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Maths M.C.Q (1 Marks)

Stastics · CBSE STD 10 (CBSE - English Medium). 30 questions.

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M.C.Q (1 Marks)

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30 questions · 29 auto-graded MCQ + 1 self-marked written.

MCQ 11 Mark
If the 'less than' type ogive and 'more than' type ogive intersect each other at $(20.5,15.5)$ then the median of the given data is
  • A
    36.0
  • ✓
    20.5
  • C
    15.5
  • D
    5.5
Answer
Correct option: B.
20.5
(b)
The less than ogive curve gives cumulative frequency (probability) for $x \leq a$.
The more than ogive curve gives cumulative frequency (probability) for $x \geq a$.
They intersect exactly at the median because cumulative frequency will be $50 \%$ of the total at median. So, median is 20.5
Hence the correct option is (b).

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MCQ 21 Mark
Relationship among mean, median and mode is:
  • A
    3 Median = Mode + 2 Mean
  • B
    3 Mean $=$ Median +2 Mode
  • C
    3 Mode $=$ Mean $=2$ Median
  • D
    Mode $=3$ Mean -2 Median
Answer
a - The empirical relationship between the three measures of central tendency is Median = Mode +2 Mean
Hence, the correct option is (a).

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MCQ 31 Mark
If the mode of some data is $7$ and their mean is also $7$ , then their median is:
  • A
    $10$
  • B
    $9$
  • C
    $8$
  • ✓
    $7$
Answer
Correct option: D.
$7$
The relation between mean, median and mode is Mode $=3$ Median $-2$ Mean
Substitute mode $=7$ and mean $=7$ in above equation,
$7=3 \times \text { Median }-2 \times 7$
$\Rightarrow 7=3 \times \text { Median }-14$
$\Rightarrow 3 \times \text { Median }=21$
Divide the above equation by $3 ,$
$\text { Median }=\frac{21}{3}=7$
Hence, the correct option is $(d).$
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MCQ 41 Mark
The mode of the numbers $2,3,3,4,5,4,4,5,3,4,2,6,7$ is:
  • A
    2
  • B
    3
  • ✓
    4
  • D
    5
Answer
Correct option: C.
4
(c)
As mode is defined as value that has a higher frequency in the given set of numbers, the correct answer is 4 .
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MCQ 51 Mark
For the following frequency distribution
Classes: $0-5$ $5-10$ $10-15$ $15-20$ $20-25$
Frequency: $8$ $10$ $19$ $25$ $8$
The upper limit of median class is
  • A
    $15$
  • B
    $10$
  • ✓
    $20$
  • D
    $25$
Answer
Correct option: C.
$20$
Class $f$ $cf$
$0-5$ $8$ $8$
$5-10$ $10$ $18$
$10-15$ $19$ $37$
$15-20$ $25$ $62$
$20-25$ $8$ $70$
  $N = 70$  
$N=70$
$\frac{N}{2}=35$
$cf$ just greater than $\frac{ N }{2}$ is $62$
$\therefore 15-20$ is median class
Upper limit $= 20$
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MCQ 61 Mark
Type of cumulative frequency distribution in which class intervals are added in bottom to top order is classified as.
  • ✓
    More than type distribution
  • B
    Marginal distribution
  • C
    Variation distribution
  • D
    Less than type distribution
Answer
Correct option: A.
More than type distribution
(a)
Type of cumulative frequency distribution in which class intervals are added in bottom to top order is classified as 'More than type distribution.
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MCQ 71 Mark
Type of cumulative frequency distribution in which class intervals are added in top to bottom order is classified as
  • A
    Variation distribution
  • ✓
    Less than type distribution
  • C
    More than type distribution
  • D
    Marginal distribution.
Answer
Correct option: B.
Less than type distribution
(b)
Type of cumulative frequency distribution in which class intervals are added in top to bossttom order is classified as Less than type distribution.
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MCQ 81 Mark
'Less than type' and 'more than type' distribution are types of
  • A
    Class distribution
  • B
    Cumulative class distribution
  • ✓
    Cumulative frequency distribution
  • D
    Upper limit distribution
Answer
Correct option: C.
Cumulative frequency distribution
(c)
'Less than type' and 'More than type' distribution are types of cumulative frequency distribution.
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MCQ 91 Mark
Class frequency is divided by number of observations in frequency distribution to convert it into.
  • A
    relative margin distribution
  • B
    relative variable distribution
  • ✓
    relative frequency distribution
  • D
    relative width distribution
Answer
Correct option: C.
relative frequency distribution
(c)
When class frequency is divided by number of observations in frequency distribution to convert it into relative frequency distribution.
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MCQ 101 Mark
'Less than type' cumulative frequency distribution is considered as correspondent to
  • ✓
    upper limit of class interval
  • B
    lower limit of class interval
  • C
    upper limit of range
  • D
    lower limit of range
Answer
Correct option: A.
upper limit of class interval
(a)
'Less than type' cumulative frequency distribution is considered as correspondent to upper limit of class interval.
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MCQ 111 Mark
Cumulative frequency polygon is also called
  • ✓
    ogive
  • B
    his togram
  • C
    absicea
  • D
    sigma
Answer
Correct option: A.
ogive
(a)
Cumulative frequency polygon is also called ogive.
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MCQ 121 Mark
Total number of observations. Which are below a certain value are known as
  • A
    Class boundaries
  • B
    Class marks
  • ✓
    Cumulative frequency
  • D
    Variances
Answer
Correct option: C.
Cumulative frequency
(c)
Total number of observations which are below a certain value are known as cumulative frequency.
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MCQ 131 Mark
The abscissa of the point of intersection of the Less Then Type and of the more Than Type cumulative frequency curved of a grouped data gives its
  • A
    mean
  • ✓
    median
  • C
    mode
  • D
    none of these
Answer
Correct option: B.
median
(b)
The abscissa of the point of intersection of the Less Than Type and of the More Than Type cumulative frequency curved of a grouped data give its median.
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MCQ 141 Mark
The cumulative frequency table is useful in determining the
  • A
    mean
  • ✓
    median
  • C
    mode
  • D
    all the these
Answer
Correct option: B.
median
(b)
The cumulative frequency table is useful in determining the median.
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MCQ 151 Mark
Consider the following frequency distribution:
Class0-1010-2020-3030-4040-5050-60
Frequency391530185

