# How to modify the mean?

I have data collected in consecutive time periods using two sensors (i.e. sensor1 and sensor2) as follows.

time      1,    2,    3,   ............,   8,    9
sensor1  0.92, 0.35, 0.18, ............, 0.36, 0.12
sensor2  0.95, 0.39, 0.09, ............, 0.18, 0.32


The difference of the values in the two sensors are due to environmental conditions, hardware issues etc. I want to combine these two measures of sensor1 and sensor2. So, what I initailly did was taking the mean as follows.

time      1,    2,    3,   ............,   8,    9
sensor1  0.92, 0.35, 0.18, ............, 0.36, 0.12
sensor2  0.95, 0.39, 0.09, ............, 0.18, 0.38
mean    0.935, 0.37, 0.135, ............,0.27, 0.25


Considering the mean seems to be a good approximantion. However, I want to favour the values of sensor2 more than sensor1 when combining the two measures. The reason for this is that sensor2 to is more robust to environmental changes than sensor1.

In that case, I am thinking of something beyond taking the mean. Since, my statistical knowledge is not good, I am not sure if there is any method I can use for this. My main objective is favouring sensor2 more than sensor1.

I am happy to provide more details if needed.

Calculate the weighted mean. If you want to give sensor2 a 70% weight, you can calculate the respective weighted means via

$$\text{weighted mean} = 0.7 x_{\text{sensor_2}} + 0.3 x_{\text{sensor_1}}$$

Make sure the weights add up to 1!