How many TV's are there in your household?” was one of the
questions on a questionnaire sent to 5000 people in Japan.
The collected data resulted in the following distribution:
Number of TVs/Household
0 1 2 3 4 5 or more
Percentage
1.9 31.4 23.0 24.4 13.0 6.3
One of these households is selected at random.
To find the percentages, I used the following formula:
percentile of value x =
# of values less than x
------------------------ * 100
total # of values
A) What percentage of the households have at least one TV?
31.4+23+24.4+13.0+6.3
--------------------- * 100 - 19.6%
5
B) What percentage of the households have at most 3 TV's?
1.9+31.4+23.0+24.4
------------------ * 100 =16.1%
4
My questions is: What did I do wrong and how do you solve this?
Thank you
Miss Patte
Work it from the other end, so you are using fewer values. You are less likely to make mistakes.
A. 100(1.00 - .019) = ?
B. 100(1.00 - .193) = ?
To find the correct percentages, you need to consider the cumulative percentages for each category.
A) To find the percentage of households with at least one TV, you need to add up the cumulative percentages for all categories except for "0 TVs per household."
1.9% (0 TVs per household) is the percentage of households with zero TVs. So, the percentage of households with at least one TV is 100% - 1.9% = 98.1%.
B) To find the percentage of households with at most three TVs, you need to add up the cumulative percentages for the categories with three or fewer TVs.
The cumulative percentages for each category up to three TVs are:
1.9% (0 TVs per household)
1.9% + 31.4% = 33.3% (1 TV per household)
33.3% + 23.0% = 56.3% (2 TVs per household)
56.3% + 24.4% = 80.7% (3 TVs per household)
Hence, the percentage of households with at most three TVs is 80.7%.
Therefore, the correct answers are:
A) 98.1% (percentage of households with at least one TV)
B) 80.7% (percentage of households with at most three TVs)