<|im_start|>system
You are a helpful assistant. You first think about the reasoning process in the mind and then provide the user with the answer. You should try to truely solve the question by yourself without cheating.  <|im_end|>
<|im_start|>user
 In a high school, there are 400 male students and 600 female students in the second year. To analyze the final physics survey test scores, a sample is obtained using stratified random sampling based on the male-to-female ratio. In the sample, the average score of male students is 80 points with a variance of 10, and the average score of female students is 60 points with a variance of 20. Based on this, the variance of the final physics survey test scores for the second year of high school can be estimated as ______. Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags.<|im_end|>
<|im_start|>assistant
Let me solve this step by step.
<think>
user
112
In a high school, there are 400 male students and 600 female students in the second year. To analyze the final physics survey test scores, a sample is obtained using stratified random sampling based on the male-to-female ratio. In the sample, the average score of male students is 80 points with a variance of 10, and the average score of female students is 60 points with a variance of 20. Based on this, the variance of the final physics survey test scores for the second year of high school can be estimated as ______.
test