Statistics — Previous Year Questions (Class 10 Mathematics)
Statistics covers mean, median, mode, and frequency distributions for grouped and ungrouped data. Essential for data interpretation and decision-making acr
TL;DR: Statistics covers mean, median, mode, and frequency distributions for grouped and ungrouped data. Essential for data interpretation and decision-makin…
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Statistics covers mean, median, mode, and frequency distributions for grouped and ungrouped data. Essential for data interpretation and decision-making acr
Statistics — Previous Year Questions with Solutions
Q (2023, 1 mark): Find the mean of data: 5, 8, 12, 10, 6, 8, 9.
Answer: Mean = (5 + 8 + 12 + 10 + 6 + 8 + 9) / 7
= 58 / 7
= 8.29 (approximately)
Q (2022, 2 marks): Find median and mode of: 2, 3, 3, 5, 5, 5, 7, 8, 8.
Answer: Arranging in order (already ordered): 2, 3, 3, 5, 5, 5, 7, 8, 8
Total observations = 9 (odd)
Median = middle value = 5th value = 5
Mode = most frequent value = 5 (appears 3 times)
Q (2023, 3 marks): For grouped data with classes 0-10, 10-20, 20-30, 30-40 and frequencies 5, 8, 12, 7 respectively, find the mean.
Answer: Class midpoints: 5, 15, 25, 35
Frequencies: 5, 8, 12, 7
Mean = Σ(midpoint × frequency) / Σfrequency
= (5×5 + 15×8 + 25×12 + 35×7) / (5+8+12+7)
= (25 + 120 + 300 + 245) / 32
= 690 / 32
= 21.56 (approximately)
Q (2021, 3 marks): Find the median class and median for grouped data: class 10-20, 20-30, 30-40, 40-50 with frequencies 4, 8, 6, 2.
Answer: Total frequency N = 4 + 8 + 6 + 2 = 20
Median class corresponds to N/2 = 10
Cumulative frequencies: 4, 12, 18, 20
Median class = 20-30 (CF reaches 12, which > 10)
Using formula: Median = L + ((N/2 - CF)/f) × w
where L = 20, N/2 = 10, CF = 4 (previous), f = 8, w = 10
Median = 20 + ((10 - 4)/8) × 10
= 20 + (6/8) × 10
= 20 + 7.5
= 27.5
Q (2022, 2 marks): The mean of 5 observations is 12. If 4 observations are 10, 14, 8, 15, find the 5th observation.
Answer: Mean = (sum of all observations) / number of observations
12 = (10 + 14 + 8 + 15 + x) / 5
12 × 5 = 47 + x
60 = 47 + x
x = 13
Q (2023, 2 marks): For data 3, 5, 7, 9, 11, if each observation is increased by 5, how does the mean change?
Answer: Original mean = (3 + 5 + 7 + 9 + 11) / 5 = 35 / 5 = 7
New data: 8, 10, 12, 14, 16
New mean = (8 + 10 + 12 + 14 + 16) / 5 = 60 / 5 = 12
Mean increases by 5 (same as the increment added to each observation)
Frequently Asked Questions
What is the difference between mean, median, and mode?
Mean is the average of all values. Median is the middle value when data is ordered. Mode is the most frequently occurring value. Each is useful in different contexts.
How do you find the median for grouped data?
Find the median class (cumulative frequency >= N/2). Use formula: Median = L + ((N/2 - CF)/f) × w, where L is lower limit, CF is previous cumulative frequency, f is class frequency, and w is class width.
More Class 10 Mathematics PYQs
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