Statistics: 1 mark Questions (CBSE Class 10)

While calculating mean of a grouped frequency distribution using step deviation method $\left(u=\frac{x-a}{h}\right)$ it was found that $\overline{x}$ = 62, a = 47.5, h = 5. The value of $\overline{u}$ is :

1. (A)3
2. (B)14.5
3. (C)2.9
4. (D)3.1

Assertion (A) : Median of a data is the value of $\frac{N}{2}$, where N represents sum of all frequencies.
Reason (R) : Median divides the whole distribution in two equal parts.

1. (A)Both, Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of the Assertion (A).
2. (B)Both, Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of the Assertion (A).
3. (C)Assertion (A) is true, but Reason (R) is false.
4. (D)Assertion (A) is false, but Reason (R) is true.

If the mean and mode of a data are 12 and 21 respectively, then its median is :

1. (A)6
2. (B)13.5
3. (C)15
4. (D)14

The mean and median of a frequency distribution are 43 and 43.4 respectively. The mode of the distribution is :

1. (A)43.4
2. (B)42.4
3. (C)44.2
4. (D)49.3

The median and mode of a distribution are 25.2 and 26.1 respectively. The mean of the distribution is :

1. (A)24.75
2. (B)24.25
3. (C)24.3
4. (D)25.5

Mean and Median of a frequency distribution are 43 and 40 respectively. The value of mode is

1. (A)34
2. (B)43
3. (C)38.5
4. (D)41.5

While calculating mean of a grouped frequency distribution, step deviation method was used $\left(\frac{x-a}{h}=u\right)$. It was found that $\bar{x}=64$, h = 5 and a = 62.5. The value of $\bar{u}$ is

1. (A)0.5
2. (B)1.5
3. (C)0.3
4. (D)7.5

The class mark of the median class of the following data is :
Class Interval: 10 – 25, 25 – 40, 40 – 55, 55 – 70, 70 – 85, 85 – 100
Frequency: 2, 3, 7, 6, 6, 6

1. (A)40
2. (B)55
3. (C)47.5
4. (D)62.5

The following distribution shows the number of runs scored by some batsmen in test matches :
Runs Scored: 3000 – 4000, 4000 – 5000, 5000 – 6000, 6000 – 7000
Number of Batsmen: 5, 10, 9, 8
The lower limit of the modal class is :

1. (A)3000
2. (B)4000
3. (C)5000
4. (D)6000

In the formula of mode given by mode $=l+\frac{f_1-f_0}{2f_1-f_0-f_2}\times h$,
$f_1$ denotes the :

1. (A)frequency of the modal class
2. (B)frequency of class preceding modal class
3. (C)frequency of class succeeding modal class
4. (D)cumulative frequency of modal class

For a distribution, if mean = median = a, then its mode is :

1. (A)$3a$
2. (B)$2a$
3. (C)$a$
4. (D)$0$

The following table shows the marks scored by 23 students of a class.
Marks: 0 – 10, 10 – 20, 20 – 30, 30 – 40, 40 – 50
Number of Students: 5, 3, 4, 8, 3
The lower limit of the modal class is :

1. (A)10
2. (B)20
3. (C)30
4. (D)40

For a distribution, if mean = 15 and mode = 12, then its median is :

1. (A)12
2. (B)13
3. (C)14
4. (D)15

Assertion (A) : Median marks of students in a class test is 16. It means half of the class got marks less than 16.
Reason (R) : Median divides the distribution in two equal parts.

1. (A)Both, Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).
2. (B)Both, Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of Assertion (A).
3. (C)Assertion (A) is true, but Reason (R) is false.
4. (D)Assertion (A) is false, but Reason (R) is true.

Which of the following depends on all observations of a given data ?

1. (A)Median
2. (B)Mean
3. (C)Range
4. (D)Mode

To calculate mean of a grouped data, Rahul used assumed mean method. He used d = $(x-A)$, where A is assumed mean. Then $\overline{x}$ is equal to

1. (A)A + $\overline{d}$
2. (B)A + h$\overline{d}$
3. (C)h (A + $\overline{d}$)
4. (D)A $-$ h$\overline{d}$

Mode and Mean of a data are $15x$ and $18x$, respectively. Then the median of the data is :

1. (A)$x$
2. (B)$11x$
3. (C)$17x$
4. (D)$34x$

What is the mode of a data if median and mean of the same data are $9.6$ and $10.5$, respectively ?

