Median from Ogives

Q.

Marks obtained by 200 students in an examination are given below: Draw an ogive for the given distribution taking 2 cm = 10 marks on one axis and 2 cm = 20 students on the other axis. Using the graph, determine

(i) The median marks.

(ii) The number of students who failed if minimum marks required to pass in the exam is 40.

(iii) If scoring 85 and more marks is considered as grade one, find the number of students who secured grade one in the examination.

1. i) 57.5, ii) 46, iii) 10

2. i) 57.5, ii) 46, iii) 16

3. i) 57.5, ii) 56, iii) 10

4. i) 56.5, ii) 49, iii) 10

Q. By using ogive when we find the value of the median, first we calculate $(\frac{n}{2}{)}^{th}$ th term and mark it on the ____.

1. y-axis
2. x-axis
3. z-axis
4. None of the above

Q. The weight of 50 workers is given below:
$\begin{array}{cc}WeightinKg& No.ofWorkers\\ 50-60& 4\\ 60-70& 7\\ 70-80& 11\\ 80-90& 14\\ 90-100& 6\\ 100-110& 5\\ 110-120& 3\end{array}$
Draw an ogive of the given distribution using a graph sheet. Take 2 cm = 10 kg on one axis and 2 cm = 5 workers along the other axis. Use a graph to estimate the following:
(i) the upper and lower quartiles
(ii) If weighing 95 kg and above is considered overweight, find the number of workers who are overweight. [6 MARKS]

Q. 70 students marks are represented with class intervals in a frequency distribution table. You are given the ogive for this data set. If you are going to find the median value then what will be the calculated mark you need to know to draw the horizontal line from y-axis?

1. 35
2. 45
3. 40
4. 20

Q.

Question 14(iv)
50 students enter for a school javelin throw competition. The distance (in metres) thrown are recorded below :

$\begin{array}{cccccc}Distance\left(inm\right)& 0-20& 20-40& 40-60& 60-80& 80-100\\ Numberofstudents& 6& 11& 17& 12& 4\end{array}$


Are the median distance calculated in (ii) and (iii) same?

Q.

The table shows the Distribution of the Scores obtained by 155 shooters in a shooting competition.

$\begin{array}{cc}\text{Scores}& \text{No. of shooters}\\ 0-10& 10\\ 10-20& 12\\ 20-30& 15\\ 30-40& 8\\ 40-50& 20\\ 50-60& 24\\ 60-70& 7\\ 70-80& 11\\ 80-90& 30\\ 90-100& 18\end{array}$

Use a graph sheet to draw an ogive for the distribution.

Estimate the number of shooters who obtained a score of more than 85%.

1. 40
2. 28
3. 34
4. 37

Q.

The table shows the Distribution of the Scores obtained by 155 shooters in a shooting competition.

$\begin{array}{cc}\text{Scores}& \text{No. of shooters}\\ 0-10& 10\\ 10-20& 12\\ 20-30& 15\\ 30-40& 8\\ 40-50& 20\\ 50-60& 24\\ 60-70& 7\\ 70-80& 11\\ 80-90& 30\\ 90-100& 18\end{array}$

Use a graph sheet to draw an ogive for the distribution.

Using the graph estimate the median.
$\left[4Marks\right]$

Q. What is the median class for the following data given below?

Time(min)	$10-20$	$20-30$	$30-40$	$40-50$
Running race(km)	$10$	$20$	$3$	$4$

1. $20-30$
2. $40-50$
3. $10-20$
4. $30-40$

Q. If in a moderately skewed distribution the values of mode and mean are $6\lambda$ and $9\lambda$ respectively, then the value of the median is

1. $8\lambda$
2. $6\lambda$
3. $7\lambda$
4. $5\lambda$

Q.

Draw appropriate graph to depict the runs scored by the Indian team. [2 MARKS]

$\begin{array}{cc}Players& Score\\ Rahul& 90\\ Sachin& 99\\ Saurav& 56\\ Sehwag& 30\\ Gambhir& 30\\ Yuvraj& 48\\ Kohli& 82\\ Zaheer& 0\\ Nehra& 1\\ Mishra& 19\end{array}$

Q. In an arranged discrete series in which total number of observation $n$ are even, then median $n$ is :

1. ${\left(\frac{n+1}{2}\right)}^{th}$ item (term)
2. $\frac{n^{th}}{2}$ item (term)
3. ${[\left(\frac{n+1}{2}\right)+1]}^{th}$ item (term)
4. The average of $\frac{n^{th}}{2}$ and ${\left(\frac{n+3}{2}\right)}^{th}$ item (term)

Q. A student draws a cumulative frequency curve for the marks obtained by $40$ students of a class as shown below. Find the median marks obtained by the students of the class

1. Median marks $=40$
2. Median marks $=50$
3. Median marks $=45$
4. Median marks $=55$

Q. During the medical check-up of $35$ students of a class, their weights were recorded as follows:

Weight (in kg)	Number of students
Less than $38$ Less than $40$ Less than $42$ Less than $44$ Less than $46$ Less than $48$ Less than $50$ Less than $52$	$0$ $3$ $5$ $9$ $14$ $28$ $32$ $35$

Draw a less than type ogive for the given data. Hence obtain the median weight from the graph and verify the result by using the formula.

Q. If the ratio of mode and median of a distribution is $6:5$, then the ratio of its mean and median is

1. $9:10$
2. $8:11$
3. $9:7$
4. $8:9$

Q. Median of the odd divisors of $360$ is

1. the mean of 4th and 5th item
2. the mean of 5th and 6th item
3. none of these
4. the mean of 3rd and 4th item

Q. Median of ${}^{2n}{C}_0{,}^{2n}{C}_1{,}^{2n}{C}_2,....{,}^{2n}{C}_n$ (when $n$ is even) is

1. ${}^{2n}{C}_{\frac{n}{2}}$
2. ${}^{2n}{C}_{\frac{n-1}{2}}$
3. ${}^{2n}{C}_{\frac{n+1}{2}}$
4. None of these

Q. Draw less than type cumulative frequency curve and find the median for the following data.

Seif study time daily in minutes	30 - 60	60 - 90	90 - 120	120 - 150	150 - 180	180 - 210
Number of students	5	16	38	96	48	17

1. Median $\approx$ 135.94
2. Median $\approx$130
3. Median $\approx$125
4. Median $\approx$110

Q. Question 5

Refer to Q.4 above. Draw the less than type ogive for this data and use it to find the median weight.

Q. Following is the frequency distribution of weight of seeds. Draw both the types of ogive curves and find the median

Weight (in mg)	11 - 20	21 - 30	31 - 40	41 - 50	51 - 60
No. of seeds	18	22	30	16	4

1. Median $\approx$ 26
2. Median $\approx$ 37
3. Median $\approx$ 22
4. Median $\approx$ 32.17

Q. The monthly consumption of electricity (in units) of some families of a locality is given in the following frequency distribution:

Monthly consumption (in units)	$140-160$	$160-180$	$180-200$	$200-220$	$220-240$	$240-260$	$260-280$
Number of families	$3$	$8$	$15$	$40$	$50$	$30$	$10$

Prepare a 'more than type' given for the following frequency distribution.