The data describes the life expectancy for males in 160 countries. The following statements analyze the data distributions for countries with low per capita income and countries with high per capita income. Which of the following statements is valid? Check all that apply.

(A) Typically, countries with low per capita income have a male life expectancy of 60 to 70 years, and countries with high per capita income have a male life expectancy of 70 to 80 years.
(B) The overall range in life expectancy for males living in countries with low per capita income is higher than the range in life expectancy for males living in countries with high per capita income.
(C) It is unusual for countries with high per capita income to have relatively shorter male life expectancy.
(D) The percentage of high per capita income countries with a male life expectancy of 70 years or more is greater than the percentage of low per capita income countries with a male life expectancy of less than 70 years.

Typically, countries with low per capita income have a male life expectancy of 60 to 70 years, and countries with high per capita income have a male life expectancy of 70 to 80 years.

Taking the mean of male life expectancy for low per capital income countries using the midpoint of the data widths

Mean = [(47×2) + (52×8) + (57×16) + (62×18) + (67×18) + (72×8)]/70

Mean = 61.71

Taking the mean of male life expectancy for high per capital income countries using the midpoint of the data widths

Mean = [(52×1) + (57×1) + (62×6) + (67×7) + (72×32) + (77×31) + (82×12)]/90

Mean = 73.61

This statement can be accepted because the mean male life expectancy for low per capital income countries is indeed between 60 and 70 while the mean male life expectancy for high per capital income countries is indeed between 70 and 80.

Statement B

The overall range in life expectancy for males living in countries with low per capita income is higher than the range in life expectancy for males living in countries with high per capita income.

The range is the highest number minus lowest number.

Range for low per capital countries using the midpoint again = 72 - 47 = 25

Range for high per capital countries using the midpoint again = 82 - 52 = 30

The range of male life expectancy for the high per capital income countries is higher than the range of male life expectancy for low per capital income countries. Hence, this statement is false and does not apply.

Statement C

It is unusual for countries with high per capita income to have relatively shorter male life expectancy.

From the data attached, it is evident that the male life expectancy for high per capital income countries skews to the right with more of the values concentrated on the high male life expectancy ages and only a few on the lower end of male life expectancies.

Hence, it is unusual for countries with high per capita income to have relatively shorter male life expectancy.

This statement applies.

Statement D

The percentage of high per capita income countries with a male life expectancy of 70 years or more is greater than the percentage of low per capita income countries with a male life expectancy of less than 70 years.

The percentage of people in the distribution with male life expectancy of 70 years or more for high per capital income countries = (32+31+12)/90 = 0.833 = 83.3%

The percentage of people in the distribution with male life expectancy less than 70 years for low per capital income countries = (18+18+16+8+2)/70 = 0.886 = 88.6%

83.3% < 88.6%

Hence, this statement is false too.