1. (A)$7.8$
2. (B)$12.3$
3. (C)$8.4$
4. (D)$7$

If the mean of $2,9,x+6,2x+3,5,10,5$ is 7, then the value of $x$ is :

1. (A)9
2. (B)6
3. (C)5
4. (D)3

The mean of seven observations is 17. If the mean of the first four observations is 15 and that of the last four observations is 18, then the fourth observation is :

1. (A)14
2. (B)13
3. (C)12
4. (D)10

The cumulative frequency for calculating median is obtained by adding the frequencies of all the :

1. (A)classes up to the median class
2. (B)classes following the median class
3. (C)classes preceding the median class
4. (D)all classes

If mean and median of given set of observations are 10 and 11 respectively, then the value of mode is :

1. (A)10.5
2. (B)8
3. (C)13
4. (D)21

If mean and mode of given set of observations are 10 and 13 respectively, then the value of median is :

1. (A)19
2. (B)4
3. (C)11
4. (D)43

If mode and median of given set of observations are 13 and 11 respectively, then the value of mean is :

1. (A)17
2. (B)7
3. (C)10
4. (D)28

If $x$ median + $y$ mean = $z$ mode; is the empirical relationship between mean, median and mode, then the value of $x+y+z$ is

1. (A)6
2. (B)3
3. (C)2
4. (D)1

Following data shows the marks obtained by 100 students in a class test :
Marks obtained: 20, 29, 28, 33, 42, 38, 43, 25
Number of students: 6, 28, 24, 15, 2, 4, 1, 20
The median will be the average of which two observations ?

1. (A)29 and 33
2. (B)25 and 28
3. (C)28 and 29
4. (D)33 and 38

If the mode of some observations is 10 and sum of mean and median is 25, then the mean and median respectively are

1. (A)12 and 13
2. (B)13 and 12
3. (C)10 and 15
4. (D)15 and 10

If the maximum number of students has obtained 52 marks out of 80, then

1. (A)52 is the mean of the data.
2. (B)52 is the median of the data.
3. (C)52 is the mode of the data.
4. (D)52 is the range of the data.

The mean and median of a statistical data are 21 and 23 respectively. The mode of the data is :

1. (A)27
2. (B)22
3. (C)17
4. (D)23

If a certain variable $x$ divides a statistical data arranged in order into two equal parts, then the value of $x$ is called the :

1. (A)mean
2. (B)median
3. (C)mode
4. (D)range

The annual rainfall record of a city for 66 days is given in the following table :
Rainfall (in cm) : 0–10, 10–20, 20–30, 30–40, 40–50, 50–60
Number of days : 22, 10, 8, 15, 5, 6
The difference of upper limits of modal and median classes is :

1. (A)10
2. (B)15
3. (C)20
4. (D)30

If the mean and median of a data are 10 and 11 respectively, then mode of the data is :

1. (A)12
2. (B)8
3. (C)20
4. (D)13

If for a distribution, ${\sum }_1^n{f}_i{x}_i=132+5p$, ${\sum }_1^n{f}_i=20$ and the mean of the distribution is 8.1, then the value of p is :

1. (A)3
2. (B)6
3. (C)4
4. (D)5

The following distribution gives the daily income of 50 workers of a factory :
Income (in ₹): 400–424, 425–449, 450–474, 475–499, 500–524
Number of workers: 12, 14, 8, 6, 10
The lower limit of the modal class is :

1. (A)425
2. (B)449
3. (C)$424.5$
4. (D)$425.5$

The median group in the following frequency distribution is :
Class: 0–10, 10–20, 20–30, 30–40, 40–50, 50–60
Frequency: 5, 8, 20, 15, 7, 5

1. (A)10–20
2. (B)20–30
3. (C)30–40
4. (D)40–50

The mode and mean of a data are 7 and 8 respectively. Then, the median of the data is :

1. (A)$\frac{23}{3}$
2. (B)$\frac{13}{3}$
3. (C)$\frac{1}{13}$
4. (D)33

If the mean and mode of a frequency distribution are 28 and 16 respectively, then its median is :

1. (A)22
2. (B)23.5
3. (C)24
4. (D)24.5

If the difference of mode and median of a data is 24, then the difference of median and mean of the same data is :

1. (A)8
2. (B)12
3. (C)24
4. (D)34

In a frequency distribution, the mid-value of a class is 10 and the width of the class is 6. The lower limit of the class is :

1. (A)6
2. (B)7
3. (C)8
4. (D)12

For some data $x_1,x_2,......x_n$ with respective frequencies $f_1,f_2,.....f_n$, the value of ${\sum }_1^n{f}_i\left(x_i-\bar{x}\right)$ is equal to :

1. (A)$n\bar{x}$
2. (B)1
3. (C)$\sum f_i$
4. (D)0

The middle most observation of every data arranged in order is called :

1. (A)mode
2. (B)median
3. (C)mean
4. (D)deviation

If value of each observation in a data is increased by 2, then median of the new data

1. (A)increases by 2
2. (B)increases by 2n
3. (C)remains same
4. (D)decreases by 2

After an examination, a teacher wants to know the marks obtained by maximum number of the students in her class. She requires to calculate _____ of marks.

