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
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
The correct answers to the above question in:
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.
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Read more model question set 1 Based Quantitative Aptitude Questions and Answers
Question : 1
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 : 2
Read the following information carefully to answer the questions that follow. The average age of 6 persons living in a house is 23.5 years. Three of them are majors and their average age is 42 years. The difference in ages of the three minor children is same.What is the median of the ages of minor children?
a) 5 years
b) 7 years
c) 3 years
d) Cannot be determined
Answer »Answer: (a)
Total age of six persons = 23.5 × 6 = 141 years
Total age of three major persons = 42 × 3 = 126 years
∴ Total age of three minor children = 141 – 126 = 15 years
The difference in ages of the three minor children is same.
Therefore, we take ages may be:
5, 5, 5; 3, 5, 7; 2, 5, 8 and 1, 5, 9
In all the cases, median will be 5 years.
Median age of minor children = 5 years.
Question : 3
Consider the following statements related to cumulative frequency polygon of a frequency distribution, the frequencies being cumulated from the lower end of the range :
1. The cumulative frequency polygon gives an equivalent representation of frequency distribution table.
2. The cumulative frequency polygon is a closed polygon with one horizontal and one vertical side. The other sides have non–negative slope.
Which of the above statements is / are correct ?
a) Only 2
b) Both 1 and 2
c) Only 1
d) Neither 1 nor 2
Answer »Answer: (c)
Here, Statement 1 is correct but Statement 2 is not correct.
Question : 4
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 : 5
If each of n numbers xi = i (i = 1, 2, 3,..... n) is replaced by (i + 1) $x_i$ , then the new mean is
a) ${n(n + 1)}/2$
b) ${(n + 1)(n + 2)}/{3n}$
c) ${n + 3}/2$
d) ${(n + 1)(n + 2)}/3$
Answer »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.
Question : 6
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.
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