Statistics MCQ Questions & Answers in Statistics and Probability | Maths

The 'less than' ogive curve and the 'more than' ogive curve intersect at median.

$$\eqalign{ & \overline x = \frac{{2 + 3 + a + 11}}{4} \cr & = \frac{a}{4} + 4 \cr & \sigma = \sqrt {\sum {\frac{{x_i^2}}{n} - {{\left( {\overline x } \right)}^2}} } \cr & \Rightarrow \,\,3.5 = \sqrt {\frac{{4 + 9 + {a^2} + 121}}{4} - {{\left( {\frac{a}{4} + 4} \right)}^2}} \cr & \Rightarrow \,\,\frac{{49}}{4} = \frac{{4\left( {134 + {a^2}} \right) - \left( {{a^2} + 256 + 32a} \right)}}{{16}} \cr & \Rightarrow 3{a^2} - 32a + 84 = 0 \cr} $$

If each of $$n$$ observations is multiplied by a constant $$C,$$ the standard deviation also gets multiplied by $$C.$$