How to calculate weighted mean

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If i have interest rates for instance

1 week = 0.123%

1 month = 0. 345%

3 month =0.567%

6 month = 0.678%

12 month = 0.890%

how do you calculate 4month, 5month, 8 month, 10month?

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To compare say, between 1 week and 1 month, you can start with the week rate and do $(1+0.00123)^4 = 1.004929085$ which is $0.4929 \%$. The geometric mean is the proper one to use: E.g., if you want to bring the 12-month rate to 1-month, you would do $(1+0.00890)^{1/12} = 1.00073866$ which is $0.07 \%$ per month.