Write conclusion

Question

How can i write finding and conclusion after caculating the result of standard deviation? I can caculate the standard deviation question properly, but i can't write the finding on this question. I mean, eg. I get the result of mean value is 35. The standard variation value are 17 and 6 separately.

Answer 1

If you want to report them separately, use the method below:

$x=\bar x \pm s$

Where: $\bar x$ is mean and $s$ is the standard deviation.

• For the first data set, as $\bar x=35$ and $s=17$, then: $x=35 \pm 17$
• For the second data set, as $\bar x=35$ and $s=6$, then: $x=35 \pm 6$

But if you want to combine all results and report only one $x$, then you should use the method @Remy mentioned in his answer.

Answer 2

Under the assumption that the population variances are the same, you can find the pooled sample standard deviation as follows:

$$s_{pooled}=\sqrt\frac{(n_1-1) s_1^2+(n_2-1) s_2^2}{n_1+n_2-2} $$

where $n_1$ and $n_2$ are the number of observations in populations $1$ and $2$, respectively.

In this case, our degrees of freedom becomes $$df=n_1+n_2-2$$

Under the assumption that the population variances are not the same, you can find the unpooled sample standard deviation as follows

$$s_{unpooled}=\sqrt{\frac{s_1^2}{n_1}+\frac{s_2^2}{n_2}}$$

but this makes $$df=\frac{\left(\frac{s_1^2}{n_1}+\frac{s_2^2}{n_2}\right)^2}{\frac{1}{n_1-1}\left(\frac{s_1^2}{n_1}\right)^2+\frac{1}{n_2-1}\left(\frac{s_2^2}{n_2}\right)^2}$$