Mean of Grouped Data

Find the mean age in years from the frequency distribution given below:

$\begin{array}{|cccccccc|}\hline \text{ Age in years }& 25-29& 30-34& 35-39& 40-44& 45-49& 50-54& 55-59\\ \text{ No. of persons }& 4& 14& 22& 16& 6& 5& 3\\ \hline\end{array}$

If $x_i$'s are the mid-points of the class intervals of grouped data, $f_i$'s are the corresponding frequencies and $\overline{x}$ is the mean, then $\sum _{}^{}{f}_i\left(x_i-\overline{x}\right)$ is equal to

While computing mean of grouped data, we assume that the frequencies are

In the formula: $\overline{x}=a+h\left(\frac{{\displaystyle \sum _{}^{}}{f}_i{u}_i}{\sum _{}^{}{f}_i}\right)$, for finding the mean of grouped frequency distribution, $u_i=$

In the formula: $\overline{x}=a+\frac{{\displaystyle \sum _{}^{}}{f}_i{d}_i}{\sum _{}^{}{f}_i}$ for finding the mean of the grouped data, $d_i\text{'}s$ are deviations from $a$ (assumed mean) of

In a grouped frequency distribution, the mid-values of the classes are used to measure which of the following central tendency?

The measure of a central tendency of a statistical data which takes into account all the data is

The mean of the following distribution is $2.6$

The value of $p$ is

The mean of the following frequency distribution is $57.6$ and the sum of the observations is $50$. Find the missing frequencies $f_1$ and $f_2$:

$\begin{array}{|lcccccc|}\hline \text{ Class }& 0-20& 20-40& 40-60& 60-80& 80-100& 100-120\\ \text{ Frequency }& 7& f_1& 12& f_2& 8& 5\\ \hline\end{array}$

The daily expenditure of $100$ families are given below. Calculate $f_1$ and $f_2$, if the mean daily expenditure is $₹188$.

$\begin{array}{|lccccc|}\hline \text{ Expenditure (in }₹\text{ ) }& 140-160& 160-180& 180-200& 200-220& 220-240\\ \text{ No. of families }& 5& 25& f_1& f_2& 5\\ \hline\end{array}$

Find the mean of the following distribution: 

$\begin{array}{|lcccccccc|}\hline \text{ Classes }& 4-8& 8-12& 12-16& 16-20& 20-24& 24-28& 28-32& 32-36\\ \text{ Frequency }& 2& 12& 15& 25& 18& 12& 13& 3\\ \hline\end{array}$

Calculate the arithmetic mean of the following frequency distribution:

$\begin{array}{|lccccc|}\hline \text{ Class intervals }& 0-80& 80-160& 160-240& 240-320& 320-400\\ \text{ Frequency }& 22& 35& 44& 25& 24\\ \hline\end{array}$

The mean of a number of observations is the sum of the values of all observations divided by the ___ of observations.

In a class test, marks obtained by $120$ students are given in the following frequency distribution table. It is given that the mean is $59$, find the missing frequencies $x$ and $y$.

The mean of the following frequency distribution is $53$. But the frequencies $f_1$ and $f_2$ in the classes $20-40$ and $60-80$ are missing. Find the missing frequencies.

The mean of the following frequency distribution is $62.8$. Find the missing frequency $x$.

The arithmetic mean of the following frequency distribution is $53$. Find the value of $k$.

A class teacher has the following absentee record of $40$ students of a class for the whole term. If the mean number of days a student was absent is $k$, find $k$.

The following table gives the number of pages written by Sarika for completing her own book for $30$ days:

If the mean number of pages written per day is $k$, find $k$.

The frequency distribution table of an agricultural holding in a village is given below:

If the mean area held by a family is $k$ hectares, find $k$.