Subject Experts Solutions for Chapter: Statistics, Exercise 1: Practice Exercise

If the monthly expenditure pattern of a person who earns a monthly salary of $15000$ is represented in a pie diagram, then the sector angle of an item on transport expenses measures $15°$. What is his monthly expenditure on transport?

Consider the following data

What is the variability in the wages of the workers in factory $A$?

The regression coefficients of a bivariate distribution are $-0.64$ and $-0.36$. Then, the correlation coefficient of the distribution is

If $m$ is the geometric mean of ${\left(\frac{\mathrm{y}}{\mathrm{z}}\right)}^{{\log }_{\mathrm{e}}\left(\mathrm{yz}\right)}, {\left(\frac{\mathrm{z}}{\mathrm{x}}\right)}^{{\log }_{\mathrm{e}}\left(\mathrm{zx}\right)}$ and ${\left(\frac{\mathrm{x}}{\mathrm{y}}\right)}^{{\log }_{\mathrm{e}}\left(\mathrm{xy}\right)}$, then what is the value of $m$?

What is the mean deviation from the mean of the numbers $10, 9, 21, 16, 24$ ?

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

The mean of the series ${\mathrm{x}}_1, {\mathrm{x}}_2, \dots , {\mathrm{x}}_{\mathrm{n}}$ is $\overline{\mathrm{X}}$. If ${\mathrm{x}}_2$ is replaced by $\mathrm{\lambda }$, then what is the new mean?

Consider the following statements in terms of histogram.

I. 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.

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

Which of the above statement(s) is/are correct?