Question

In the following formula $x = a + h(\dfrac{{{f_i}{u_i}}}{{{f_i}}})$, for finding the mean of grouped frequency distribution, ${u_i}$ =
1) $\left( {{x_i} + a} \right)/h$
2) $h\left( {{x_i} - a} \right)$
3) $\left( {{x_i} - a} \right)/h$
4) $\left( {a - {x_i}} \right)/h$

Answer 1

Hint: The above formula of the question is based on the step deviation method which is used in statistics for calculating the mean of the grouped data.
Formula of the grouped frequency is given as:
$x = a + h(\dfrac{{{f_i}{u_i}}}{{{f_i}}})$, where $x_i$ is the data values, a is the assumed mean h is the class size and ui is the modified class mark after shift of origin and change of scale..
Using the given hint we will find the formula for ${u_i}$.

Complete step-by-step answer:
Let us first explain the step deviation method used in statics for calculating the mean of grouped data.
Step deviation method of finding mean is a basic procedure to reduce the mathematical calculations when we do not have to use the calculator and numbers are difficult to calculate.
In step deviation method first we consider the class marks of all the class intervals and call them xi .
After that variable is changed from ${x_i}$ to ${d_i}$ , which is equal to ${d_i} = {x_i} - A$, A is the assumed mean. We then change the variable from ${d_i}$ to ${u_i} = \dfrac{{{x_i} - A}}{h}$ , where h is the class width , whose reciprocal is the scaling factor. After finding the mean $\mathop u\limits^ - $ , we get back to $\mathop x\limits^ - $ by dividing $\mathop u\limits^ - $ by the scaling factor and then adding the assumed mean.
$\mathop x\limits^ - = A + h\mathop u\limits^ - $ .
Thus, from the formula we can conclude that ${u_i} = \dfrac{{{x_i} - a}}{h}$ .

Option 3 is correct.

Note:
Statistical formulas methods are very useful in comparing data in a graphical form such as used in cricket matches for analyzing the score of a player, a team etc,. In the similar manner the same graphs are used by companies to represent their annual growth and other things, Share market sites also use the data in graphical figures for comparing the profit and loss.