The modal class is
  • A
    $10-20$
  • B
    $20-30$
  • ✓
    $30-40$
  • D
    $50-60$
Answer
Correct option: C.
$30-40$
(c)
The class $30-40$ has maximum frequency. So, the modal class is $30-40$.
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MCQ 161 Mark
Which of the following measures of central tendency is influenced by extreme values?
  • ✓
    Mean
  • B
    Median
  • C
    Mode
  • D
    None of these
Answer
Correct option: A.
Mean
(a)
Only mean is affected by extreme values, while both median and mode remain unaffected.
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MCQ 171 Mark
The median and mode of a frequency distribution are 26 and 29 respectively. Then, the mean is
  • A
    27.5
  • ✓
    24.5
  • C
    28.4
  • D
    25.8
Answer
Correct option: B.
24.5
(b)
$\because$ Mode $=3$ median -2 mean
$\Rightarrow 2$ mean $=3$ median - mode
$\Rightarrow 2$ mean $=3 \times 26-29=49$
$\Rightarrow$ Mean $=\frac{49}{2}=24.5$
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MCQ 181 Mark
The mean and mode of a frequency distribution are 28 and 16 respectively. The median is
  • A
    22
  • B
    23.5
  • ✓
    24
  • D
    24.5
Answer
Correct option: C.
24
(c)
$\because 3$ median $=$ mode +2 mean
3 median $=16+2 \times 28=72$
Median $=\frac{72}{3}=24$
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MCQ 191 Mark
For a symmetrical frequency distribution, we have
  • A
    mean $<$ mode $<$ median
  • B
    mean $>$ mode $>$ median
  • ✓
    mean $=$ mode $=$ median
  • D
    mode $=\frac{1}{2}($ mean + median $)$
Answer
Correct option: C.
mean $=$ mode $=$ median
(c)
We must have, mean $=$ mode $=$ median.
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MCQ 201 Mark
The mean of $2,7,6$ and $x$ is 15 and the mean of $18,1,6, x$ and $y$ is 10 . What is the value of $y$ ?
  • A
    5
  • B
    10
  • ✓
    20
  • D
    30
Answer
Correct option: C.
20
(c)
We have $\left(\frac{2+7+6+x}{4}\right)=5 \Rightarrow 15+x=20$
$\Rightarrow x=20-15=5$
Also, $\left(\frac{18+1+6+x+y}{5}\right)=10 \Rightarrow 25+5+y$ $=50$
$
\Rightarrow y=50-30=20
$
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MCQ 211 Mark
If the media of the data $4,7, x -1, x -3,16,25$ written in ascending order, is $13$ then $x$ is equal to
  • A
    $13$
  • B
    $14$
  • ✓
    $15$
  • D
    $16$
Answer
Correct option: C.
$15$
Clearly, median of $6$ observations
$=$ Mean of $3^{\text {rd }}$ and $4^{\text {th }}$ observations
$=\frac{(x-1)+(x-3)}{2}$
$=\frac{2 x-4}{2}$
$=x-2$
$\therefore x-2=13 $
$\Rightarrow x=13+2$
$=15$
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MCQ 221 Mark
The mean of $20$ numbers is zero of them, at the most, how many may be greater then zero?
  • A
    $0$
  • B
    $1$
  • C
    $10$
  • ✓
    $19$
Answer
Correct option: D.
$19$
$\text { Mean of } 20 \text { numbers }=0$
$\therefore \text { Sum of } 20 \text { numbers }=0 \times 20=0$
It is possible that $19$ of these numbers may be positive and if their sum is a, the $20^{\text {th }}$ number is $(-a)$.
