The median of the following data is 50. Find the values of $p$ and $q$, if the sum of all the frequencies is 90.
Marks: | 20-30 | 30-40 | 40-50 | 50-60 | 60-70 | 70-80 | 80-90 |
Frequency: | $p$ | 15 | 25 | 20 | $q$ | 8 | 10 |
Given:
The median of the given data is 50. The sum of all the frequencies is 90.
To do:
We have to find the values of $p$ and $q$.
Solution:
Median $= 50$ and $N = 90$
$78 + p + q = 90$
$p+q =90 - 78 = 12$
$q = 12-p$.....….(i)
Median $= 50$ which lies in the class 50-60.
$l = 50, f= 20, F = 40+p$ and $h = 60-50=10$
Median $=l+(\frac{\frac{\mathrm{N}}{2}-\mathrm{F}}{f}) \times h$
$50=50+\frac{\frac{90}{2}-(40+p)}{20}\times 10$
$50-50=\frac{45-40-p}{2}$
$0(2)=5-p$
$0=5-p$
$p=5$
$q = 12 - 5 = 7$ [From (i)]
The values of $p$ and $q$ are $5$ and $7$ respectively.
- Related Articles
- Find the mode of the following distribution.Class-interval:0-1010-2020-3030-4040-5050-6060-7070-80Frequency:5871228201010
- Change the following distribution to a 'More than type' distribution. Hence, draw the 'more than type' ogive for this distribution.Class-interval:20-3030-4040-5050-6060-7070-8080-90Frequency:108122462515
- If the mean of the following distribution is 27, find the value of $p$.Class:0-810-2020-3030-4040-50Frequency:8$p$121310
- If the median of the following data is 32.5, find the missing frequencies.Class interval:0-1010-2020-3030-4040-5050-6060-70TotalFrequency:$f_1$5912$f_2$3240
- Find the missing frequencies in the following distribution, if the sum of the frequencies is 120 and the mean is 50.Class:0-2020-4040-6060-8080-100Frequency:17$f_1$31$f_2$19.
- The marks in science of 80 students of class X are given below: Find the mode of the marks obtained by the students in scienceMarks:0-1010-2020-3030-4040-5050-6060-7070-8080-9090-100Frequency:35161213205411
- Find out the missing frequencies of the following series if the AM is 35 and the number of items is 100:Class interval0-1010-2020-3030-4040-5050-6060-70Frequency510?4203?
- Find the mode of the following distribution.Class:0-1010-2020-3030-4040-5050-6060-70Frequency:81010161267
- An incomplete distribution is given as follows:Variable:0-1010-2020-3030-4040-5050-6060-70Frequency:1020?40?2515You are given that the median value is 35 and the sum of all frequencies is 170. Using the median formula, fill up the missing frequencies.
- The line segment joining the points $(3, -4)$ and $(1, 2)$ is trisected at the points $P$ and $Q$. If the coordinates of $P$ and $Q$ are $(p, -2)$ and $(\frac{5}{3}, q)$ respectively. Find the values of $p$ and $q$.
- An incomplete distribution is given below:Variable:10-2020-3030-4040-5050-6060-7070-800Frequency:1230-65-2518 You are given that the median value is 46 and the total number of items is 230.Using the median formula fill up missing frequencies.
- If $p=-2,\ q=-1$ and $r=3$, find the value of $p-q-r$.
- Given that \( \frac{4 p+9 q}{p}=\frac{5 q}{p-q} \) and \( p \) and \( q \) are both positive. The value of $\frac{p}{q}$ is
- Find the mean, median and mode of the following data:Classes:0-2020-4040-6060-8080-100100-120120-140Frequency:681012653
- Find the values of \( p \) and \( q \) for which the following system of linear equations has infinite number of solutions:$2x+3y=9$$(p+q)x+(2p-q)y=3(p+q+1)$
Kickstart Your Career
Get certified by completing the course
Get Started