Question

12. Find the unknown entries a, b, c, d, e, in the following distribution of heights of
students in a class
Cumulative frequency
Height
(in cm)
150-155
155-160
160-165
165-170
170-175
175-180
Total ​

Answer 1

a=12

b=13 [which makes the cumulative frequency 25 i.e.12+13 ]

c=35

d=8 [ which makes the cumulative freq. 35+8=43]

e=5 [which makes the cumulative freq. 43+5=48]

f=50

Check: Given 12+b+10+d+e+2=50

put the values

12+13+10+8+5+2=50 Hence Correct findings

Answer 2

Answer:

a=12, b=13, c=35, d=8, e=5 and f=50

Step-by-step explanation:

Cumulative frequency

Height (in cm)           Frequency           Calculated Cumulative frequency

150-155                          12                            12

155-160                            b                             12+b

160-165                           10                             12+b+10

165-170                            d                             12+b+10+d

170-175                            e                              12+b+10+d+e

175-180                            2                              12+b+10+d+e+2

Total ​                            50

Compare the given cumulative frequency  and calculated cumulative frequency .

$a=12$

$12+b=25\Rightarrow b=13$

$c=12+b+10$

$c=12+13+10$

$c=35$

$12+b+10+d=43$

$35+d=43\rightarrow d=8$

$12+b+10+d+e=48$

$43+e=48\Rightarrow e=5$

$f=12+b+10+d+e+2$

$f=48+2=50$

Therefore, a=12, b=13, c=35, d=8, e=5 and f=50.