The mean and median of a distribution are $14$ and $15$ respectively. The value of mode is :
- A$16$
- ✓$17$
- C$18$
- D$13$
Answer: B.
View full solution →Question types
Stastics question types
295 questions across 8 question groups — pick any mix to generate a Maths paper with step-by-step answer keys.
295
Questions
8
Question groups
5
Question types
01
M.C.Q (1 Marks)
208 Q→02Assertion (A) & Reason (B) MCQ
17 Q→03Fill In The Blanks[1 Marks ]
3 Q→041 Marks Question
30 Q→052 Marks Questions
5 Q→063 Marks Question
14 Q→075 Marks Questions
13 Q→08Case study (4 Marks)
5 Q→Sample Questions
Stastics questions
One sample from each question group in this chapter. Select any group above to see the full set with answer keys.
The marks of $20$ students in a test were as follows : $\{5, 6, 8, 9, 10, 11, 11, 12, 13, 13, 14, 14, 15, 15, 15, 16, 16, 18, 19, 20\}$ The mode is :
- A$20$
- B$10$
- ✓$15$
- D$25$
Answer: C.
View full solution →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$\text{l}-\begin{Bmatrix}\text{h}\times\frac{\Big(\frac{\text{N}}{2}-\text{cf}\Big)}{\text{f}}\end{Bmatrix}$
- DNone of these.
Answer: A.
View full solution →In formula $\overline{\text{x}}=\text{a+h}\frac{\sum\text{f}_i\text{u}_i}{\sum\text{f}_i}$ for finding the mean,$\text{u}_\text{i}=$
- ✓$\frac{\text{x}_\text{i}\text-{a}}{\text{h}}$
- B$\frac{\text{a}-\text{x}_\text{i}}{\text{h}}$
- C$\text{h}(\text{x}_\text{i}-\text{a})$
- D$\frac{\text{x}_\text{i}+\text{a}}{\text{h}}$
Answer: A.
View full solution →The relation between mean, mode and median is :
- AMode $= (3 \times$ mean$) − (2 \times$ median$)$
- ✓Mode $= (3 \times$ median$) − (2 \times$ mean$)$
- CMode $= (3 \times$ mean$) − (2 \times$ mode$)$
- DMode $= (3 \times$ median$) − (2 \times $ mode$)$
Answer: B.
View full solution →Directions : In the following questions, a statement of assertion $(A)$ is followed by a statement of reason $(R).$ Mark the correct choice as :
Assertion : Consider the following frequency distribution :
he mode of the above data is $12.4.$
Reason : The value of the variable which occurs most often is the mode.
Assertion : Consider the following frequency distribution :
| Class interval | $3-6$ | $6-9$ | $9-12$ | $12-15$ | $15-18$ | $18-21$ |
| Frequency | $2$ | $5$ | $21$ | $23$ | $10$ | $12$ |
Reason : The value of the variable which occurs most often is the mode.
- ABoth assertion $(A)$ and reason $(R)$ are true and reason $(R)$ is the correct explanation of assertion $(A)$.
- ✓Both assertion $(A)$ and reason $(R)$ are true but reason $(R)$ is not the correct explanation of assertion $(A)$.
- CAssertion $(A)$ is true but reason $(R)$ is false.
- DAssertion $(A)$ is false but reason $(R)$ is true.
Answer: B.
View full solution →Directions : In the following questions, a statement of assertion $(A)$ is followed by a statement of reason $(R).$ Mark the correct choice as:
Assertion : If the value of mode and mean is $60$ and $66$ respectively, then the value of median is $64.$
Reason : Median $=\ ($mode $+\ 2$ mean$)$
Assertion : If the value of mode and mean is $60$ and $66$ respectively, then the value of median is $64.$
Reason : Median $=\ ($mode $+\ 2$ mean$)$
- ABoth assertion $(A)$ and reason $(R)$ are true and reason $(R)$ is the correct explanation of assertion $(A)$.
- BBoth assertion $(A)$ and reason $(R)$ are true but reason $(R)$ is not the correct explanation of assertion $(A)$.
- ✓Assertion $(A)$ is true but reason $(R)$ is false.
- DAssertion $(A)$ is false but reason $(R)$ is true.
Answer: C.
