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

Answer:

f=11

Mode=4

Median=4

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

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

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

$(\bar x)=\frac{\sum f_ix_i}{\sum f_i}$

Using the formula

$3.5=\frac{79+3f}{21+f}$

$73.5+3.5f=79+3f$

$3.5f-3f=79-73.5$

$0.5f=5.5$

$f=\frac{5.5}{0.5}=11$

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

$Median=\frac{(\frac{n}{2})^{th}+(\frac{n}{2}+1)^{th}}{2}$

Median=$\frac{16th+17th}{2}=\frac{4+4}{2}=\frac{8}{2}=4$