Math Olympiad Test: Statistics- 2 - Class 10 MCQ

# Math Olympiad Test: Statistics- 2 - Class 10 MCQ

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## 15 Questions MCQ Test Olympiad Preparation for Class 10 - Math Olympiad Test: Statistics- 2

Math Olympiad Test: Statistics- 2 for Class 10 2024 is part of Olympiad Preparation for Class 10 preparation. The Math Olympiad Test: Statistics- 2 questions and answers have been prepared according to the Class 10 exam syllabus.The Math Olympiad Test: Statistics- 2 MCQs are made for Class 10 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Math Olympiad Test: Statistics- 2 below.
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Math Olympiad Test: Statistics- 2 - Question 1

### If the numbers 25, 31, x -3, 37, x + 4, 42, 43, 45, 46 are in ascending order and their median is 39. What is the number x?

Detailed Solution for Math Olympiad Test: Statistics- 2 - Question 1

The given data in ascending order is 25, 31, x - 3, 37, x + 4, 42, 43, 45, 46
n = 9 (odd)

Math Olympiad Test: Statistics- 2 - Question 2

### The median of first five natural numbers be 3. If 6 is included. then what is the median, Also find the difference of two medians respectively?

Detailed Solution for Math Olympiad Test: Statistics- 2 - Question 2

First 5 natural numbers are 1, 2, 3, 4, 5 n = 5 (odd)
∴ Median = n +1/2 th = 5 + 1/2 th = 3rd term
⇒ Median = 3
1, 2, 3, 4, 5, 6
Median = 1/2 (3 + 4) = 7/2 = 3.5
Difference = 3 .5 - 3 = 0.5

Math Olympiad Test: Statistics- 2 - Question 3

### What is the mean, median, mode of the following data respectively? 0, 2, 2, 3, 3, 3, 4, 5, 5, 5, 5, 6, 6, 7, 8, 8

Detailed Solution for Math Olympiad Test: Statistics- 2 - Question 3

Math Olympiad Test: Statistics- 2 - Question 4

What is the mean of the following data?

Detailed Solution for Math Olympiad Test: Statistics- 2 - Question 4

Math Olympiad Test: Statistics- 2 - Question 5

What is the median of the following distribution?

Detailed Solution for Math Olympiad Test: Statistics- 2 - Question 5

N = 8 + 10 + 11 + 16 + 20 + 25 + 15 + 9 + 6 = 120
∴ N/2 = 120/2 = 60
60 lies in between 45 - 65
∴ Variate =  5

Math Olympiad Test: Statistics- 2 - Question 6

What is the mode of the following distribution?

Detailed Solution for Math Olympiad Test: Statistics- 2 - Question 6

Class 12 - 15 has maximum frequency
12 - 15 is the modal class

Math Olympiad Test: Statistics- 2 - Question 7

If a mode exceeds a mean by 12 then the mode exceeds the median by:

Detailed Solution for Math Olympiad Test: Statistics- 2 - Question 7

Given: The mode of a series exceeds its mean by 12.
Formula used: Mode = 3 × Median - 2 × Mean
Calculation: Mode - Mean = 12
As, Mode = 3 × Median - 2 × Mean
⇒ Mode - Mean = 3 × Median - 3 × Mean      [Subtracting Mean from both sides]
⇒ 12 = 3 × (Median - Mean)
⇒ Median - Mean = 12/3 = 4      ----(1)
Again, Mode - Median = 2 × Median - 2 × Mean
⇒ Mode - Median = 2 × 4 = 8
Then, Mode exceeds the median by 8.
∴ The mode exceeds the median by 8.

Math Olympiad Test: Statistics- 2 - Question 8

The mode of the data 6, 4, 3, 6, 4, 3, 4, 6, 5 and x can be

Detailed Solution for Math Olympiad Test: Statistics- 2 - Question 8

Here,

Clearly frequency of all 3,4, and 6 are 3. So all of these can be modes of the given distribution.

Math Olympiad Test: Statistics- 2 - Question 9

If the difference between the mode and median is 2, then the difference between the median and mean is  (in the given order).

Detailed Solution for Math Olympiad Test: Statistics- 2 - Question 9

Concept: Relation between mode, median and mean is given by:
Mode = 3 × median – 2 × mean
Given: Mode – median = 2
As we know
Mode = 3 × median – 2 × mean
Now, Mode = median + 2
⇒ (2 + median) = 3median – 2mean
⇒ 2Median - 2Mean = 2
⇒ Median - Mean = 1
∴ The difference between the median and mean is 1.

Math Olympiad Test: Statistics- 2 - Question 10

The median of the data 5, 6, 7, 8, 9, 10 is ______.

Detailed Solution for Math Olympiad Test: Statistics- 2 - Question 10

If the no. of observations is even then the median of the data is the average of (n/2) and (n/2 + 1) observations.

Hence median of the data  observations.

Math Olympiad Test: Statistics- 2 - Question 11

What is the mode of the given data?

Detailed Solution for Math Olympiad Test: Statistics- 2 - Question 11

The variate having highest frequency is the mode.

Math Olympiad Test: Statistics- 2 - Question 12

If the mean of first n natural number is 15, what is the value of n?

Detailed Solution for Math Olympiad Test: Statistics- 2 - Question 12

Math Olympiad Test: Statistics- 2 - Question 13

The number of problems worked out by a student on seven days of a week are 5, 9, 15, 11, 13, 17, 7, then what is the sum of lower quartile and upper quartile?

Detailed Solution for Math Olympiad Test: Statistics- 2 - Question 13

The given data in ascending order is 5, 7, 9, 11, 13, 15, 17
n = 7 (odd)

Math Olympiad Test: Statistics- 2 - Question 14

Find the median of the following data

Detailed Solution for Math Olympiad Test: Statistics- 2 - Question 14

N = 60
N/2 = 30
c.f just greater than 30 is 50
Median class is 30 - 60

= 30 + 10 = 40

Math Olympiad Test: Statistics- 2 - Question 15

What is the mode of the given data?
7, 8, 5, 6, 8, 3, 12 ,11, 8, 6, 8, 7, 8, 5, 3, 8

Detailed Solution for Math Olympiad Test: Statistics- 2 - Question 15

Here the frequency of 8 is maximum. (6 times)
∴ Mode =  8

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