If the total number of observations is 20, $$\sum {x_i^{}} $$ = 1000 and $$\sum {x_i^2} $$ = 84000, then what is the variance of the distribution?

The mean of the series x₁, x₂, ........, x_n is $$\overline X $$. If x₂ is replaced by $$\lambda$$, then what is the new mean?

For the data 3, 5, 1, 6, 5, 9, 5, 2, 8, 6 the mean, median and mode are x, y and z, respectively. Which one of the following is correct?

Consider the following statements in respect of a histogram.

1. The total area of the rectangles in a histogram is equal to the total area bounded by the corresponding frequency polygon and the X-axis.

2. When class intervals are unequal in a frequency distribution, the area of the rectangle is proportional to the frequency.

Which of the above statements is/are correct?