The formula $\ldots \ldots$ represents the empirical relationship between the measures of central tendency.

For some given data, if $M = 15.4$ and $\bar{x} = 14.5$, then $Z = \dots$

For a given frequency distribution,$n=100, A=15$ and $\bar{x}=15$. Then,$\Sigma f_{i} d_{i} = \ldots$

Find the mean,median and mode of the following frequency distribution:

Class	$0-50$	$50-100$	$100-150$	$150-200$	$200-250$	$250-300$	$300-350$
Frequency	$10$	$15$	$30$	$20$	$15$	$8$	$2$

The mileage $(km/l)$ of $50$ cars of the same model was tested by a manufacturer and details are tabulated as given below:

Mileage $(km/l)$	$10-12$	$12-14$	$14-16$	$16-18$
Number of cars	$7$	$12$	$18$	$13$

Find the mean mileage.
The manufacturer claimed that the mileage of the model was $16 \, km/l$. Do you agree with this claim?

In a frequency distribution,the modal class is $70-85$ with frequency $25$. The frequencies of the classes succeeding and preceding the modal class are $20$ and $8$ respectively. Then,the values of $f_{0}, f_{1}$ and $f_{2}$ are respectively.