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Mean, Median, Mode of Grouped Data Maths - Mean, Median, Mode of Grouped Data

CBSE - STD 10 - Maths (CBSE - English Medium). 144 questions in this chapter.

Question types

Mean, Median, Mode of Grouped Data question types

144 questions across 5 question groups — pick any mix to generate a Maths paper with step-by-step answer keys.

144
Questions
5
Question groups
5
Question types
Sample Questions

Mean, Median, Mode of Grouped Data questions

One sample from each question group in this chapter. Select any group above to see the full set with answer keys.

Q 1M.C.Q (1 Marks)1 Mark
Median =?
  • ✓
    $\text{l+}\begin{Bmatrix}\text{h}\times\frac{\Big(\frac{\text{N}}{2}-\text{cf}\Big)}{\text{f}}\end{Bmatrix}$
  • B
    $\text{l+}\begin{Bmatrix}\text{h}\times\frac{\Big(\text{cf}-\frac{\text{N}}{2}\Big)}{\text{f}}\end{Bmatrix}$
  • C
    $\text{l}-\begin{Bmatrix}\text{h}\times\frac{\Big(\frac{\text{N}}{2}-\text{cf}\Big)}{\text{f}}\end{Bmatrix}$
  • D
    None of these.

Answer: A.

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Q 2M.C.Q (1 Marks)1 Mark
The relation between mean, mode and median is:
  • A
    Mode = (3 × mean) − (2 × median)
  • ✓
    Mode = (3 × median) − (2 × mean)
  • C
    Mode = (3 × mean) − (2 × mode)
  • D
    Mode = (3 × median) − (2 × mode)

Answer: B.

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Q 3M.C.Q (1 Marks)1 Mark
Each question consists of two statements, namely, Assertion (A) and Reason (R). For selecting the correct answer: use the following code:
Assertion (A)
Consider the following frequency distribution:
Class interval
3-6
6-9
9-12
12-15
15-18
18-21
Frequency
2
5
21
23
10
12
The mode of the above data is 12.4.
Reason (R)
The value of the variable which occurs most often is the mode.
  • A
    Both Assertion (A) and Reason (R) are true and Reason (R) is a correct explanation of Assertion (A).
  • ✓
    Both Assertion (A) and Reason (R) are true but Reason (R) is a not a correct explanation of Assertion (A).
  • C
    Assertion (A) is true and Reason (R) is false.
  • D
    Assertion (A) is false and Reason (R) is true

Answer: B.

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Q 4M.C.Q (1 Marks)1 Mark
Each question consists of two statements, namely, Assertion (A) and Reason (R). For selecting the correct answer: use the following code:
Assertion (A) Reason (R)
If the median and mode of a frequency distribution are 150 and 154 respectively, then its mean is 148. Mean, median and mode of a frequency distribution are related as: mode = 3median - 2mean
  • ✓
    Both Assertion (A) and Reason (R) are true and Reason (R) is a correct explanation of Assertion (A).
  • B
    Both Assertion (A) and Reason (R) are true but Reason (R) is a not a correct explanation of Assertion (A).
  • C
    Assertion (A) is true and Reason (R) is false.
  • D
    Assertion (A) is false and Reason (R) is true.

Answer: A.

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Q 61 Marks Question1 Mark
Consider the following frequency distribution:
Class
0-5
6-11
12-17
18-23
24-29
Frequency
13
10
15
8
11
Find the upper limit of the median class.
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Q 81 Marks Question1 Mark
The annual profit earned by 30 shops of a shopping complex in a locality are recorded in the table shown below:
Profit (in lakhs Rs.)
Number of shops
More than or equal to 5
30
More than or equal to 10
28
More than or equal to 15
16
More than or equal to 20
14
More than or equal to 25
10
More than or equal to 30
7
More than or equal to 35
3
If we draw the frequency distribution table for the above data, find the frequency corresponding to the class 20-25.
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Q 91 Marks Question1 Mark
In the table given below, the times taken by 120 athletes to run a 100 m hurdle race are given:
Class
13.8-14
14-14.2
14.2-14.4
14.4-14.6
14.6-14.8
14.8-15
Frequency
2
4
15
54
25
20
Find the number of athletes who completed the race in less than 14.6 seconds.
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Q 102 Marks Questions2 Marks
Following is the distribution of marks of 70 students in a periodical test:
Marks
Less than 10
Less than 20
Less than 30
Less than 40
Less than 50
Number of students
3
11
28
48
70
Draw a cumulative frequency for the above data.
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Q 122 Marks Questions2 Marks
The distributions X and Y with total number of observations 36 and 64, and mean 4 and 3 respectively are combined. What is the mean of resulting distribution X + Y?
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Q 142 Marks Questions2 Marks
Find the mean of the following frequency distribution using step-deviation method:
Class
84-90
90-96
96-102
102-108
108-114
114-120
Frequency
15
22
20
18
20
25
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Q 153 Marks Question3 Marks
What is the cumulative frequency of the modal class of the following distribution?
Class
3-6
6-9
9-12
12-15
15-18
18-21
21-24
Frequency
7
13
10
23
4
21
16
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Q 173 Marks Question3 Marks
In a frequency distribution table with 12 classes, the class width is 2.5 and the lowest class boundary is 8.1, then what is the upper class boundary of the highest class?
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Q 183 Marks Question3 Marks
The observations 29, 32, 48, 50, x, x + 2, 72, 78, 84, 95 are arranged in ascending order. What is the value of x if the median of the data is 63?
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Q 193 Marks Question3 Marks
??The following frequency distribution gives the monthly consumption of electricity of 64 consumers of locality.
Monthly consumption (in units)
65-85
85-105
105-125
125-145
145-165
165-185
Number of consumers
4
5
13
20
14
8
Form a 'more than type' cumulative frequency distribution.
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Q 205 Marks Questions5 Marks
Calculate the missing frequency from the following distribution, it being given that the median of the distribution is 24.
Age (in years)
0-10
10-20
20-30
30-40
40-50
Number of persons
5
25
?
18
7
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Q 215 Marks Questions5 Marks
Given below is the distribution of total household expenditure of 200 manual workers in a city:
Expenditure (in Rs) No. of manual workers
1000-1500 24
1500-2000 40
2000-2500 31
2500-3000 28
3000-3500 32
3500-4000 23
4000-4500 17
4500-5000 5
Find the expenditure done by maximum number of manual workers.
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Q 235 Marks Questions5 Marks
The following are the ages of 300 patients getting medical treatment in a hospital on a particular day:
Age (in years)
10-20
20-30
30-40
40-50
50-60
60-70
Number of patients
60
42
55
70
53
20
Form a 'less than type' cumulative frequency distribution.
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Q 245 Marks Questions5 Marks
In an annual examination, marks (out of 90) obtained by students of class X in mathematics are given below:
Marks obtained 0-15 15-30 30-45 45-60 60-75 75-90
Number of students 2 4 5 20 9 10
Find the mean marks.
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