Question

For the following set of data, find the population standard deviation, to the nearestthousandth.Data Frequency658593163184208521

Answer 1

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

The standard deviation is 5.959