View full solution →Directions : In the following questions, a statement of assertion $(A)$ is followed by a statement of reason $(R).$ Mark the correct choice as:
Assertion : If the value of mode and mean is $60$ and $66$ respectively, then the value of median is $64.$
Reason : Median $= ($mode $+\ 2 $ mean$)$
Assertion : If the value of mode and mean is $60$ and $66$ respectively, then the value of median is $64.$
Reason : Median $= ($mode $+\ 2 $ mean$)$
- ABoth assertion $(A)$ and reason $(R)$ are true and reason $(R)$ is the correct explanation of assertion $(A)$.
- BBoth assertion $(A)$ and reason $(R)$ are true but reason $(R)$ is not the correct explanation of assertion $(A)$.
- ✓Assertion $(A)$ is true but reason $(R)$ is false.
- DAssertion $(A)$ is false but reason $(R)$ is true.
Answer: C.
View full solution →Directions: In the following questions, a statement of assertion $(A)$ is followed by a statement of reason $(R).$ Mark the correct choice as :
Assertion : Consider the following frequency distribution:
Reason : The class having maximum frequency is called the modal class.
Assertion : Consider the following frequency distribution:
| Class interval | $10-15$ | $15-20$ | $20-25$ | $25-30$ | $30-35$ |
| Frequency | $5$ | $9$ | $12$ | $6$ | $8$ |
- ABoth assertion $(A)$ and reason $(R)$ are true and reason $(R)$ is the correct explanation of assertion $(A)$.
- BBoth assertion $(A)$ and reason $(R)$ are true but reason $(R)$ is not the correct explanation of assertion $(A)$.
- CAssertion $(A)$ is true but reason $(R)$ is false.
- ✓Assertion $(A)$ is false but reason $(R)$ is true.
Answer: D.
View full solution →Directions: In the following questions, a statement of assertion $(A)$ is followed by a statement of reason $(R)$. Mark the correct choice as :
Assertion: Consider the following frequency distribution:
The median class is $12-16.$
Reason : Let $\text{n}=\sum\text{f}_\text{i}$ Then, the class whose cumulative frequency is just lesser than$\big(\frac{\text{n}}{2}\big)$is the median class.
Assertion: Consider the following frequency distribution:
| Class interval | $0-4$ | $4-8$ | $8-12$ | $12-16$ | $16-20$ |
| Frequency | $6$ | $3$ | $5$ | $20$ | $10$ |
Reason : Let $\text{n}=\sum\text{f}_\text{i}$ Then, the class whose cumulative frequency is just lesser than$\big(\frac{\text{n}}{2}\big)$is the median class.
- ABoth assertion $(A)$ and reason $(R)$ are true and reason $(R)$ is the correct explanation of assertion $(A)$.
- BBoth assertion $(A)$ and reason $(R)$ are true but reason $(R)$ is not the correct explanation of assertion $(A)$.
- ✓Assertion $(A)$ is true but reason $(R)$ is false.
- DAssertion $(A)$ is false but reason $(R)$ is true.
Answer: C.
View full solution →In the formula $\bar{\text{x}}=\text{a}+\Big(\frac{\sum\text{f}_\text{i}\text{u}_\text{i}}{\sum\text{f}_\text{i}}\Big)\times\text{h},\text{u}_\text{i}=$ _________.
View full solution →The arithmetical mean of distribution $3,7,9, x, 5$ is 6 , then value of $x$ will be ___________
View full solution →The mode of the distribution 3, 5, 7, 4, 2, 1, 4, 3, 4 is ___________
Write the median class of the following distribution:
| Classes | Frequency |
| 0 - 10 | 4 |
| 10 - 20 | 4 |
| 20 - 30 | 8 |
| 30 - 40 | 10 |
| 40 - 50 | 12 |
| 50 - 60 | 8 |
| 60 - 70 | 4 |
Find the median class of the following data:
| Marks obtained | 0 - 10 | 10 - 20 | 20 - 30 | 30 - 40 | 40 - 50 | 50 - 60 |
| Frequency | 8 | 10 | 12 | 22 | 30 | 18 |
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”?
Two right circular cones have their heights in the ratio 1 : 3 and radii in the ratio 3 : 1, what is the ratio of their volumes?
