SOLUTION: Hello, I would appreciate help with this problem The information below shows​ eighth-grade mathematics test scores in State A and State B. The scores are separated according

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Question 1139102: Hello,
I would appreciate help with this problem
The information below shows​ eighth-grade mathematics test scores in State A and State B. The scores are separated according to the sex of the students. Also shown are the state averages for both sexes.

State A
(Male) - 294
(Female) - 263
(Average for both sexes) - 289
State B
(Male) - 296
(Female) - 265
(Average for both sexes) - 286

Now consider the information below that gives the actual percentages of males and females in each state. Use these percentages to verify that the overall average test score in state A is 289​, and in state B is 286 as claimed above.

State A
(Male) - 85​%
(Female) - 15​%
State B
(Male) - 68​%
(Female) - 32​%
Thank you
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
you are given:

State A
(Male) - 294
(Female) - 263
(Average for both sexes) - 289
State B
(Male) - 296
(Female) - 265
(Average for both sexes) - 286

you are also given:

State A
(Male) - 85​%
(Female) - 15​%
State B
(Male) - 68​%
(Female) - 32​%
Thank you

you would use this second set of information to determine the overall percentages.

for state A:

male average of 294 * male percent of 85% gives a male weighted average of .85 * 294 = 249.9.

female average of 263 * female percent of 15% give a female weighted average of .15 * 263 = 39.45.

add up the two weighted averages to get an overall weighted average of 289.35.

round to the nearest whole number to get an overall weighted average for state A of 289.

that checks with the information given.

for state B:

male average of 296 * male percent of 68% gives a male weighted average of .68 * 296 = 201.28.

female average of 265 * female percent of 32% gives a female weighted average of .32 * 265 = 84.8

add up the two weighted averages to get an overall weighted average of 286.08.

round to the nearest whole number to get an overall weighted average for state B of 286.

that checks with the information given.

looks like the information given is accurate.

the weighted average for each category is the average for each category times the percent of each category of the total.

any questions, email dtheophilis@gmail.com