Find the unknown entries $a, b, c, d, e, f$ in the following distribution of heights of students in a class:
Height (in $cm$) Frequency Cumulative frequency
$150-155$ $12$ $a$
$155-160$ $b$ $25$
$160-165$ $10$ $c$
$165-170$ $d$ $43$
$170-175$ $e$ $48$
$175-180$ $2$ $f$
Total $50$ -

Vedclass pdf generator app on play store
Vedclass iOS app on app store
(A) To find the unknown entries,we use the definition of cumulative frequency,where each entry is the sum of the frequency of the current class and all previous classes.
$1$. For the first class $(150-155)$,the cumulative frequency is equal to the frequency: $a = 12$.
$2$. For the second class $(155-160)$,the cumulative frequency is $12 + b = 25$. Thus,$b = 25 - 12 = 13$.
$3$. For the third class $(160-165)$,the cumulative frequency is $c = 12 + b + 10 = 12 + 13 + 10 = 35$.
$4$. For the fourth class $(165-170)$,the cumulative frequency is $c + d = 43$. Substituting $c = 35$,we get $35 + d = 43$,so $d = 43 - 35 = 8$.
$5$. For the fifth class $(170-175)$,the cumulative frequency is $43 + e = 48$. Thus,$e = 48 - 43 = 5$.
$6$. For the sixth class $(175-180)$,the cumulative frequency is $f = 48 + 2 = 50$. Thus,$f = 50$.
Therefore,the values are: $a = 12, b = 13, c = 35, d = 8, e = 5, f = 50$.

Explore More

Similar Questions

Find the mean of the following frequency distribution:
Class $0-10$ $10-20$ $20-30$ $30-40$ $40-50$ $50-60$ $60-70$ $70-80$
Frequency $2$ $4$ $10$ $20$ $18$ $20$ $16$ $10$

Find the mean of the distribution:
Class $1-3$ $3-5$ $5-7$ $7-10$
Frequency $9$ $22$ $27$ $17$

Calculate the mean of the following frequency distribution:
Class $80-90$ $90-100$ $100-110$ $110-120$ $120-130$ $130-140$ $140-150$ $150-160$ $160-170$
Frequency $6$ $18$ $78$ $80$ $100$ $72$ $0$ $40$ $6$
(in $.55$)

For a given frequency distribution,$A=49.5, \Sigma f_{i}=40, \Sigma f_{i} u_{i}=-5$ and $c=20$. Then,mean $\bar{x}=$ ............

In the formula $M = l + \frac{(\frac{n}{2} - cf)}{f} \times h$ for the median,$l = \ldots \ldots \ldots$

Vedclass Products

For Students

Vedclass Test Series

Mock tests in real JEE/NEET style with performance analysis. 5-day free trial.

Start Free Trial
For Teachers

Exam Paper Generator

Generate Set A/B/C/D exam papers from 7.5L+ questions in 2 minutes. 3 chapters free.

Try Free
For Institutes

Online Exam Module

Live online exams with unlimited students, 360° analytics & white-label branding.

See Demo