Question

The mean of the following frequency distribution is 145. Find the values of f1 and f2.
Class Intervals Frequency
0 – 50 8
50 – 100 f1
100 – 150 32
150 – 200 26
200 – 250 f2
250 – 300 7
Total 100

Answer 1

$\sf\large\underline{Given:}$

• $\rm{The\: mean\:of\: distribution=145}$
• $\rm{The\:sum\:of\: frequency=100}$

$\sf\large\underline{To\: Find:}$

• $\rm{The\: value\:of\:f_1\:f_2=?}$

$\sf\large\underline{Solution:}$

• By applying formula to calculate the unknown value of frequency here]

$\sf\large\underline{Formula\: used:}$

$\rm{\implies Mean=\dfrac{\sum\:fx}{\sum\:f}}$

• Now find out the equation here]
• Here notice 1st to the refer attachment]

$\rm{\implies sum\:of\: frequency=100}$

$\rm{\implies 73+f_{1}+f_{2}=100}$

$\rm{\implies f_{1}+f_{2}=100-73}$

$\rm{\implies f_{1}+f_{2}=27------(i)}$

• similarly calculate 2nd equation by applying above formula here]

$\rm{\implies 145=\dfrac{10675+75f_{1}+225f_{2}}{100}}$

$\rm{\implies 14500=10675+75f_{1}+225f_{2}}$

$\rm{\implies 75f_{1}+225f_{2}=14500-10675}$

$\rm{\implies 75f_{1}+225f_{2}=3825----(ii)}$

• In eq 1st multiplying by 75 than subtract]

$\rm{\implies 75f_{1}+75f_{2}=2025}$

$\rm{\implies 75f_{1}+225f_{2}=3825}$

• By solving equation we get here]

$\rm{\implies -150f_{2}=-1800}$

$\rm{\implies f_{2}=12}$

• Now putting the value of f2=12 in eq 1st]

$\rm{\implies f_{1}+f_{2}=27}$

$\rm{\implies f_{1}+12=27}$

$\rm{\implies f_{1}+=27-12}$

$\rm{\implies f_{1}=15}$

Hence,

$\sf{\implies The\: value\:of\:f_{1}=15,\:\:f_{2}=12}$

Answer 2

bu solving the problems

The mean of the following frequency distribution is 145. Find the values of f1 and f2.

Class Intervals Frequency

0 – 50 8

50 – 100 f1

100 – 150 32

150 – 200 26

200 – 250 f2

250 – 300 7

Total 100

solution

solution equation 1 and 2

F1=25.5 Nd F2=8.5