Question

Use the frequecy distribution to answer the question.

Data Values Frequency
3.0 - 6.9 5
7.0 - 10.9 4
11.0 - 14.9 8
15.0 - 18.9 6
19.0 - 22.9 5
What is the sample mean?

Answer 1

Take the center of each section as the data point using average:
(1/2) * (endpoint1 - endpoint2)

mean = sum x*Prob(x)

mean = 0.5*(6.9+3)*P(3 <= x <= 6.9) +
0.5*(10.9 +7)*P(7 <= x <= 10.9) +
0.5*(14.9 +11)*P( 11<= x <= 14.9) +
0.5*(18.9 + 15)*P(15 <= x <= 18.9) +
0.5*(22.9 + 19(*P(19 <= x <= 22.9)

= 0.5*(6.9+3)*4/28 + 0.5*(10.9 + 7)*4/28 +
0.5*(14.9 + 11)*8/28 + 0.5*(18.9 + 15)*6/28 +
0.5*(22.9 + 19)*5/28

= 13.05892857142857...

Ans. 13.0589 285714 285714 285714 ...