I am trying to solve this question below since a few hours now but cannot wrap my head around it: The problem
The following information was obtained related to the sales of a product in two shops in Delhi and Mumbai: \begin{array}{l|l|l|l}\text{Delhi}&\bar{x}=3.5&\sum x=40&\sum x^2=275&n_1=12\\\hline\text{Mumbai}&\bar{y}=5&\sum y=48&\sum y^2=235&n_2=10\end{array} Is there a evidence of significant difference in the sales in Delhi and Mumbai? Test at 5% level of significance. (Use $t_{0.05}=2.086$ at $V=20$)
I am having trouble finding the Standard Deviation of the sample. Since the formula for finding the same requires the data points themselves, not the sum of all the data points, it is not possible (according to me) to find the Standard Deviation.
What I have tried:
I have tried substituting the value of (∑(x^2) - x̄) in the formula for standard deviation but to no avail.
The issue I am encountering:
How can I find the standard deviation of the samples? I have everything I need to find the t value of the samples except the standard deviation of the samples.