Mode is:
- ALeast frequent value.
- BMiddle most value.
- ✓Most frequent value.
- DNone of these.
Answer: C.
View full solution →Question types
Statistics question types
270 questions across 8 question groups — pick any mix to generate a Maths paper with step-by-step answer keys.
270
Questions
8
Question groups
5
Question types
01
M.C.Q (1 Marks)
110 Q→02Assertion (A) & Reason (B) MCQ
4 Q→03Fill In The Blanks[1 Marks ]
15 Q→041 Marks Question
22 Q→052 Marks Questions
13 Q→063 Marks Question
46 Q→075 Marks Questions
50 Q→08Case study (4 Marks)
10 Q→Sample Questions
Statistics questions
One sample from each question group in this chapter. Select any group above to see the full set with answer keys.
Consider the following frequency distribution:
The difference of the upper limit of the median class and the lower limit of the modal class is:
| Class: | 65-85 | 85-105 | 105-125 | 125-145 | 145-165 | 165-185 | 185-205 |
| Frequency: | 4 | 5 | 13 | 20 | 14 | 7 | 4 |
- A0
- B19
- ✓20
- D38
Answer: C.
View full solution →In the formula $\bar{\text{x}}=\text{a}+\text{h}\Big(\frac{1}{\text{N}}\sum\text{f}_\text{i}\text{u}_\text{i}\Big),$ for finding the mean of grouped frequency distribution $\text{u}_\text{i}=$
- A$\frac{\text{x}_\text{i}+\text{a}}{\text{h}}$
- B$\text{h}(\text{x}_\text{i}-\text{a})$
- ✓$\frac{\text{x}_\text{i}-\text{a}}{\text{h}}$
- D$\frac{\text{a}-\text{x}_\text{i}}{\text{h}}$
Answer: C.
View full solution →If the mode of the data : 16, 15, 17, 16, 15, x, 19, 17, 14 is 15, then x =
- ✓15
- B16
- C17
- D19
Answer: A.
View full solution →If the difference of mode and median of a data is 24, then the difference of median and mean is:
- ✓12
- B24
- C8
- D36
Answer: A.
View full solution →Statement-1 (A): If a = 55.5, N = 100, h = 20, $\Sigma f_i u_i=60$, then $\bar{X}=67.5$.
Statement-2 (R): Mean of a grouped data is given by $\bar{X}=a+h\left(\frac{1}{N} \Sigma f_i u_i\right)$.
Statement-2 (R): Mean of a grouped data is given by $\bar{X}=a+h\left(\frac{1}{N} \Sigma f_i u_i\right)$.
- ✓Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-5
- BStatement-1 is true, Statement-2 is true; Statement-2 is not a correct explanation for Statement-5
- CStatement-1 is true, Statement-2 is false.
- DStatement-1 is false, Statement-2 is true
Answer: A.
View full solution →Statement-1 (A): The mean of 1, 4, 7, 10,..., 301 is 151.
Statement-2 (R): The mean of the series $a, a+d, a+2 d, \ldots, a+2 n d$, is $a+n d$.
Statement-2 (R): The mean of the series $a, a+d, a+2 d, \ldots, a+2 n d$, is $a+n d$.
- ✓Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-4
- BStatement-1 is true, Statement-2 is true; Statement-2 is not a correct explanation for Statement-4
- CStatement-1 is true, Statement-2 is false.
- DStatement-1 is false, Statement-2 is true
Answer: A.
View full solution →Statement-1 (A): The algebraic sum of the deviations of a frequency distribution from its mean is zero.
Statement-2 (R): Mode of a frequency distribution cannot be determined graphically.
Statement-2 (R): Mode of a frequency distribution cannot be determined graphically.
- AStatement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-3
- BStatement-1 is true, Statement-2 is true; Statement-2 is not a correct explanation for Statement-3
- ✓Statement-1 is true, Statement-2 is false.
- DStatement-1 is false, Statement-2 is true
Answer: C.
