Class 10 Mean of Grouped Data — practice questions with answers
Statistics and Probability · 5 sample questions from the school syllabus. Try each one, then open the answer and the worked solution.
1. In a grouped frequency table, what does the symbol 'fi' represent?
AThe class mark of a class
BThe frequency of a class
CThe total of all frequencies
DThe class width
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Answer: B) The frequency of a class
fi denotes the frequency, i.e. the number of observations falling in the i-th class.
2. Using the data of the previous type (sum fi*xi = 120, sum fi = 4), the mean is:
A60
B33
C27
D30
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Answer: D) 30
Mean = 4120 = 30.
3. The mean of 50 observations in a grouped table is 30. Later it was found that an entry with frequency contributing fi*xi = 200 was wrongly read; the correct contribution should have been 320 (frequencies unchanged, total still 50). What is the corrected mean?
A35.4
B32.4
C29.4
D64.8
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Answer: B) 32.4
Original sum fi*xi = 30*50 = 1500. Corrected sum = 1500 - 200 + 320 = 1620. Corrected mean = 501620 = 32.4.
4. In a step-deviation table with equal class width h = 10, the class for which ui=0 is 65-75. Which class carries ui=−3?
A30-40
B45-55
C95-105
D35-45
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Answer: D) 35-45
ui=0 means xi=a, so a is the class mark of 65-75, i.e. a = 70. Then ui=−3 needs xi=a−3h=70−30=40, which is the class mark of 35-45. "30-40" takes a = 65, the lower limit, instead of the class mark 70; "45-55" moves only two steps of h; "95-105" moves up instead of down (that is ui=+3).
5. Copies of a newspaper sold per day by 100 vendors of a district: 0-100: 12, 100-200: 22, 200-300: f, 300-400: 20, 400-500: 16. Find the mean number of copies sold per vendor.
A256
B250
C206
D306
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Answer: A) 256
The missing frequency comes from the total: f = 100 - (12 + 22 + 20 + 16) = 30. Class marks 50, 150, 250, 350, 450 give ∑fixi=600+3300+7500+7000+7200=25600, so the mean is 10025600=256 copies. "250" simply quotes the class mark of the middle class; "206" uses the lower limits as xi; "306" uses the upper limits.