Finding Mode for Grouped Data When Class Intervals Are Given

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, slope; $q=f_1$, frequency of lower class
4. p = l, size of class interval; $q=f_1$, frequency of modal class

Q.

The following data shows monthly savings of 100 families . Calculate the mode of the given frequency distribution.

$$\begin{array}{cc}Monthlysavings\left(Rs\right)& Numberoffamilies\\ 1000-2000& 14\\ 2000-3000& 15\\ 3000-4000& 21\\ 4000-5000& 27\\ 5000-6000& 25\end{array}$$

1. 700-800

2. 600-700

3. 900-1000

4. 800 - 900

Q.

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

1. True

2. False

Q.

In the fromula for mode of a grouped data ,

mode $=l+\left[\frac{t_1-t_0}{2f_1-f_0-f_2}\right]\times h$ ,

where symbols have their usual meaning $f_1$ represents

1. Frequency of Modal class

2. Frequency of the class preceding the modal class

3. Frequency of the class succeeding the modal class

4. Frequency of median class

Q.

Which of the following formulae correctly depicts the mode of a modal class?

1. Cumulative frequency of previous class

2. Frequency of preceeding class

3. Frequency of modal class

4. Frequency of succeding class.

Q.

The following data shows monthly savings of 100 families . Calculate the mode of the given frequency distribution.

$$\begin{array}{cc}Monthlysavings\left(Rs\right)& Numberoffamilies\\ 1000-2000& 14\\ 2000-3000& 15\\ 3000-4000& 21\\ 4000-5000& 27\\ 5000-6000& 25\end{array}$$

1. 700-800

2. 600-700

3. 900-1000

4. 800 - 900

Q.

The mode for the given data is ___ .

$$\begin{array}{cccccccc}\text{IQ}& 60-70& 70-80& 80-90& 90-100& 100-110& 110-120& 120-130\\ \text{No. of pupils}& 2& 3& 5& 16& 14& 13& 7\end{array}$$

1. 98.46
2. 96.25
3. 95.84
4. 95.98

Q.

The following data shows the warranty period of different components. Find the modal warranty period.

$$\begin{array}{ccccccc}Warrantyperiod\left(years\right)& 0-1& 1-2& 2-3& 3-4& 4-5& 5-6\\ Numberofcomponents& 6& 10& 16& 25& 16& 20\end{array}$$

1. 3
2. 3.25
3. 3.5
4. 4

Q.

Find the mode of the following data. $$\begin{array}{cccccc}\text{Class interval}& 0-10& 10-20& 20-30& 30-40& 40-50\\ \text{Frequency}& 7& 13& 14& 5& 11\end{array}$$

1. 20
2. 30
3. 21
4. 25

Q.

For the following distribution, the modal class is

$\begin{array}{cc}Marks& Numberofstudents\\ Below10& 3\\ Below20& 12\\ Below30& 27\\ Below40& 57\\ Below50& 75\\ Below60& 80\end{array}$

1. 30-40

2. 50-60

3. 10-20

4. 20-30