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The table displays the frequency of scores for a calculus class on an exam. The mean of the exam scores is 3.5. Score 1 2 3 4 5 Frequency 1 3 f 13 4 a. What is the value of f in the​ table? b. What is the mode of all the exam​ scores? c. What is the median of all the exam​ scores?

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lublana

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]

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