Data And Their Representations
NIOS · Class 10 · Maths
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Explore the full setFind the range of this data set: 23, 45, 12, 67, 89, 34, 56, 78, 21, 90
Answer
Step 1: Arrange in order: 12, 21, 23, 34, 45, 56, 67, 78, 89, 90. Step 2: Range = Maximum - Minimum = 90 - 12 = 78. Answer: Range = 78…
Create a frequency table for: 2, 3, 2, 4, 3, 2, 5, 3, 2, 4, 3, 2
Answer
Step 1: Count each value. Step 2: Create table: Value | Frequency 2 | 5 3 | 4 4 | 2 5 | 1 Total | 12 This shows value 2 appears most frequently (5 times).
For classes 10-20, 20-30, 30-40, find the class marks.
Answer
Formula: Class mark = (Lower limit + Upper limit) ÷ 2 Step 1: For 10-20: (10 + 20) ÷ 2 = 15 Step 2: For 20-30: (20 + 30) ÷ 2 = 25 Step 3: For 30-40: (30 + 40) ÷ 2 = 35 Answer: Class marks are 15, 25…
Create grouped frequency table for marks: 45, 67, 23, 78, 89, 34, 56, 67, 45, 78, 23, 89, 56, 67. Use class intervals of size 20.
Answer
Step 1: Range = 89 - 23 = 66 Step 2: Classes: 20-40, 40-60, 60-80, 80-100 Step 3: Count frequencies: Marks | Frequency 20-40 | 3 (23, 23, 34) 40-60 | 4 (45, 45, 56, 56) 60-80 | 5 (67, 67,…
Find cumulative frequency for: Classes 0-10(f=5), 10-20(f=8), 20-30(f=12), 30-40(f=6)
Answer
Step 1: First class CF = frequency = 5 Step 2: Add each frequency to previous CF: Class | Frequency | Cumulative Frequency 0-10 | 5 | 5 10-20 | 8 | 5 + 8 = 13 20-30 | 12 …
From cumulative frequency table: Below 20(15), Below 40(24), Below 60(35), Below 80(45). Find the frequency table.
Answer
Step 1: First class frequency = 15 Step 2: Subtract previous CF from current CF: Class | Frequency 0-20 | 15 20-40 | 24 - 15 = 9 40-60 | 35 - 24 = 11 60-80 | 45 - 35 = 10 Total | 45 Thi…
How many students scored less than 60 marks if CF table shows: Below 20(8), Below 40(15), Below 60(28), Below 80(35)?
Answer
Step 1: Identify the cumulative frequency for 'Below 60' Step 2: From table, Below 60 = 28 Answer: 28 students scored less than 60 marks. Note: Cumulative frequency directly gives the count of obser…
When do you use a histogram instead of a bar graph?
Answer
Use histogram when: 1. Data is continuous and grouped (like heights 150-160 cm) 2. No gaps between bars (adjacent classes) 3. Area represents frequency, not just height Use bar graph when: 1. Data is…
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