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Unit Test 7: Statistics & Probability

Class 10 Mathematics (Standard)

Time: 1 Hour Max. Marks: 30

General Instructions:

  • The question paper consists of 15 questions divided into 4 sections: A, B, C, and D.
  • Section A: 6 MCQs of 1 mark each.
  • Section B: 4 Short Answer questions of 2 marks each.
  • Section C: 4 Short Answer questions of 3 marks each.
  • Section D: 1 Case Study based question of 4 marks.
  • Use of calculators is not permitted.
SECTION A (1 Mark Each)
[1] 1. The relationship between mean, median and mode for a moderately skewed distribution is:
[1] 2. Which of the following cannot be the probability of an event?
[1] 3. If P(E) = 0.07, then the probability of 'not E' is:
[1] 4. The cumulative frequency table is useful in determining the:
[1] 5. A die is thrown once. The probability of getting an even number is:
[1] 6. The mean of first 5 prime numbers is:
SECTION B (2 Marks Each)
[2] 7. A bag contains 5 red balls and some blue balls. If the probability of drawing a blue ball is double that of a red ball, determine the number of blue balls in the bag.
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[2] 8. The mean of 5 observations x, x+2, x+4, x+6 and x+8 is 11. Find the value of x.
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[2] 9. Two coins are tossed simultaneously. Find the probability of getting at least one head.
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[2] 10. Find the mode of the following data: 2, 6, 4, 5, 0, 2, 1, 3, 2, 3.
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SECTION C (3 Marks Each)
[3] 11. Find the mean of the following distribution:
Class: 0-10, 10-20, 20-30, 30-40, 40-50
Frequency: 3, 10, 11, 9, 7
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[3] 12. One card is drawn from a well-shuffled deck of 52 cards. Find the probability of getting: (i) a king of red color (ii) a face card (iii) a red face card.
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[3] 13. A box contains 90 discs which are numbered from 1 to 90. If one disc is drawn at random from the box, find the probability that it bears (i) a two-digit number (ii) a perfect square number (iii) a number divisible by 5.
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[3] 14. The median of the following data is 28.5. Find the values of x and y, if the total frequency is 60.
Class: 0-10, 10-20, 20-30, 30-40, 40-50, 50-60
Frequency: 5, x, 20, 15, y, 5
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SECTION D (Case Study - 4 Marks)
[4] 15. Case Study: Survey on Heights

The heights of 50 students of a class are given below:
Height (in cm): 130-135, 135-140, 140-145, 145-150, 150-155, 155-160
Number of Students: 4, 10, 12, 14, 8, 2

(i) Find the median class of the data. (1 Mark)
(ii) Find the modal class of the data. (1 Mark)
(iii) Find the mean height of the students. (2 Marks)
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TOTAL SCORE

0 / 6 (MCQ)

(Subjective answers submitted for review)

Solution Key (MCQs)

Q1. (b) Mode = 3 Median - 2 Mean

This is the empirical relationship between the three measures of central tendency.

Q2. (b) -1.5

Probability cannot be negative.

Q3. (a) 0.93

P(not E) = 1 - P(E) = 1 - 0.07 = 0.93.

Q4. (b) Median

Cumulative frequency curves (ogives) are used to find the median.

Q5. (a) 1/2

Even numbers on a die are 2, 4, 6. Probability = 3/6 = 1/2.

Q6. (a) 5.6

Primes: 2, 3, 5, 7, 11. Sum = 28. Mean = 28/5 = 5.6.