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Statistics

Karnataka Board · Class 10 · Mathematics

Flashcards for Statistics — Karnataka Board Class 10 Mathematics. Quick Q&A cards covering key concepts, definitions, and formulas.

45 questions20 flashcards5 concepts
20 Flashcards
Card 1Mean of Ungrouped Data

Find the mean of the data: 5, 8, 12, 15, 20, 22, 25 using the direct method.

Answer

Step 1: Add all values → 5 + 8 + 12 + 15 + 20 + 22 + 25 = 107 Step 2: Count observations → n = 7 Step 3: Apply formula → Mean = Sum/n = 107/7 = 15.29 Answer: Mean = 15.29

Card 2Mean of Grouped Data - Direct Method

Calculate the mean for this frequency distribution: Marks: 10, 20, 30, 40, 50 Frequency: 2, 5, 8, 3, 2

Answer

Step 1: Create table with fi × xi 10×2=20, 20×5=100, 30×8=240, 40×3=120, 50×2=100 Step 2: Find totals → Σfi = 2+5+8+3+2 = 20, Σfixi = 20+100+240+120+100 = 580 Step 3: Apply formula → Mean = Σfixi/Σfi

Card 3Mean of Grouped Data - Assumed Mean Method

Find the mean using assumed mean method for: Class intervals: 0-10, 10-20, 20-30, 30-40 Frequencies: 5, 10, 15, 8 (Take a = 25)

Answer

Step 1: Find class marks → 5, 15, 25, 35 Step 2: Calculate di = xi - a = xi - 25 → -20, -10, 0, 10 Step 3: Find fidi → 5×(-20)=-100, 10×(-10)=-100, 15×0=0, 8×10=80 Step 4: Calculate totals → Σfi = 38,

Card 4Mean of Grouped Data - Step Deviation Method

Calculate mean using step-deviation method: Class: 20-30, 30-40, 40-50, 50-60 Freq: 4, 6, 8, 2 (a = 45, h = 10)

Answer

Step 1: Find class marks → 25, 35, 45, 55 Step 2: Calculate ui = (xi - a)/h = (xi - 45)/10 → -2, -1, 0, 1 Step 3: Find fiui → 4×(-2)=-8, 6×(-1)=-6, 8×0=0, 2×1=2 Step 4: Calculate totals → Σfi = 20, Σf

Card 5Mode of Ungrouped Data

Find the mode of: 2, 3, 4, 3, 5, 3, 6, 4, 3, 2

Answer

Step 1: Count frequency of each value 2 appears 2 times, 3 appears 4 times, 4 appears 2 times, 5 appears 1 time, 6 appears 1 time Step 2: Identify highest frequency → 4 (for value 3) Step 3: Value wit

Card 6Mode of Grouped Data

Find mode for grouped data: Class: 0-10, 10-20, 20-30, 30-40 Freq: 5, 12, 8, 3 Find modal class and calculate mode.

Answer

Step 1: Identify modal class → 10-20 (highest frequency = 12) Step 2: Identify values → l=10, h=10, f1=12, f0=5, f2=8 Step 3: Apply formula → Mode = l + [(f1-f0)/(2f1-f0-f2)] × h Step 4: Calculate → M

Card 7Median of Ungrouped Data

Find the median of: 12, 8, 15, 20, 6, 14, 18, 10, 16

Answer

Step 1: Arrange in ascending order → 6, 8, 10, 12, 14, 15, 16, 18, 20 Step 2: Count observations → n = 9 (odd) Step 3: Find middle position → (n+1)/2 = (9+1)/2 = 5th position Step 4: Identify 5th valu

Card 8Median of Grouped Data

Calculate median for: Class: 10-20, 20-30, 30-40, 40-50 Freq: 4, 8, 12, 6 Find median class and median value.

Answer

Step 1: Find cumulative frequencies → 4, 12, 24, 30 Step 2: Calculate n/2 → 30/2 = 15 Step 3: Identify median class → 30-40 (cf = 24 > 15) Step 4: Apply formula → Median = l + [(n/2 - cf)/f] × h Step

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Frequently Asked Questions

What are the important topics in Statistics for Karnataka Board Class 10 Mathematics?

Statistics covers several key topics that are frequently asked in Karnataka Board Class 10 board exams. Focus on the core concepts listed on this page and practise related questions to build confidence.

Start by understanding all key concepts. Practise previous year questions from this chapter. Revise formulas and definitions regularly. Use flashcards for quick revision before the exam.

There are 20 flashcards for Statistics covering key definitions, formulas, and concepts. Use them daily for 10–15 minutes for best results.

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