Mode of Grouped Frequency Distribution

Q.

Find the mode of the given data.

$$\begin{array}{cc}\text{Class}& \text{Frequency}\\ 0-5& 200\\ 5-10& 250\\ 10-15& 225\\ 15-20& 300\\ 20-25& 275\end{array}$$

1. 18.25
2. 18.5
3. 19.75
4. 18.75

Q.

The marks obtained by the sudents of a class, in an exam which was out of 50 marks, is given below.

$\begin{array}{cc}\text{Marks}& \text{Number of students}\\ 5& 1\\ 7& 2\\ 11& 2\\ 16& 3\\ 21& 5\\ 24& 6\\ 28& 3\\ 32& 5\\ 34& 8\\ 39& 6\\ 43& 4\\ 45& 2\\ 49& 3\end{array}$ [4 MARKS]

(i)Find mode for the ungrouped data.

(ii) Represent the same as grouped data, with class intervals of width = 10 and find the mode for the grouped data.

Q. If the preceding and succeeding classes of the modal class have the same frequency, then the mode will be the _______ .

1. midpoint of the modal class
2. upper limit of the modal class
3. lower limit of the modal class
4. midpoint of the preceding class

Q. What is the slope of the line joining the points $(x_1,y_1)$ and $(x_2,y_2)$?

1. $\frac{y_1}{x_2-x_1}$
2. $\frac{y_2-y_1}{x_2-x_1}$
3. $\frac{y_2}{x_1-x_2}$
4. $\frac{y_2}{x_2}$

Q. The following is the formula for finding the mode of grouped data. State what p and q are.
$Mode=p+\frac{q-f_0}{(q-f_0)+(q-f_2)}\times h$

1. p = l, lower limit of modal class; $q=f_1$, frequency of modal class
2. p = l, middle value of modal class; $q=f_1$, frequency of modal class
3. p = l, size of class interval; $q=f_1$, frequency of modal class
4. p = l, slope; $q=f_1$, frequency of lower class

Q. Identify the modal class, the upper limit of the modal class and the lower limit of the modal class for the given data:
$\begin{array}{ccccccc}Age\left(inyears\right)& 5-15& 15-25& 25-35& 35-45& 45-55& 55-65\\ Numberofpatients& 6& 11& 21& 23& 14& 5\end{array}$

1. 15-55, 11, 31
2. 35-45, 35, 45
3. 15-25, 11, 21
4. 35-45, 45, 35

Q. Find the mode of the given data.

$$\begin{array}{cc}Class& Frequency\\ 0-5& 200\\ 5-10& 250\\ 10-15& 225\\ 15-20& 300\\ 20-25& 275\end{array}$$

1. 18.75