Show that the two formulae for the standard deviation of ungrouped data .
σ=√1n∑(xi−¯¯¯¯¯X)2 and σ′=√1n∑x2i−¯¯¯¯¯X2 are equivalent , where ¯¯¯¯¯X=1n∑xi
PQ. Show that the two formulae for the standard deviation of ungrouped data δ=√1n∑(xi−¯X)2 and δ=√1n∑(xi−¯X)2 are equivalent, wehere ¯X=1n∑xi.