Using the empirical formula, find the mode of a distribution whose mean is 8.32 and the median is 8.05.
A survey conducted on 20 households in a locality by a group of students resulted in the following frequency table for the number of family members in a household:
Find the mode of this data.
| Family size | 1-3 | 3-5 | 5-7 | 7-9 | 9-11 |
| Number of families | 7 | 8 | 2 | 2 | 1 |
The wickets taken by a bowler in 10 cricket matches are as follows :
2, 6, 4, 5, 0, 2,1, 3, 2, 3
Find the mode of the above data.
2, 6, 4, 5, 0, 2,1, 3, 2, 3
Find the mode of the above data.
The distribution given below shows the number of wickets taken by bowlers in one-day cricket matches. Find the mean number of wickets by choosing a suitable method. What does the mean signify?
| Number of Wickets | 20-60 | 60-100 | 100-150 | 150-250 | 250-350 | 350-450 |
| Number of Bowlers | 7 | 5 | 16 | 12 | 2 | 3 |
The table below gives the percentage distribution of female teachers in the primary schools of rural areas of various states and union territories (U.T.) of India. Find the mean percentage of female teachers by all the three methods discussed in this section.
| Percentage of female teachers | 15 - 25 | 25 - 35 | 35 - 45 | 45 - 55 | 55 - 65 | 65 - 75 | 75 - 85 |
| Number of states/U.T. | 6 | 11 | 7 | 4 | 4 | 2 | 1 |
The marks obtained by 30 students of Class X of a certain school in a mathematics paper consisting of 100 marks are presented in the table given below. Find the mean of the marks obtained by the students in mathematics paper.
View full solution →| Marks obtained $(x_i)$ | 10 | 20 | 36 | 40 | 50 | 56 | 60 | 70 | 72 | 80 | 88 | 92 | 95 |
| Number of Students $(f_i)$ | 1 | 1 | 3 | 4 | 3 | 2 | 4 | 4 | 1 | 1 | 2 | 3 | 1 |
A student noted the number of cars passing through a spot on a road for $100$ periods each of $3$ minutes and summarized it in the table given below. Find the mode of the data:
View full solution →| Number of cars | 0-10 | 10-20 | 20-30 | 30-40 | 40-50 | 50-60 | 60-70 | 70-80 |
| Frequency | 7 | 14 | 13 | 12 | 20 | 11 | 15 | 8 |
The given distribution shows the number of runs scored by some top batsmen of the world in one-day international cricket matches.
Find the mode of the data.
| Runs scored | Number of batsmen |
| 3000-4000 | 4 |
| 4000-5000 | 18 |
| 5000-6000 | 9 |
| 6000-7000 | 7 |
| 7000-8000 | 6 |
| 8000-9000 | 3 |
| 9000-10000 | 1 |
| 10000-11000 | 1 |
The following data gives the information on the observed lifetimes (in hours) of $225$ electrical components:
Determine the modal lifetimes of the components.
View full solution →| Lifetimes (in hours) | 0-20 | 20-40 | 40-60 | 60-80 | 80-100 | 100-120 |
| Frequency | 10 | 35 | 52 | 61 | 38 | 29 |
The following table gives the literacy rate (in percentage) of $35$ cities. Find the mean literacy rate.
View full solution →| Literacy rate (in %) | 45-55 | 55-65 | 65-75 | 75-85 | 85-95 |
| Number of cities | 3 | 10 | 11 | 8 | 3 |
A class teacher has the following absentee record of $40$ students of a class for the whole term. Find the mean number of days a student was absent.
View full solution →| Number of days | 0-6 | 6-10 | 10-14 | 14-20 | 20-28 | 28-38 | 38-40 |
| Number of students | 11 | 10 | 7 | 4 | 4 | 3 | 1 |
The following distribution gives the state-wise teachers-student ratio in higher secondary schools of India. Find the mode and mean of this data. Interpret the two measures:
| Number of students per teacher | Number of states/U.T. |
| 15 - 20 | 3 |
| 20 - 25 | 8 |
| 25 - 30 | 9 |
| 30 - 35 | 10 |
| 35 - 40 | 3 |
| 40 - 45 | 0 |
| 45 - 50 | 0 |
| 50 - 55 | 2 |
The following data gives the distribution of total monthly household expenditure of 200 families of a village. Find the modal monthly expenditure of the families. Also, find the mean monthly expenditure:
| Expenditure (in ₹) | Frequency |
| 1000-1500 | 24 |
| 1500-2000 | 40 |
| 2000-2500 | 33 |
| 2500-3000 | 28 |
| 3000-3500 | 30 |
| 3500-4000 | 22 |
| 4000-4500 | 16 |
| 4500-5000 | 7 |
The following table shows the ages of the patients admitted in a hospital during a year:
Find the mode and the mean of the data given above. Compare and interpret the two measures of central tendency.
