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Math Olympiad Test: Statistics- 2


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15 Questions MCQ Test Mathematics Olympiad for Class 9 | Math Olympiad Test: Statistics- 2

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Math Olympiad Test: Statistics- 2 - Question 1

The no. of class intervals, if the magnitude of class interval is 4 will be:
Data: 31, 23, 19, 29, 20, 16, 22, 10, 13, 34, 33, 38, 36, 24, 18, 15, 12, 30, 27, 23, 20

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

Range = 38 – 10 = 28
∴ number of class intervals = 28/4 = 7 

Math Olympiad Test: Statistics- 2 - Question 2

The class marks of a distribution are:
52, 47, 57, 67, 62, 72, 82, 87, 97, 92, 102.
Q. The lower and upper limits of first class interval will be:

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

 Upper limit = 

Lower limit = 
= 44.5
[h = difference between any two marks = 52 – 47 = 5] 

Math Olympiad Test: Statistics- 2 - Question 3

Tallys are usually marked in a bunch of:

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

Tallies are usually marked in groups of five. The first four tallies are marked vertically and the fifth tally is marked diagonally across the first 4.

Math Olympiad Test: Statistics- 2 - Question 4

The mid–value and upper limit of a class interval are 41 and 47 respectively. The class size will be:

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

Upper limit = mid value + 
47 = 41 + 

∴ Class size = (47 – 41) × 2
= 12

Math Olympiad Test: Statistics- 2 - Question 5

The x-and y-axes in the histogram represent:

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

x-axis represents class interval, y-axis represents frequency. 

Math Olympiad Test: Statistics- 2 - Question 6

In the ‘more–than’ type of ogive the cumulative frequency is plotted against:

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

More than distribution of cumulative frequency plot is a kind of Ogive frequency distribution in which the frequencies are decreasing from top to bottom. 
So, we consider lower limits as abscissa and more than cumulative frequencies as ordinate.

Math Olympiad Test: Statistics- 2 - Question 7

The frequency of students is highest in the class interval:

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

∵ The class interval, 30 – 40, has highest peak,
∴ It has highest frequency. 

Math Olympiad Test: Statistics- 2 - Question 8

The mean of x1, x2, ……., xn is , then the value of:

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


⇒ x1 + x2 + x3 + x4 ……. + xn = n
⇒ x1 + x2 + x3 …… + xn

Math Olympiad Test: Statistics- 2 - Question 9

If each number in (Prob - 17) is multiplied by k, the new mean will be: 

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

Given 

Math Olympiad Test: Statistics- 2 - Question 10

The mean of 10 numbers is 16. If two consecutive numbers are excluded, the new mean is 18. The sum of the excluded numbers is: 

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


⇒ x1 + x2 …… + x10 = 16 ……. (i)
Let x2 and x3 are removed, then,

⇒ x1 + x4 + ….. + x10 = 144 …….(ii) 
Now, Eq. (i) – (ii) 
x2 + x3 = 160 – 144 = 16

Math Olympiad Test: Statistics- 2 - Question 11

The sum of deviations of a set of n values x1, x2, …… xn measured from 50 is – 10 and the sum of deviations of the values from 46 is 70. The value of n is: 

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

…(i)
…(ii)
Subtracting eq. (i), from eq. (ii),
46n – (–50 n) = 70 – (–10) 
⇒ 4n = 80
⇒ n = 20

Math Olympiad Test: Statistics- 2 - Question 12

The mean of the following distribution is:

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


Math Olympiad Test: Statistics- 2 - Question 13


Total = 120
Mean =  50
f1, f2 =

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

f1 + f2 + 17 + 32 + 19 = 120
⇒ f1 + f2 = 52 …(i)
Mean

⇒ 50 × 120 = 170 + 1600 + 1710 + + 30f1 + 70f2
⇒ 30f1 + 70f2 = 2520
⇒ 371 + 7f2 = 252 ……..(ii)
From eq (i) and eq (ii).
f1 = 28, f2 = 24

Math Olympiad Test: Statistics- 2 - Question 14

The new median, of the following data, if 37 is replaced by 5.
7, 9, 16, 25, 31, 36, 37, 39, 40, 42, 43

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

If 37 ⟶ 5, then, the new data will be:
5, 7, 9, 16, 25, 31, 36, 39, 40, 42, 43
∵ No. of numbers = 11
∴ = 6th number will be the median. 

Math Olympiad Test: Statistics- 2 - Question 15

The mode of the following data is:
29, 40, 41, 46, 45, 44, 43, 29, 40, 41, 46, 44,  44, 47, 49, 53, 29, 57, 44, 43, 41, 28, 16, 26.

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

∵ 44 is repeated 4 times, i.e., maximum no. of times.
∴ Mode = 44

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