Math Olympiad Test: Statistics- 2 - Class 9 MCQ

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

 Upper limit = 

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

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.

Upper limit = mid value + 
47 = 41 + 

∴ Class size = (47 – 41) × 2
= 12

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

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.

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

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

Given 

⇒ 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

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

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

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

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