| Age (in years) | 5-15 | 15-25 | 25-35 | 35-45 | 45-55 | 55-65 |
| Number of patients | 6 | 11 | 21 | 23 | 14 | 5 |
In a retail market, fruit vendors were selling mangoes kept in packing boxes. These boxes contained varying number of mangoes. The following was the distribution of mangoes according to the number of boxes.
Find the mean number of mangoes kept in a packing box. Which method of finding the mean did you choose?
| Number of mangoes | 50-52 | 53-55 | 56-58 | 59-61 | 62-64 |
| Number of boxes | 15 | 110 | 135 | 115 | 25 |
The following distribution shows the daily pocket allowance of children of a locality. The mean pocket allowance is ₹ 18. Find the missing frequency f.
| Daily pocket allowance (in ₹) | 11-13 | 13-15 | 15-17 | 17-19 | 19-21 | 21-23 | 23-25 |
| Number of children | 7 | 6 | 9 | 13 | f | 5 | 4 |
100m Race
A stopwatch was used to find the time that it took a group of students to run 100m.
|
Time (in sec)
|
0-10
|
10-20
|
20-30
|
30-40
|
40-50
|
|
No. of students
|
4
|
11
|
14
|
5
|
6
|
- The construction of cummulative frequency table is useful in determining the:
- Estimate the mean time taken by a student to finish the race:
- What wiil be the lower limit of the modal class?
Or
The sum of upper limits of median class and modal class is:
Marks obtained by 40 students of a class-10 in an examination. Out of 50 are given below:
|
Marks
|
0-10
|
10-20
|
20-30
|
30-40
|
40-50
|
|
No. of Students
|
3
|
11
|
9
|
12
|
5
|
- While computing mean of a grouped data, we assume that the frequencies are:
- What will be the upper limit of the median class?
- The sum of lower limit of model class and upper limit of median class is:
Or
Estimate the mean marks obtain by a student:
The DAV public school organized a free health check-up camp for the 60 students of class 10th. They have provided the BMI report to each student. This report estimates the body fat and is a good measure of risk for diseases that can occur with overweight and obesity. On the basis of this report, the following graph is made which describes the weight (in kg) of the students:
- The empirical relationship between mean, median and mode is:
- Identify the modal class in the given graph.
- Calculate the mode weight of the students.
Or
Find the median weight of the students if the mean weight is 55.2 kg.
Recently the half-yearly examination was conducted in DAV public school. The mathematics teacher maintains a record of the marks of 100 students. On the basis of the recorded data of the marks obtained in Mathematics, the histogram is given below:
- The construction of the cumulative frequency table is useful in determining the...
- Identify the modal class from the given graph are?
- Find the mode of the distribution of marks obtained by the students in an examination.
Or
Given the mean of the above distribution is 53, using empirical relationship estimate the value of its median.
On a paricular day, National Highway Authority of india (NHAI) Checked the toll tax collection of a particular toll plaza in rajasthan.
The following table shows the toll tax paid by drivers and the number of vehicles on that particular day.
|
Toll tax (in ₹)
|
30-40 | 40-50 | 50-60 | 60-70 | 70-80 |
|
Number of vehicles
|
80 |
100
|
120
|
70
|
40
|
- The mean of toll tax received by NHAI by direct method is?
- If A is taken as assumed mean, then the possible value of A is?
- The mean of toll tax received by NHAI by assumed mean method is?
Or
The average toll tax received by NHAI in a day, from that particular toll plaza, is?
Generate a Stastics paper free
Pick question groups from the list above, set marks and difficulty, and export a branded PDF with step-by-step answer keys. First 3 chapters free — no signup.