Question

Given that ${d_i}$ is the deviation of a class mark ${y_i}$ from $a$, the assumed mean and ${f_i}$ is the frequency, if ${M_g} = x + \dfrac{{\sum {{f_i}{d_i}} }}{{\sum {{f_i}} }}$, then $x$ is
A. Lower limit
B. Assumed mean
C. Number of observations
D. Class size

Answer 1

Hint: There are two types of series in statistics. One is a discrete series and the other is a continuous series. Discrete series is formed by ungrouped data and continuous series is formed by grouped data. In both the series, all the class intervals along with their corresponding frequencies are listed in a table. Frequency means number of repetitions of an observation given in the data. Mean is a measurement of the central tendency of a given data. There are three methods of calculating the mean of a given data. One of the methods is the assumed mean method. The formula is given in the question and the interpretation of a symbol used in the formula is asked.

Complete step by step solution:
There are three methods of calculating the mean of a given data. One of the methods is the assumed mean method. There is a particular procedure for finding the mean of a data using the assumed mean method.
First, you have to make a table representing the given values and frequencies $\left( {{f_i}} \right)$. Together with these two columns, some extra columns are needed.
The values are given as one of the two forms. One is ungrouped and the other is grouped.
For grouped data, the class marks ${y_i}$ are also calculated and shown in the table.
You have to assume a number as a mean $a$ of the data from the middle of the column of class marks.
Then make a column for deviations ${d_i}$ of each class marked ${y_i}$ from the assumed mean $a$ and make another column for the products ${f_i}{d_i}$.
After making all the columns in a table, you need a formula to find the mean of the given data.
The formula is ${M_g} = a + \dfrac{{\sum {{f_i}{d_i}} }}{{\sum {{f_i}} }}$, where ${M_g}$ represents the mean of the grouped data and all other symbols have been interpreted already.
Comparing this formula with the given formula, we get $x = a$ i.e., $x$ is assumed mean.

Option ‘B’ is correct

Note: The formula is not appropriate for discrete series. It is one of the necessary methods for finding the mean of a grouped data in case of continuous series. Be careful about placing the symbols. Many students can’t remember the actual place of the symbols and obtain a wrong meaning.