Answer :
step 1
find out the mean
Mean=[6*5+8*5+9*3+16*3+18*4+20*8+21*5]/(5+5+3+3+4+8+5)
Mean=[30+40+27+48+72+160+105]/33
Mean=482/33
Mean=14.606
step 2
For each value of the data set, subtract the mean and squared the result, then multiply by the frequency
so
[(6-14.606)^2]*5 =370.31618
[(8-14.606)^2]*5=218.19618
[(9-14.606)^2]*3=94.28171
[(16-14.606)^2]*3=5.829708
[(18-14.606)^2]*4=46.076944
[(20-14.606)^2]*8=232.761888
[(21-14.606)^2]*5=204.41618
step 3
Adds the values in step 2
S=1,171.87879
step 3
Divide the sum by the sun of the frequency values
S/33
1,171.87879/33
To obtain the standard deviation, find out the square root
√(1,171.87879/33)
=5.959
therefore