View full solution →Statement-1 (A): For a moderately asymmetric distribution, Mode - Median = 2 (Median-Mean)
Statement-2 (R): For a symmetric distribution, Mean Median = Mode
Statement-2 (R): For a symmetric distribution, Mean Median = Mode
- AStatement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1
- ✓Statement-1 is true, Statement-2 is true; Statement-2 is not a correct explanation for Statement-1
- CStatement-1 is true, Statement-2 is false.
- DStatement-1 is false, Statement-2 is true
Answer: B.
View full solution →If the mean of 26, 19, 15, 24 and x is x, then median of the data is ____________ .
If a < b < 2a and mean and median of a, b and 2a are 15 and 12 respectively, then a = ____________ .
Given that a, b, c, d are non-zero integers such that a < b < c < d If the mean and median of a, b, c, d are equal to zero, then a =____________ and b = ____________ .
If the average of a, b, c, d is the average of b and c, then the value a -b - c + d is ____________ .
If mode - median = 2, then median - mean = ____________ .
Which measure of central tendency is given by the x-coordinate of the point of intersection of the 'more than' ogive and 'less than' ogive?
Which measure of central tendency can be determine graphically?
Find the mode of the following data:
3, 3, 7, 4, 5, 3, 5, 6, 8, 9, 5, 3, 5, 3, 6, 9, 7, 4
3, 3, 7, 4, 5, 3, 5, 6, 8, 9, 5, 3, 5, 3, 6, 9, 7, 4
Write the modal class for the following frequency distribution:
|
Class
|
10-15
|
15-20
|
20-25
|
25-30
|
30-35
|
35-40
|
|
Frequency
|
30
|
35
|
75
|
40
|
30
|
15
|
What is the value of the median of the data using the graph in the following figure of less than ogive and more than ogive?
The monthly profits (in Rs.) of 100 shops are distributed as follows:
Draw the frequency polygor it.
| Profits per shop | 0-50 | 50-100 | 100-150 | 150-200 | 200-250 | 250-300 |
| No. of shops | 12 | 18 | 27 | 20 | 17 | 6 |
Find the mode of the following distribution.
|
Class-interval
|
25-30
|
30-35
|
35-40
|
40-45
|
45-50
|
50-60
|
|
Frequency
|
25
|
34
|
50
|
42
|
38
|
14
|
Find the mode of the following distribution:
|
Class-interval
|
0-10
|
10-20
|
20-30
|
30-40
|
40-50
|
50-60
|
60-70
|
70-80
|
|
Frequency
|
5
|
8
|
7
|
12
|
28
|
20
|
10
|
10
|
n the graphical representation of a frequency distribution, if the distance between mode and mean isk times the distance between median and mean, then write the value of k.
Find the mode of the following distribution.
|
Class-interval
|
10-15
|
15-20
|
02-25
|
25-30
|
30-35
|
35-40
|
|
Frequency
|
30
|
45
|
75
|
35
|
25
|
15
|
Find the mean of each of the following frequency distributions:
View full solution →|
Class interval
|
$10-30$
|
$30-50$
|
$50-70$
|
$70-90$
|
$90-110$
|
$110-130$
|
|
Frequency
|
$5$
|
$8$
|
$12$
|
$20$
|
$3$
|
$2$
|
The marks scored by 750 students in an examination are given in the form of a frequency distribution table:
Prepare a cumulative frequency table by less than method and
draw on ogive.
|
Marks
|
No. of students
|
|
600-640
|
16
|
|
640-680
|
45
|
|
680-720
|
156
|
|
720-760
|
284
|
|
760-800
|
172
|
|
800-840
|
59
|
|
840-880
|
18
|
draw on ogive.
The following table gives the number of children of $150$ families in a village:
Find the average number of children per family.
