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) ${n(n + 1)}/2$
(b) ${(n + 1)(n + 2)}/{3n}$
(c) ${n + 3}/2$
(d) ${(n + 1)(n + 2)}/3$
The correct answers to the above question in:
Answer: (d)
$(i + 1)x^i = (i + 1)x^i$ where i = 1, 2, 3, ------- n
$Σ↖{n}↙{i = 1}(i + 1)$ = 1.2 + 2.3 + 3.4 + 4.5 + -------meters
= $Σ↖{n}↙{n = 1} T_n$
= Σ n (n + 1)
= $Σn^2 + Σn$
= ${(n + 1)n(2n + 1)}/6 + {n(n + 1)}/2$
Mean = $1/n [{(n + 1) n (2n + 1)}/6 + {n(n + 1)}/2]$
= ${(n + 1)}/2 [{2n + 1}/3 + 1]$
= ${(n + 1)}/2 {(2n + 4)}/3$
= ${(n + 1)(n + 2)}/3$
So, option (d) is correct.
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Read more model question set 1 Based Quantitative Aptitude Questions and Answers
Question : 1
An individual purchases three qualities of pencils. The relevant data is given below :
Quality | Price per Pencil (in Rs.) | Money spent (in Rs.) |
A | 1.00 | 50 |
B | 1.50 | x |
C | 2.00 | 20 |
a) Rs. 30
b) Rs.40
c) Rs.10
d) Rs.60
Answer »Answer: (a)
Number of Type A pencil = ${50}/1$ = 50
Number of Type B pencil = $x/{1.50}$
Number of Type C pencil = ${20}/2$ = 10
Average = ${\text"Total money spent"}/{\text"totalno.of pencil"}$ = 1.25
= ${x + 50 + 20}/{50 + 10 + {x/{1.50}}}$ = 1.25
= 70 + x = 1.25 $(60 + x/{1.50})$
70 + x = 75.00 + ${1.25}/{1.50}$x
x - ${125}/{150}$ x = 5
= ${25}/{150}$ x = 5
x = 30
Question : 2
The following table gives the frequency distribution of life length in hours of 100 electric bulbs having median life 20 h.
Life of bulbs(in hours) | Number of bulbs |
8-13 | 7 |
13-18 | x |
18-23 | 40 |
23-28 | y |
28-33 | 10 |
33-38 | 2 |
a) 24
b) 14
c) 27
d) 11
Answer »Answer: (b)
Number of total bulbs = 100
∴ 7 + x + 40 + y + 10 + 2 = 100
⇒ x + y = 41 ... (i)
Life of bulbs (in hours) | Number of bulbs | Cumulative Frequency |
8 - 13 | 7 | 7 |
13 - 18 | x | 7 + x |
18 - 23 | 40 | 47 + x |
23 - 28 | y | 47 + x + y |
28 - 33 | 10 | 57 + x + y |
33 - 38 | 2 | 59 + x + y |
N = 100 |
The median life is 20 h, so median interval will be (18-23).
Here, l = 18, $N/2$ = 50
c = 7 + x, f = 40, h = 5
∴ Median = l + ${(N/2 - C)}/f$ × h
⇒ 20 = 18 + ${(50 – 7 – x)}/{40}$ × 5
⇒ 2 = ${50 – 7 – x}/8$
⇒ 16 = 50 – 7 – x
⇒ x = 43 – 16
⇒ x = 27
Missing frequency 'y' is 14.
Question : 3
What is the difference between the number of boys studying Mathematics and the number of girls studying Physics?
a) 30
b) 60
c) 20
d) 80
Answer »Answer: (a)
Difference in the number of boys studying Mathematics and Physics = 180 – 150 = 30
Question : 4
Which one among the following statements is not correct?
a) For average rate of increase when the rate of population growth is given, geometric mean is best suitable
b) For average rate of speed when different distances are covered by different rates of speed, harmonic mean is best suitable
c) For size of readymade garments, mode is the best suitable measure
d) For average level of intelligence of students in a class, arithmetic mean is the best suitable
Answer »Answer: (d)
Since, intelligence of students is an attribute, arithmetic mean is not suitable method.
Question : 5
What is the mode of the frequency distribution of SeriesII?
a) 36
b) 46
c) 26
d) 56
Answer »Answer: (b)
Mode of frequency distribution of series II is 46.
Question : 6
Read the following information carefully to answer the questions that follow. The arithmetic mean, geometric mean and median of 6 positive numbers a, a, b, b, c, c, where a < b < c are $7/3$, 2, 2, respectively.What is the mode?
a) 2
b) 1, 2 and 4
c) 1
d) None of these
Answer »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
Mode = 3 (Median) – 2 (Mean)
= $3(2) - 2(7/3) = {18 - 14}/3 = 4/3$
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