Sample QuestionsMedian, Quartiles and Mode questions
One sample from each question group in this chapter. Select any group above to see the full set with answer keys.
The median of the observations $11,12,14,(x-2),(x+4),(x+9), 32,38$ and 47 arranged in ascending order is 24. Find the value of $x$ and hence find the mean.
View full solution →The mean of the observations $23,(x-5), 36,(x-9),(x-1)$ and 28 is 21 . Find the value of $x$ and hence find the median.
View full solution →The marks scored by 16 students in a class test are: $3,6,8,13,15,5,21,23,17,10,9,1,20,21,18,12$. Find (a) the median (b) lower quartile (c) upper quartile
View full solution →Find the median of $17,26,60,45,33,32,29,34,56$. If 26 is replaced by 62 , find the new median.
View full solution →The median of the following observations $11,12,14,18,(x+4), 30,32,35,41$ arranged in ascending order is 24 . Find $x$.
View full solution →40 students enter for a game of shot-put competition. The distance thrown (in metres) is recorded below:| Distance (in m) | 12 - 13 | 13 - 14 | 14 - 15 | 15 - 16 | 16 - 17 | 17 - 18 | 18 - 19 |
| Number of Students | 3 | 9 | 12 | 9 | 4 | 2 | 1 |
Use a graph paper to draw an ogive for the above distribution.
Use a scale of 2cm = 1 m on one axis and 2cm = 5 students on the other axis.
Hence using your graph find:
(a) the median
(b) upper quartile
(c) the number of students who cover a distance which is above $16 \frac{1}{2} \mathrm{~m}$. View full solution →Use Graph paper for this question.
A survey regarding height (in cm) of 60 boys belonging to Class 10 of a school was conducted. The following data was recorded:
| Height (in cm) | 135 - 140 | 140 - 145 | 145 - 150 | 150 - 155 | 155 - 160 | 160 - 165 | 165 - 170 |
| No. of boys | 4 | 8 | 20 | 14 | 7 | 6 | 1 |
Taking 2cm = height of 10 cm along one axis and 2cm = 10 boys along the other axis, draw an ogive for the above distribution. Use the graph to estimate the following:
(a) the median
(b) lower Quartile
(c) if above 158 cm is considered as the tall boys of the class, find the number of boys in the class who are tall.
The daily wages of 80 workers in a project are given below:
| Wages in (₹) | 400 - 450 | 450 - 500 | 500 - 550 | 550 - 600 | 600 - 650 | 650 - 700 | 700 - 750 |
| No. of workers | 2 | 6 | 12 | 18 | 24 | 13 | 5 |
Use a graph paper to draw an ogive for the above distribution. (Use a scale of 2cm = ₹50 on x-axis and 2cm = 10 workers on y-axis). Use your ogive to estimate:
(a) the median wage of the workers.
(b) the lower quartile wage of workers.
(c) the number of workers who earn more than ₹625 daily.
The table shows the distribution of the scores obtained by 160 shooters in a shooting competition. Use a graph sheet and draw an ogive for the distribution. (Take 2 cm 10 scores on the x-axis and 2 cm 20 shooters on the y-axis).
| Scores | 0 - 10 | 10 - 20 | 20 - 30 | 30 - 40 | 40 - 50 | 50 - 60 | 60 - 70 | 70 - 80 | 80 - 90 | 90 - 100 |
| No. of shooters | 9 | 13 | 20 | 26 | 30 | 22 | 15 | 10 | 8 | 7 |
Use your graph to estimate the following:
(a) The median
(b) The interquartile range
(c) The number of shooters who obtained a score of more than 85%.
(Use a graph paper for this question.) The daily pocket expenses of 200 students in a school are given below:
| Pocket expenses (in ₹) | 0-5 | 5-10 | 10-15 | 15-20 | 20-25 | 25-30 | 30-35 | 35-40 |
| No. of students (Frequency) | 10 | 14 | 28 | 42 | 50 | 30 | 14 | 12 |
Draw a histogram representing the above distribution and estimate the mode from the graph .
Draw a histogram for the following frequency distribution and find the mode from the graph :
| Class | 0 - 5 | 5 - 10 | 10 - 15 | 15 - 20 | 20 - 25 |
| Frequency | 2 | 5 | 18 | 14 | 8 |
A Mathematics aptitude test of 50 students was recorded as follows :
| Marks | 50 - 60 | 60 - 70 | 70 - 80 | 80 - 90 | 90 - 100 |
| Number of students | 4 | 8 | 14 | 19 | 5 |
Draw a histogram for the above data using a graph paper and locate the mode.
The distribution given below shows the marks obtained by 25 students in an aptitude test. Find the median and mode of the distribution.
| Marks obtained | 5 | 6 | 7 | 8 | 9 | 10 |
| Number of students | 3 | 9 | 6 | 4 | 2 | 1 |
In a class of 40 students, marks obtained by the students in a class test (out of 10) are given below :
| Marks | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
| Number of students | 1 | 2 | 3 | 3 | 6 | 10 | 5 | 4 | 3 | 3 |
Calculate the following for the given distribution :
(a) Median (b) Mode
If the median of the data $24,25,26, x+2, x+3,30,31,34$ arranged in order is 27.5 , then the value of $x$ is:
View full solution →The difference between upper quartile $\left(\mathrm{Q}_3\right)$ and lower quartile $\left(\mathrm{Q}_1\right)$ is called
View full solution →The middle quarlite is also known as:
Quartiles divide the whole set of observations into $\qquad$ equal parts.
View full solution →In a grouped frequency distribution, the class with maximum frequency is called:
Assertion (A) : For a given data, we have mean $=24$, median $=22$ and mode $=18$.
Reason (R) : For a data, the value of mean, median and mode may be equal.
- A
- ✓
- C
Both A and R are true, and R is the correct reason for A .
- D
Both A and R are true, and R is incorrect reason for A .
Answer: B.
View full solution →Assertion (A) : We can always estimate median and mode of a data from the frequency polygon (ogive).
Reason (R) : The observation which has highest frequency in a data is called mode of the data.
- A
- B
- C
Both A and R are true, and R is the correct reason for A .
- ✓
Both A and R are true, and R is incorrect reason for A .
Answer: D.
View full solution →Assertion (A) : The upper quartile of the data $11,5,6,15,15,18,13,3,17,8,20$ is 17 .
Reason (R) : The observations which divide the whole set of observations into four equal parts are known as quartiles.
- A
- ✓
- C
Both A and R are true, and R is the correct reason for A .
- D
Both A and R are true, and R is incorrect reason for A .
Answer: B.
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