View full solution →|
No of children (x)
|
$0$
|
$1$
|
$2$
|
$3$
|
$4$
|
$5$
|
|
No of familles (f)
|
$10$
|
$21$
|
$55$
|
$42$
|
$15$
|
$7$
|
Find the mean of each of the following frequency distributions:
View full solution →|
Class interval
|
$0-10$
|
$10-20$ | $20-30$ | $30-40$ | $40-50$ |
|
Frequency
|
$9$ | $12$ |
$15$
|
$10$
|
$14$ |
The number of students absent in a class were recorded every day for $120 $days and the:
View full solution →|
No of Students absent (x)
|
$0$
|
$1$
|
$2$
|
$3$
|
$4$
|
$5$
|
$6$
|
$7$
|
|
No of days (y)
|
$1$
|
$4$
|
$10$
|
$50$
|
$34$
|
$15$
|
$4$
|
$2$
|
An incomplete distribution is given as follows:
You are given that the median value is 35 and the sum of all the frequencies is 170. Using the median formula, fill up the missing frequencies.
|
Variable
|
0-10
|
10-20
|
20-30
|
30-40
|
40-50
|
50-60
|
60-70
|
|
Frequency
|
10
|
20
|
?
|
40
|
?
|
25
|
15
|
The table below shows the daily expenditure on food of 25 households in a locality:
|
Daily expenditure (in Rs.)
|
100-150
|
150-200
|
200-250
|
250-.300
|
300-350
|
|
Number of households
|
4
|
5
|
12
|
2
|
3
|
The following table gives the frequency distribution of married women by age at marriage:
Calculate the median and interpret the results.
|
Age (in years)
|
Frequency
|
|
15-19
|
53
|
|
20-24
|
140
|
|
25-29
|
98
|
|
30-34
|
32
|
|
35-39
|
12
|
|
40-44
|
9
|
|
45-49
|
5
|
|
50-54
|
3
|
|
55-59
|
3
|
|
60 and above
|
2
|
A survey regarding the height (in cm) of 51 girls of class X of a school was conducted and the following data was obtained.
Find the median height.
|
Hight in cm
|
Number of girls
|
|
Less than 140
|
4
|
|
Less than 145
|
11
|
|
Less than 150
|
29
|
|
Less than 155
|
40
|
|
Less than 160
|
46
|
|
Less than 165
|
51
|
Find the missing frequency (p) for the following distribution whose mean is 7.68.
| x | 3 | 5 | 7 | 9 | 11 | 13 |
| f | 6 | 8 | 15 | P | 8 | 4 |
A 100 race was organized in a school sports eet. The tie was recorded with the help of a stopwatch. A table shown below describes the tie in which the race was finished by the nuber of student.
(i) The lower liit of the odal class, is
(a) 30$\quad$ (b) 40$\quad$ (c) 60$\quad$ (d) 20
(ii) The average tie taken by the student to finish the race, is
(a) 40$\quad$ (b) 47$\quad$ (c) 50$\quad$ (d) 30
(iii) The cuulative frequency table is constructed to deterine
(a) Mean$\quad$ (b) Mode$\quad$ (c) Median$\quad$ (d) All of the above
(iv) How any students finished the race within 1 inute
(a) 30$\quad$ (b) 40$\quad$ (c) 19$\quad$ (d) 29
View full solution →| Tie (in sec.) | 0-20 | 20-40 | 40-60 | 60-80 | 80-100 |
| No. of students | 6 | 13 | 10 | 3 | 8 |
(i) The lower liit of the odal class, is
(a) 30$\quad$ (b) 40$\quad$ (c) 60$\quad$ (d) 20
(ii) The average tie taken by the student to finish the race, is
(a) 40$\quad$ (b) 47$\quad$ (c) 50$\quad$ (d) 30
(iii) The cuulative frequency table is constructed to deterine
(a) Mean$\quad$ (b) Mode$\quad$ (c) Median$\quad$ (d) All of the above
