180 + 200)/5 = 750/5 = 150 litres.(b) What value do students promote by highlighting this statistical data?
Core Values Depicted: Resource conservation, water preservation, ecological civic duty, and evidence-based awareness to stop resource wastage.Ans: (a) 150 litres | (b) Conservation of Water & Social Awareness
📚 DAV Class 7 Maths Chapter 12: Data Handling – Complete Solutions Index
| Worksheet / Section | Core Statistical Measures | Solution Link |
|---|---|---|
| Worksheet 1 | Arithmetic Mean & Range Calculations | View Worksheet 1 → |
| Worksheet 2 | Median of Odd & Even Data Sets | View Worksheet 2 → |
| Worksheet 3 | Mode of Raw & Frequency Data | View Worksheet 3 → |
| Worksheet 4 | Bar Graphs, Double Bar Graphs & Scales | View Worksheet 4 → |
| Brain Teasers, HOTS & VBQs | Comprehensive Review, Weight Changes & Proofs | Current Page |