Statistics Model Questions Set 1 Section-Wise Topic Notes With Detailed Explanation And Example Questions
MOST IMPORTANT quantitative aptitude - 1 EXERCISES
The following question based on Statistics topic of quantitative aptitude
(a) 2
(b) 3
(c) 1
(d) 4
The correct answers to the above question in:
Answer: (d)
a < b < c
Total numbers = 6
Increasing order a, a, b, b, c, c
∴ Median = ${\text"(6/2)th term + (6/2 + 1)th term"}/2$
= ${\text"3rd term + 4th term"}/2$
2 = ${b + b}/2$ = b
Arithmetic mean = ${a + a + b + b + c + c}/6$
⇒ $7/3 = {a + b + c}/3$
⇒ a + b + c = 7
⇒ a + c = 7 – 2 = 5 ... (i)
Geometric mean = $(a^2 × b^2 × c^2)^{1/6}$
⇒ 2 = $(abc)^{1/3}$
⇒ abc = 8
⇒ ac = $8/2$ = 4 ... (ii)
⇒ c = $4/a$
From equation (i),
a + $4/a$ = 5
⇒ ${a^2 + 4}/a$ = 5
⇒ $a^2$ – 5a + 4 = 0
⇒ $a^2$ – 4a – a + 4 = 0
⇒ a(a – 4) – 1(a – 4) = 0
⇒ (a – 4) (a – 1) = 0
if a = 1 then c = 4
a = 4 then c = 1
a = 1, c = 4 and b = 2
The value of c is 4.
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Read more model question set 1 Based Quantitative Aptitude Questions and Answers
Question : 1
Consider the following data:
| x | 1 | 2 | 3 | 4 | 5 |
| f | 3 | 5 | 9 | - | 2 |
a) 6
b) 7
c) 4
d) 8
Answer »Answer: (a)
| x | f | xf |
| 1 | 3 | 3 |
| 2 | 5 | 10 |
| 3 | 9 | 27 |
| 4 | $f_1$ | $4f_1$ |
| 5 | 2 | 10 |
| Total | 19 + $f_1$ | 50 + $4f_1$ |
∴ Mean = ${Σx_if_i}/{Σ_i}$
⇒ 2.96 = ${50 + 4f_1}/{19 + f_1}$ [given]
⇒ 56.24 + 2.96 $f_1 = 50 + 4f_1$
⇒ 6.24 = 1.04 $f_1$
⇒ $f_1$ = 6
Question : 2
What is the median of the data 3, 5, 9, 4, 6, 11, 18?
a) 6.5
b) 7
c) 6
d) 7.5
Answer »Answer: (c)
Arrange the number ascending order
3, 4, 5, 6, 9, 11, 18
Therefore $4^{th}$ term out of 7 is Median.
∴ Median = 6
Question : 3
A new frequency distribution is constructed by doubling each frequency of the original distribution keeping the other entries intact. The following measures are computed for both the tables:
I. Arithmetic mean
II. Median
III. Harmonic mean
Which of the following statements with reference to above is correct?
a) Corresponding values of I and III only are equal in both the distributions
b) Corresponding values of II and III only are equal in both the distributions
c) Corresponding values of I and II only are equal in both the distributions
d) Corresponding values of I, II and III are equal in both the distributions
Answer »Answer: (d)
If we double each value of original frequency distribution, then mean, median and harmonic mean remain same. Hence, option (d) is correct. Since, in case observation since arithmetic mean, median and harmonic mean is dependent of change of origin but if we multiply the frequency of same quantity, then, these are independent.
Question : 4
In a pi-diagram there are three sectors. If the ratio of the angles of the sectors is 1 : 2 : 3, then what is the angle of the largest sector?
a) 180°
b) 150°
c) 200°
d) 120°
Answer »Answer: (b)
Sum of angles of a pie diagram = 360°
∴ θ + 2θ + 3θ = 360°
6θ = 360°
θ = 60°
Hence, angle of Largest sector
6θ = 3 × 60°
= 180°
Question : 5
The arithmetic mean of two numbers is 10 and their geometric mean is 8. What are the two numbers?
a) 12, 8
b) 16, 4
c) 15, 5
d) 18, 2
Answer »Answer: (b)
Question : 6
The following pairs relate to frequency distribution of a discrete variable and its frequency polygon. Which one of the following pairs is not correctly matched ?
a) Ordinates of the – Class vertices of the polygon frequencies
b) Abscissa of the vertices – Class marks of of the polygon the frequency distribution
c) Base line of the polygon – X-axis
d) Area of the – Total polygon frequency of the distribution
Answer »Answer: (d)
Area of the polygon gives sum of $f_i x_i$ not sum of frequency distribution $(f_i)$.
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