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MCQ 231 Mark
The median of first 8 prime numbers is
  • A
    7
  • ✓
    9
  • C
    11
  • D
    13
Answer
Correct option: B.
9
(b)
First 8 prime numbers are $2,3,5,7,11,13,17,19$ Required mean $=$ mean of fourth and fifth observations
$
=\frac{7+11}{2}=\frac{18}{2}=9
$
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MCQ 241 Mark
The median of a frequency distribution is found graphically with the help of
  • A
    a histogram
  • B
    a frequency curve
  • C
    a frequency polygon
  • ✓
    ogives
Answer
Correct option: D.
ogives
(d)
The median of a frequency distribution is found graphically with the help of ogives.
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MCQ 251 Mark
If the mean and median of a set of numbers are 8.9 and 9 respectively then the mode will be
  • A
    7.2
  • B
    8.2
  • ✓
    9.2
  • D
    10.2
Answer
Correct option: C.
9.2
(c)
$\because$ Mode $=(3$ median $)-(2$ mean $)$
$
=(3 \times 9-2 \times 8.9)=27-17.8=9.2
$
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MCQ 261 Mark
Median $=$ ?
  • ✓
    $l +\left\{ h \times \frac{\left(\frac{ N }{2}- cf \right)}{ f }\right\}$
  • B
    $1+\left\{ h \times \frac{\left( cf -\frac{ N }{2}\right)}{ f }\right\}$
  • C
    $l -\left\{ h +\frac{\left(\frac{ N }{2}- cf \right)}{ f }\right\}$
  • D
    None of these.
Answer
Correct option: A.
$l +\left\{ h \times \frac{\left(\frac{ N }{2}- cf \right)}{ f }\right\}$
(a)
Median $=1+\left\{ h \times \frac{\left(\frac{ N }{2}- cf \right)}{ f }\right\}$
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MCQ 271 Mark
The relation between mean, mode and median is
  • A
    mode $=(3 \times$ mean $)-(2 \times$ median $)$
  • ✓
    mode $=(3 \times$ median $)-(2 \times$ mean $)$
  • C
    median $=(3 \times$ mean $)-(2 \times$ mode $)$
  • D
    mean $=3 \times$ median $-(2 \times$ mode $)$
Answer
Correct option: B.
mode $=(3 \times$ median $)-(2 \times$ mean $)$
(b)
Relation between mean, mode and median is mode $=(3 \times$ median $)-(2 \times$ mean $)$
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MCQ 281 Mark
The mode of a frequency distribution is obtained graphically from
  • A
    a frequency curve
  • B
    a frequency polygon
  • ✓
    a histogram
  • D
    an ogive
Answer
Correct option: C.
a histogram
(c)
Mode of a frequency distribution can be obtained graphically from a histogram.
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MCQ 291 Mark
Which of the following cannot be determined graphically?
  • ✓
    Mean
  • B
    Median
  • C
    Mode
  • D
    None of these
Answer
Correct option: A.
Mean
(a)
Mean cannot be determined graphically.
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MCQ 301 Mark
Which of the following is not a measure of central tendency?
  • A
    Mean
  • B
    Median
  • C
    Mode
  • ✓
    Range
Answer
Correct option: D.
Range
(d)
Range is not a measure of central tendency.
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M.C.Q (1 Marks) - Maths STD 10 Questions - Vidyadip