(iv) How any students finished the race within 1 inute
(a) 30$\quad$ (b) 40$\quad$ (c) 19$\quad$ (d) 29
During edical check up of 35 students of a class, their weights were recorded as follows:
(i) The edian class of the given data is
(a) 40-42$\quad$ (b) 42-44$\quad$ (c) 44-46$\quad$ (d) 46-4
(ii) The lower liit of the odal class is
(a) 42$\quad$ (b) 44$\quad$ (c) 46$\quad$ (d) 48
(iii) The edian weight is
(a) 46.5$\quad$ (b) 47.5$\quad$ (c) 46.2$\quad$ (d) 46.8
(iv) The su of the lower liits of the edian and odal class is
(a) 86$\quad$ (b) 88$\quad$ (c) 90$\quad$ (d) 82
View full solution →| Weight less than (in kg): | 38 | 40 | 42 | 44 | 46 | 48 | 50 | 52 |
| Nuber of students: | 0 | 3 | 5 | 9 | 14 | 28 | 32 | 35 |
(i) The edian class of the given data is
(a) 40-42$\quad$ (b) 42-44$\quad$ (c) 44-46$\quad$ (d) 46-4
(ii) The lower liit of the odal class is
(a) 42$\quad$ (b) 44$\quad$ (c) 46$\quad$ (d) 48
(iii) The edian weight is
(a) 46.5$\quad$ (b) 47.5$\quad$ (c) 46.2$\quad$ (d) 46.8
(iv) The su of the lower liits of the edian and odal class is
(a) 86$\quad$ (b) 88$\quad$ (c) 90$\quad$ (d) 82
| Weight (in kg) | 100-110 | 110-120 | 120-130 | 130-140 | 130-140 |
| No. of wrestlers | 8 | 16 | 10 | 9 | 7 |
Based on the above information answer the following questions:
(i) The upper limit of the modal class is
(a) 110$\quad$ (b) 120$\quad$ (c) 130$\quad$ (d) 140
(ii) The median class is
(a) 110-120$\quad$ (b) 120-130$\quad$ (c) 130-140$\quad$ (d) 140-150
(iii) The difference of the upper limit of the median class and the lower limit of the modal class is
(a) 10$\quad$ (b) 20$\quad$ (c) 30$\quad$ (d) 40
(iv) The modal class is
(a) 110-120$\quad$ (b) 120-130$\quad$ (c) 130-140$\quad$ (d) 140-150
A stopwatch was used to find the tie that it took a group of students to run 100 . The following table exhibits the tie intervals and the nuber of students copleting the 100 race in these intervals:
(i) Estiate the ean tie taken by a student to finish the race.
(a) 54$\quad$ (b) 63$\quad$ (c) 43$\quad$ (d) 50
(ii) What will be the upper liit of odal class?
(a) 20$\quad$ (b) 40$\quad$ (c) 60$\quad$ (d) 80
(iii) The construction of cuulative frequency table is useful in deterining the
(a) Mean$\quad$ (b) Median$\quad$ (c) Mode$\quad$ (d) All of the above
(iv) The su of lower liits of edian class and odal class is
(a) 60$\quad$ (b) 100$\quad$ (c) 80$\quad$ (d) 140
View full solution →| Tie (in sec) | 0-20 | 20-40 | 40-60 | 60-80 | 80-100 |
| No. of students | 8 | 10 | 13 | 6 | 3 |
(i) Estiate the ean tie taken by a student to finish the race.
(a) 54$\quad$ (b) 63$\quad$ (c) 43$\quad$ (d) 50
(ii) What will be the upper liit of odal class?
(a) 20$\quad$ (b) 40$\quad$ (c) 60$\quad$ (d) 80
(iii) The construction of cuulative frequency table is useful in deterining the
(a) Mean$\quad$ (b) Median$\quad$ (c) Mode$\quad$ (d) All of the above
(iv) The su of lower liits of edian class and odal class is
(a) 60$\quad$ (b) 100$\quad$ (c) 80$\quad$ (d) 140
View full solution →
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