Question

if the data from two geiger counters are combined, how will the standard deviation of the new data set compare to that of each of the indivdual geiger counters?

Answer 1

Answer:

The standard deviation will be the same.

Step-by-step explanation:

Data:

Let's say we have m observations on one counter, and then n observations from another counter. The pooled sample standard deviation will be calculated as:

$\sigma _{pooled} = \sqrt{\frac{(m-1)\sigma ^{2} + (n-1)\\sigma ^{2} }{(m+n-2)} }$

where δ₁ and δ₂ are sample standard deviations from the first and second counters respectively.

Therefore, the data acts in a large part like the weighted root mean individual standard deviations where the weight is proportional to the number of observations in each sample.

If the counters have more or less the same precision, it is likely that the standard deviations are the same (from our definition above) hence

$\sigma _{1} = \sigma _{2}$

If it happens that the counters are not the same in precision, then a good estimate will be taken from the counter that has a better precision. In other words, $\sigma$ is very very low (small standard deviation)

Answer 2

Answer:

Step-by-step explanation:

Standard deviation is the measure of variation of a set of value. The standard deviation increases as the variation of the data increases.

For a two similar data values of Geiger counters, if new data set were compared to that of each of the individual Geiger counters then the standard deviation would decrease as the effect of increasing sample size. But in a situation where the Geiger counter data values are well distributed with varying data values and well distributed range in value, the standard deviation would increase.