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CBSE Class 10  >  Class 10 Test  >  Olympiad Preparation  >  Math Olympiad Test: Statistics- 4 - Class 10 MCQ

Math Olympiad Test: Statistics- 4 - Free MCQ with solutions Class 10


MCQ Practice Test & Solutions: Math Olympiad Test: Statistics- 4 (10 Questions)

You can prepare effectively for Class 10 Olympiad Preparation for Class 10 with this dedicated MCQ Practice Test (available with solutions) on the important topic of "Math Olympiad Test: Statistics- 4". These 10 questions have been designed by the experts with the latest curriculum of Class 10 2026, to help you master the concept.

Test Highlights:

  • - Format: Multiple Choice Questions (MCQ)
  • - Duration: 10 minutes
  • - Number of Questions: 10

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Math Olympiad Test: Statistics- 4 - Question 1
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The mean of six numbers is 21. If one number is excluded, then their mean is 19, the excluded number is ______.

Detailed Solution: Question 1

Let the excluded number be x and the sum of rest of numbers be y.

Then,  

⇒ 126 = x + y

Also, 19 = y/5

⇒ y = 95 

∴ From (i), x = 31.

Math Olympiad Test: Statistics- 4 - Question 2
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If 7, 2, 9 and 5 occur with frequencies 2, 3, 6 and 4 respectively,  then the arithmetic mean is _____.

Detailed Solution: Question 2

Arithmetic mean =

= 

= 

= 6.27

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Math Olympiad Test: Statistics- 4 - Question 3
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The mean of 20 observations is 12.5. By error, one observation was noted as –15 instead of 15. Then the correct mean is _____. 

Detailed Solution: Question 3

The incorrect sum of observations = 12.5 x 20 = 250

Now, correct sum = 250 - (-15) + 15 = 280

∴ Correct mean = 280/20 = 14

Math Olympiad Test: Statistics- 4 - Question 4
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Find the value of p , if the mean of the following data is 20.

Detailed Solution: Question 4

Mean = 

⇒  20 (15 + 5 p) = 295 + 100 p + 5 p2

⇒  300 + 100 p = 295 + 100 p + 5 p2

⇒ 5p2 = 5

⇒ p2 = ±1 ⇒ p = 1 ( ∵p ≠ - 1)

Math Olympiad Test: Statistics- 4 - Question 5
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If 

Detailed Solution: Question 5

⇒ 

= 25 + 2 = 27 

Math Olympiad Test: Statistics- 4 - Question 6
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 A bus maintains an average speed of 60 km/hr while going from P to Q and maintains an average speed of 90 km/hr while coming back from Q to P. The average speed of the bus is _____.

Detailed Solution: Question 6

Average speed = Total distance covered/Total time taken

Let x be the distance between P and Q.

Thus, time taken by bus from P to Q (t1) = x/60

Thus, time taken by bus from Q to P (t2) = x/90

Total distance covered = 2x  and total time taken = t1 + t2

Average speed,  = 

= 

= 72 km/hr

Math Olympiad Test: Statistics- 4 - Question 7
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Candidates of four school appear in a mathematics test. The data is as follows:

If the average score of the candidates of all the four schools is 66, find the number of candidates that appeared from school III.

Detailed Solution: Question 7

Let the number of candidates that appeared from school III- be x.

Average score of the candidates of all the four schools

= 

⇒ 9768 + 66 x = 10340 + 55 x

⇒ 11x = 572

⇒ x = 52

Math Olympiad Test: Statistics- 4 - Question 8
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Fill in the blanks.
(i) For a given data with 110 observations the ‘less than ogive’ and ‘more than ogive’ intersect at (18, 20). The median of the data is __P__.
(ii) The curve is drawn by taking upper limit of class interval along x-axis and cumulating frequency along y-axis is __Q__ than ogive.
(iii) The mean of 50 number s is 18, the new mean will be __R__ if each observation is increased by 4.
(iv) The mean of seven consecutive natural numbers is 20, then the largest number is __S__ and smallest number of them is __T__.
P, Q, R, S, T

Detailed Solution: Question 8

(i) The intersection point of less than ogive and more than ogive, the x-coordinate is the median. Median is 18.

(ii) Less than ogive is drawn by taking the upper limit of class interval along x-axis and their corresponding less than cumulative frequencies along y-axis.

(iii) Sum of 50 numbers = 50 x 18 = 900 

If each number is increased by 4, then

new sum = 900 + 4 x 50 = 1100

∴ New Mean = 1100/50 = 22

(iv) Let seven consecutive numbers are x, x + 1, x + 2, ...., x + 6.

Mean = 

⇒ 

Smallest number x = 17 Largest number = x + 6 = 17 + 6 = 23.

Math Olympiad Test: Statistics- 4 - Question 9
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Find the mean, median and mode of the following data.

Mean, Median, Mode

Detailed Solution: Question 9

To find the mean let us put the data in the table given below:


Thus, the mean of the given data is 62.4. 
Now, to find the median let us put the data in the table given below:

Now, N = 50 ⇒ N/2 = 25. 
The cumulative frequency just greater than 25 is 36 and the corresponding class is 60 – 80. 
Thus, the median class is 60 – 80. 
∴ l = 60, h = 20, N = 50, f = 12 and cf = 24. 
Now,

Hence, Mean = 62.4, Median = 61.67 and Mode = 60.21

Math Olympiad Test: Statistics- 4 - Question 10
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Find the median for the following distribution of workers. 

Detailed Solution: Question 10


Here,n = 275 ⇒ n/2 = 137.5 

Median class is 5 - 7

Median = 

= 

= 5 + 1.84 = 6.84 

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About this Class 10 Practice Test

This test contains 10 MCQs on Math Olympiad Test: Statistics- 4 with detailed solutions for each question. It is part of the Olympiad Preparation for Class 10 course on EduRev, designed to align with the current Class 10 syllabus. Each solution explains not just the correct answer but also gives you an understanding of the topic — not just to attempt the question but also help you prepare for the exam with practice.

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