Finding Mode for Grouped Data When Class Intervals Are GivenÂ

Q.

Find the mode of the following data.

$\begin{array}{cccccc}\text{Class/space interval}& 0-100& 100-200& 200-300& 300-400& 400-500\\ \text{Frequency}& 7& 11& 15& 9& 8\end{array}$

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Q.

Find the mode of the following data.

$$\begin{array}{cccccccc}Classinterval& 25-35& 35-45& 45-55& 55-65& 65-75& 75-85& 85-95\\ Frequency& 12& 16& 17& 15& 8& 19& 13\end{array}$$

Q.

1. 1 - 2
2. 6 - 7
3. 2 - 3
4. 7 - 8

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. 19
2. 18.75
3. 18.5
4. 18.25

Q. The demand of different shirt sizes, as obtained by a survey, is given below:

Size:	38	39	40	41	42	43	44	Total
Number of persons (wearing it):	26	39	20	15	13	7	5	125

Find the modal shirt sizes, as observed from the survey.

Q.

The following data shows monthly savings of 100 families . Find the difference of modal and mean monthly savings in rupees.

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

1. 700-800

2. 600-700

3. 900-1000

4. 800 - 900

Q.

Find the mode of the following data.

$$\begin{array}{cccccccc}NumberofPlants& 0-2& 2-4& 4-6& 6-8& 8-10& 10-12& 12-14\\ Number& 1& 3& 2& 4& 5& 3& 2\end{array}$$

Q.

What does the l in mode $=I+\left(\frac{f_1-f_0}{2f_1-f_0-f_2}\right)\times h$ stand for? [1 MARK]

Q.

The sum of lower limit and upper limit of modal class is

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

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Q. The demand of different shirt sizes, as obtained by a survey, is given below:

Size:	38	39	40	41	42	43	44	Total
Number of persons (wearing it):	26	39	20	15	13	7	5	125

Find the modal shirt sizes, as observed from the survey.

Q.

What do you call the class interval with the highest frequency?

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Q.

Find the mode for the following data.

$$\begin{array}{cccccc}Classintervel& 35-45& 45-55& 55-65& 65-75& 75-85\\ Frequency& 200& 250& 50& 70& 40\end{array}$$

Q.

In the formula for mode of a grouped data ,

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

where symbols have their usual meaning, $f_1$ represents:

1. Frequency of the class preceding the modal class

2. Frequency of the class succeeding the modal class

3. Frequency of median class

4. Frequency of modal class

Q. Prepare a record of heights of the students in your class. Find the modal height.

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. 25
2. 30
3. 21
4. 20

Q.

The h in the formula

Mode=I+$\left(\frac{f_1-f_0}{2f_1-f_0-f_2}\right)$$\times$h

stands for class width.

1. True

2. False

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. 15-25, 11, 21
3. 35-45, 45, 35
4. 35-45, 35, 45

Q.

The modal class of the given data is

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

1. 15 -20

2. 10-15

3. 5-10

4. 0-5

Q.

The class interval size and frequency of modal class is

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

1. 5, 300

2. 5 , 250

3. 4, 250

4. 4, 200

Q.

A survey was conducted on 20 families in a locality by a group of students .What will be the mode of the data?

$$\begin{array}{cccccc}\text{Age of family member}& 0-20& 20-40& 40-60& 60-80& 80-100\\ \text{Number of students}& 7& 8& 2& 2& 1\end{array}$$

1. 21.85

2. 23.87

3. 24.87

4. 22.86

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.

The class interval size and frequency of modal class is

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

1. 5 , 250

2. 5, 300

3. 4, 250

4. 4, 200

Q. A cricket player scored the following runs in 12 one-day matches:
50, 30, 9, 32, 60, 50, 28, 50, 19, 50, 27, 35.
Find his modal score.

Q. The marks obtained by twenty students are given as follows.
27, 22, 24, 17, 16, 15, 14, 22, 17, 15, 22, 26, 19, 22, 20, 22, 16, 15, 22, 27.
Find the modal marks.