Answer:
f=11
Mode=4
Median=4
Explanation:
We are given that
a.Mean of the exam score,[tex]\bar x[/tex]=3.5
Score(x) frequency C.F
1 1 1
2 3 4
3 f 15(4+f=4+11)
4 13 28
5 4 32
[tex]\sum f_i=1+3+f+13+4=21+f[/tex]
[tex]\sum f_ix_i=1(1)+2(3)+3(f)+4(13)+5(4)=1+6+3f+52+20=79+3f[/tex]
[tex](\bar x)=\frac{\sum f_ix_i}{\sum f_i}[/tex]
Using the formula
[tex]3.5=\frac{79+3f}{21+f}[/tex]
[tex]73.5+3.5f=79+3f[/tex]
[tex]3.5f-3f=79-73.5[/tex]
[tex]0.5f=5.5[/tex]
[tex]f=\frac{5.5}{0.5}=11[/tex]
b.Mode:The number which is repeat most times .
4 repeat most times
Hence, mode of all exam scores=4
N=32
N is even
[tex]Median=\frac{(\frac{n}{2})^{th}+(\frac{n}{2}+1)^{th}}{2}[/tex]
Median=[tex]\frac{16th+17th}{2}=\frac{4+4}{2}=\frac{8}{2}=4[/tex]
