Central Tendency & Dispersion

The harmonic mean of {a/(1-ab)} and {a/(1+ab)} is equal to :

For a set of 200 observations on a certain random variable X, the mean and standard deviation are 65.7 and 4.4 respectively. However on scrutinizing the data it is found that two observations, which should be correctly read as 71 and 83, had been wrongly recorded as 91 and 80. Obtain the correct values of the mean and the standard deviation.

The sum of deviation of values $X_i$ from their mean is:

A student while calculating the mean of $25$ observations obtained a mean of $56\text{ cm}$. It was later discovered at the time of checking that he had wrongly copied down an observation as $64$. What is the mean if the wrong value is omitted?

$X$ and $Y$ are two random variables with $\mu_x = 18.4$, $\mu_y = 33$, $\sigma_x = 8.4$, $\sigma_y = 6.4$ and $\rho_{xy} = 0.84$. The regression line of $Y$ on $X$ is:

The diameter at breast height (DBH) of $20$ trees are as follows: $1, 3, 5, 5, 7, 8, 8, 8, 8, 8, 8, 9, 9, 9, 9, 9, 10, 10, 10, 10$. What are the values of $1^{\text{st}}$ quartile ($Q_1$), $2^{\text{nd}}$ quartile ($Q_2$), and $3^{\text{rd}}$ quartile ($Q_3$)?

The relation between standard deviation (SD), mean deviation about mean (MD), and quartile deviation (QD) for a normal distribution is:

The relationship between root mean square deviation (r.m.s.d.) and standard deviation (s.d.) is:

For any discrete distribution, what is the value of $\beta_2$?

Which of the following measures of central tendency is not affected by the presence of outliers?

For a discrete data set when all the values are not same, then the relationship between mean deviation about mean (MD) and standard deviation (SD) is:

For a Poisson distribution, if mean ($m$) = $1$, then $P(1)$ is: