Given:
Frequency distribution table.
Mode = 34.5
To find:
The value of missing frequency 'f'.
Solution:
Formula for mode is
[tex]Mode=l+\dfrac{f_1-f_0}{2f_1-f_0-f_2}\times h[/tex]
where, l is lower limit of modal class, [tex]f_1[/tex] is frequency of modal class, [tex]f_0[/tex] is frequency of preceding class, [tex]f_2[/tex] is frequency of succeeding class, h is class size.
Mode is 34.5, so the modal class is 30-45. So,
[tex]l=30,f_1=f,f_0=7, f_2=3,h=45-30=15[/tex]
Putting these values in the above formula, we get
[tex]34.5=30+\dfrac{f-7}{2f-7-3}\times 15[/tex]
[tex]34.5-30=\dfrac{f-7}{2f-10}\times 15[/tex]
[tex]4.5=\dfrac{f-7}{2f-10}\times 15[/tex]
Divide both sides by 15.
[tex]\dfrac{4.5}{15}=\dfrac{f-7}{2f-10}[/tex]
[tex]0.3=\dfrac{f-7}{2f-10}[/tex]
[tex]0.3(2f-10)=f-7[/tex]
[tex]0.6f-3=f-7[/tex]
Separating variable terms, we get
[tex]0.6f-f=3-7[/tex]
[tex]-0.4f=-4[/tex]
Divide both sides by -0.4.
[tex]f=\dfrac{-4}{-0.4}[/tex]
[tex]f=10[/tex]
Therefore, the value of f is 10.
