Answer to Question #272032 in Statistics and Probability for Marcus

Question

Compute and interpret the (approximate) mean percentage of research group income allocated to grocery purchase (Hint: Use the weighted average formula)

Answer 1

random sample of 50 families, frequency distribution:

 Percent of income

  Number of families

 10 – under 20% 6

 20 – under 30%

  14

 30 – under 40%

  16

 40 – under 50%

 10

 50 – under 60%

  4

using weighted average formula with the midpoint of each interval as x_i :

$\overline{x}=\frac{\sum x_if_i}{\sum f_i}=\frac{15\cdot6+25\cdot14+35\cdot16+45\cdot10+55\cdot4}{50}=33.4\%$