1. (A)median
2. (B)mode
3. (C)mean
4. (D)range

The mean of five observations is 15. If the mean of first three observations is 14 and that of the last three observations is 17, then the third observation is

1. (A)20
2. (B)19
3. (C)18
4. (D)17

If the mean of five observations $x$, $x+2$, $x+4$, $x+6$ and $x+8$ is 11, then the value of $x$ is :

1. (A)4
2. (B)7
3. (C)11
4. (D)6

The mean of five numbers is 15. If we include one more number, the mean of six numbers becomes 17. The included number is :

1. (A)27
2. (B)37
3. (C)17
4. (D)25

If the difference of mode and median of a data is 24, then the difference of its median and mean is :

1. (A)12
2. (B)24
3. (C)8
4. (D)36

If the mean of 6, 7, p, 8, q, 14 is 9, then

1. (A)$p-q=19$
2. (B)$p+q=19$
3. (C)$p-q=21$
4. (D)$p+q=21$

For the data 2, 9, $x+6$, $2x+3$, 5, 10, 5; if the mean is 7, then the value of $x$ is :

1. (A)9
2. (B)6
3. (C)5
4. (D)3

If the mean and mode of a data are 24 and 12 respectively, then its median is :

1. (A)25
2. (B)18
3. (C)20
4. (D)22

If the mean of the first $n$ natural numbers is $\frac{5n}{9}$, then the value of $n$ is :

1. (A)5
2. (B)4
3. (C)9
4. (D)10

Median and Mode of a distribution are 25 and 21 respectively. Mean of the data using empirical relationship is :

1. (A)27
2. (B)29
3. (C)18
4. (D)$\frac{29}{3}$

The mode of the numbers 2, 3, 3, 4, 5, 4, 4, 5, 3, 4, 2, 6, 7 is :

1. (A)2
2. (B)3
3. (C)4
4. (D)5

The median class for the data given below is :
Class: 20 – 40, 40 – 60, 60 – 80, 80 – 100, 100 – 120
Frequency: 10, 12, 14, 13, 17

1. (A)80 – 100
2. (B)20 – 40
3. (C)40 – 60
4. (D)60 – 80

Mean and median of some data are 32 and 30 respectively. Using empirical relation, mode of the data is :

1. (A)36
2. (B)26
3. (C)30
4. (D)20

The time, in seconds, taken by 150 athletes to run a 100 m hurdle race are tabulated below :
Time (sec.): 13-14, 14-15, 15-16, 16-17, 17-18, 18-19
Number of Athletes: 2, 4, 5, 71, 48, 20
The number of athletes who completed the race in less than 17 seconds is

1. (A)11
2. (B)71
3. (C)82
4. (D)68

The median of first seven prime numbers is

1. (A)5
2. (B)7
3. (C)11
4. (D)13

If the mean of 6, 7, $x$, 8, y, 14 is 9, then

1. (A)$x+y=21$
2. (B)$x+y=19$
3. (C)$x-y=19$
4. (D)$x-y=21$

The mean of first ten natural numbers is

1. (A)5.5
2. (B)55
3. (C)45
4. (D)4.5

The Empirical relation between the three measures of central tendency is

1. (A)Mode = 3 Mean – 2 Median
2. (B)Mode = 2 Median – 3 Mean
3. (C)Mode = 2 Mean – 3 Median
4. (D)Mode = 3 Median – 2 Mean

The median of first 10 natural numbers is

1. (A)5
2. (B)6
3. (C)5.5
4. (D)6.5

The distribution below gives the marks obtained by 80 students on a test :
Marks: Less than 10, Less than 20, Less than 30, Less than 40, Less than 50, Less than 60
Number of Students: 3, 12, 27, 57, 75, 80
The modal class of this distribution is :

1. (A)10 – 20
2. (B)20 – 30
3. (C)30 – 40
4. (D)50 – 60

If the value of each observation of a statistical data is increased by 3, then the mean of the data

1. (A)remains unchanged
2. (B)increases by 3
3. (C)increases by 6
4. (D)increases by 3n

The empirical relation between the mode, median and mean of a distribution is :

1. (A)Mode = 3 Median – 2 Mean
2. (B)Mode = 3 Mean – 2 Median
3. (C)Mode = 2 Median – 3 Mean
4. (D)Mode = 2 Mean – 3 Median

For the following distribution :
Class: 0-5, 5-10, 10-15, 15-20, 20-25
Frequency: 10, 15, 12, 20, 9
The sum of lower limits of median class and modal class is :

1. (A)15
2. (B)25
3. (C)30
4. (D)35

For the following distribution :
Marks Below: 10, 20, 30, 40, 50, 60
Number of Students: 3, 12, 27, 57, 75, 80
The modal class is :

1. (A)10-20
2. (B)20-30
3. (C)30-40
4. (D)50-60

If the mean and the median of a data are 12 and 15 respectively, then its mode is :

1. (A)13.5
2. (B)21
3. (C)6
4. (D)14

If every term of the statistical data consisting of n terms is decreased by 2, then the mean of the data :

1. (A)decreases by 2
2. (B)remains unchanged
3. (C)decreases by 2n
4. (D)decreases by 1

If the mean and the mode of a distribution are 15 and 18 respectively, then the median of the distribution is :

1. (A)17
2. (B)15
3. (C)16
4. (D)18