Various Measures of Central Tendency

What is percentile?

If the difference of mode and median of a data is twenty-four, then find the difference of median and mean is

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

The above data gives distribution of height of a group of $60$ college students.Draw the histogram for this distribution and find the modal height. Check this result by using algebraic formula.

From the above table find the median and quartile deviation.

In a class of $50$ students, $10$ have failed and their average marks are $2.5$. The total marks secured by the entire class were $281$. Find the average marks of those who have passed.

By given table find the value of median, lower quartile, $7^{th}$ decile and ${85}^{th}$ percentile of the frequency distribution.

List any four uses of weighted arithmetic mean.

List the uses of weighted arithmetic mean.

List the uses of weighted arithmetic mean in index numbers

Write the uses of weighted arithmetic mean in grouped data

Write the uses of weighted arithmetic mean in constructing index numbers.

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

$\begin{array}{|cc|}\hline \mathrm{I} \mathrm{Q}& \mathrm{Frequency}\\ 60-70& 2\\ 70-80& 5\\ 80-90& 12\\ 90-100& 31\\ 100-110& 39\\ 110-120& 11\\ 120-130& 1\\ \hline\end{array}$

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

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

 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?

Represent the following data by component bar diagram.

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

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

Three year's result of $XII$ Class students of  a school are given in the following table. Represent this by a component bar diagram.

$$$\begin{array}{|ccccc|}\hline & Number of students& & & \\ Year& First& \text{ Second }& \text{ Third }& \\ & \text{ Div. }& \text{ Div. }& \text{ Div. }& \text{ Failed }\\ 2014& 50& 150& 250& 50\\ 2015& 60& 200& 300& 40\\ 2016& 50& 250& 350& 50\\ \hline\end{array}$

Draw a component bar diagram with the help of following table. Enrollment by gender at schools (%) of children aged 6-14 years in a District of Bihar.

$\begin{array}{|lll|}\hline \text{ Gender }& \text{ Enrolled(\%) }& \text{ Dropout(\%) }\\ \text{ Boys }& 91.5& 8.5\\ \text{ Girls }& 58.6& 41.4\\ \text{ All }& 78.0& 22.0\\ \hline\end{array}$