Measures of Central Tendency

$125,130,75,10,45,0.5,0.40,500,150,5$. Calculate the geometric and the harmonic mean of the following series of monthly expenditure of a batch of students.

 Draw a less than ogive for the following frequency distribution and find the median using ogive curve.

$\begin{array}{|cc|}\hline \mathrm{I} \mathrm{Q}& \mathrm{Frequency}\\ 60-70& 2\\ 70-80& 5\\ 80-90& 12\\ 90-100& 31\\ 100-110& 39\\ 110-120& 10\\ 120-130& 2\\ \hline\end{array}$

 Draw a less than ogive for the following frequency distribution and find the median using ogive curve.

$\begin{array}{|cc|}\hline \mathrm{I} \mathrm{Q}& \mathrm{Frequency}\\ 60-70& 2\\ 70-80& 5\\ 80-90& 12\\ 90-100& 31\\ 100-110& 39\\ 110-120& 10\\ 120-130& 5\\ \hline\end{array}$

What measure of central tendency is represented by the abscissa of the point where "less than ogive'   and 'more than ogive'  intersect?

 Draw a less than ogive for the following frequency distribution and find the median using ogive curve.

$\begin{array}{|cc|}\hline \mathrm{I} \mathrm{Q}& \mathrm{Frequency}\\ 60-70& 2\\ 70-80& 5\\ 80-90& 12\\ 90-100& 31\\ 100-110& 39\\ 110-120& 10\\ 120-130& 4\\ \hline\end{array}$

Find the harmonic mean of the following distribution of data 

$\begin{array}{|cccc|}\hline \begin{array}{c}\text{ Dividend yield }\\ \text{ (percent) }\end{array}& 2-6& 6-10& 10-14\\ \text{ Number of companies }& 16& 8& 24\\ \hline\end{array}$

Find the harmonic mean of the following distribution of data 

$\begin{array}{|cccc|}\hline \begin{array}{c}\text{ Dividend yield }\\ \text{ (percent) }\end{array}& 2-6& 6-10& 10-14\\ \text{ Number of companies }& 8& 8& 24\\ \hline\end{array}$

Find the harmonic mean of the following distribution of data 

$\begin{array}{|cccc|}\hline \begin{array}{c}\text{ Dividend yield }\\ \text{ (percent) }\end{array}& 2-6& 6-10& 10-14\\ \text{ Number of companies }& 4& 8& 24\\ \hline\end{array}$

Find the harmonic mean of the following distribution of data 

$\begin{array}{|cccc|}\hline \begin{array}{c}\text{ Dividend yield }\\ \text{ (percent) }\end{array}& 2-6& 6-10& 10-14\\ \text{ Number of companies }& 4& 8& 18\\ \hline\end{array}$

The following is the distribution of marks obtained by $105$ students in a subject in an institution. Find the Geometric mean.

$\begin{array}{|cccccccccc|}\hline \text{ Marks }& 4-8& 8-12& 12-16& 16-20& 20-24& 24-28& 28-32& 32-36& 36-40\\ \begin{array}{c}\text{ Number of }\\ \text{ Students }\left(f\right)\end{array}& 7& 4& 18& 30& 15& 12& 10& 6& 3\\ \hline\end{array}$

The following is the distribution of marks obtained by $109$ students in a subject in an institution. Find the Geometric mean.

$\begin{array}{|cccccccccc|}\hline \text{ Marks }& 4-8& 8-12& 12-16& 16-20& 20-24& 24-28& 28-32& 32-36& 36-40\\ \begin{array}{c}\text{ Number of }\\ \text{ Students }\left(f\right)\end{array}& 7& 8& 18& 30& 15& 12& 10& 6& 3\\ \hline\end{array}$

The following is the distribution of marks obtained by $108$ students in a subject in an institution. Find the Geometric mean.

$\begin{array}{|cccccccccc|}\hline \text{ Marks }& 4-8& 8-12& 12-16& 16-20& 20-24& 24-28& 28-32& 32-36& 36-40\\ \begin{array}{c}\text{ Number of }\\ \text{ Students }\left(f\right)\end{array}& 7& 7& 18& 30& 15& 12& 10& 6& 3\\ \hline\end{array}$

The following is the distribution of marks obtained by $107$ students in a subject in an institution. Find the Geometric mean.

$\begin{array}{|cccccccccc|}\hline \text{ Marks }& 4-8& 8-12& 12-16& 16-20& 20-24& 24-28& 28-32& 32-36& 36-40\\ \begin{array}{c}\text{ Number of }\\ \text{ Students }\left(f\right)\end{array}& 7& 6& 18& 30& 15& 12& 10& 6& 3\\ \hline\end{array}$

The following is the distribution of marks obtained by $106$ students in a subject in an institution. Find the Geometric mean.

$\begin{array}{|cccccccccc|}\hline \text{ Marks }& 4-8& 8-12& 12-16& 16-20& 20-24& 24-28& 28-32& 32-36& 36-40\\ \begin{array}{c}\text{ Number of }\\ \text{ Students }\left(f\right)\end{array}& 7& 5& 18& 30& 15& 12& 10& 6& 3\\ \hline\end{array}$

What are the merits and demerits of mode.

Also compute the mode for the following frequency distribution.

What are the properties of Mode. 

Find the mode of the following distribution:

What are the merits and demerits of median. Calculate the median from the following distribution:

The marks obtained in English test by $17$ students were recorded. What is the median marks of the students?

$\begin{array}{|lll|}\hline \text{ Marks out of }50& \text{ Frequency }& \text{ Cumulative frequency }\\ 0-10& 2& 2\\ 10-20& 4& 6\\ 20-30& 5& 11\\ 30-40& 4& 15\\ 40-50& 2& 17\\ \hline\end{array}$

In a class test, $30$ students obtained marks as follows;

Find the mode.

In a class test, $52$ students obtained marks as follows;

Find the mode.