Question

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?

Answer 1

f=11

Mode=4

Median=4

Step-by-step explanation:

We are given that

a.Mean of the exam score,
`\bar x`=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

`\sum f_i=1+3+f+13+4=21+f`

`\sum f_ix_i=1(1)+2(3)+3(f)+4(13)+5(4)=1+6+3f+52+20=79+3f`

`(\bar x)=(\sum f_ix_i)/(\sum f_i)`

Using the formula

`3.5=(79+3f)/(21+f)`

`73.5+3.5f=79+3f`

`3.5f-3f=79-73.5`

`0.5f=5.5`

`f=(5.5)/(0.5)=11`

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

`Median=(((n)/(2))^(th)+((n)/(2)+1)^(th))/(2)`

Median=
`(16th+17th)/(2)=(4+4)/(2)=(8)/(2)=4`