Statistics — Flashcards
Karnataka Board · Class 10 · Mathematics
20 flashcards for Statistics (Karnataka Board Class 10 Mathematics) to test yourself on key terms and facts. Sample: "Find the mean of the data: 5, 8, 12.
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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…
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 …
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,…
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…
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…
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…
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…
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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Sources & Official References
- Karnataka SSLC — kseeb.kar.nic.in
- Dept of Pre-University Education, Karnataka
- National Education Policy 2020 — education.gov.in
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