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| source: ncert_exercises |
| topic: statistics |
| class_level: class_9 |
| chapter: ch12 |
| exercise: ex12.3 |
| difficulty: intermediate |
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| Class 9 | Ch12: Statistics | Exercise 12.3 |
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| Key Formulas: |
| Mean (ungrouped) = Sum of all observations / Number of observations = Σx/n |
| Median: Arrange in order. If n odd: middle value. If n even: average of two middle values. |
| Mode: Most frequently occurring value. |
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| Q1. A survey was conducted of 40 patients admitted to a hospital. Find mean number of days. |
| Number of days: 1,2,3,4,5,6,7,8,9,10,11,12,13,14. |
| Frequency: 2,3,5,7,4,4,2,1,1,1,2,2,3,3. |
| Answer: Mean = Σ(xi×fi)/Σfi. Compute sum = 1×2+2×3+3×5+...+14×3. Divide by 40. ✅ |
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| Q2. Following data gives marks scored by students. Find mean marks. |
| Answer: Mean = Σ(xi×fi)/n. Multiply marks by frequency, sum up, divide by total students. ✅ |
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| Q3. The following distribution shows daily wages of 50 workers. Find mean wage. |
| Answer: Mean = Σ(midpoint×frequency)/50. Find midpoint of each class = (upper+lower)/2. ✅ |
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| Q4. If mean of following distribution is 2.6, find missing frequency. |
| Values: 1,2,3,4,5. Frequencies: 4,5,y,1,2. |
| Answer: Mean=2.6. Σ(x×f)=1×4+2×5+3y+4×1+5×2=4+10+3y+4+10=28+3y. Σf=4+5+y+1+2=12+y. 2.6=(28+3y)/(12+y). 2.6(12+y)=28+3y. 31.2+2.6y=28+3y. 3.2=0.4y. y=8. ✅ |
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| Q5. Thirty women examined in clinical investigation with median age 36. Find missing frequency. |
| Answer: Arrange data in order. The middle value (15th and 16th) average = 36. Use this to find missing frequency. ✅ |
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| Q6. If mode of following data is 64, find missing frequency. |
| Answer: Mode is value with highest frequency. Set up equation so 64 has the highest frequency and solve. ✅ |
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| Q7. Find mean, median and mode of the following data: |
| 14, 25, 14, 28, 18, 17, 18, 14, 23, 22, 14, 18. |
| Answer: Arrange in order: 14,14,14,14,17,18,18,18,22,23,25,28. |
| Mean = (14×4+17+18×3+22+23+25+28)/12 = (56+17+54+22+23+25+28)/12 = 225/12 = 18.75. |
| Median = (18+18)/2 = 18 (average of 6th and 7th values). |
| Mode = 14 (appears 4 times, most frequent). ✅ |
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| Q8. The following observations are arranged in ascending order. If median is 63.5, find x. |
| 29, 32, 48, 50, x, x+2, 72, 78, 84, 95. |
| Answer: n=10 (even). Median=(5th+6th)/2=(x+x+2)/2=(2x+2)/2=x+1=63.5. x=62.5. ✅ |
