Mode for Grouped Data

Q.

The relationship between Mean, Median and Mode is

1. Median = Mean + Mode

2. Mode = 3 median - 2 mean

3. Mode = 2 median - 3 mean

4. 3Mode = 2 median - 3 mean

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. 21
2. 25
3. 20
4. 30

Q. Find the mean, median and mode of the following data:

Classes:	0−50	50−100	100−150	150−200	200−250	250−300	300−350
Frequency:	2	3	5	6	5	3	1

Q.

Question 3
The following data gives the distribution of total monthly household expenditure of 200 families of a village. Find the modal monthly expenditure of the families. Also, find the mean monthly expenditure.

$\begin{array}{cc}\text{Expenditure (in Rs)}& \text{Number of families}\\ 1000-1500& 24\\ 1500-2000& 40\\ 2000-2500& 33\\ 2500-3000& 28\\ 3000-3500& 30\\ 3500-4000& 22\\ 4000-4500& 16\\ 4500-5000& 7\end{array}$

Q. Write the empirical relation between mean, mode and median.

Q.

Modal age of students in given distribution is

1. 13 years

2. 12 years

3. 14 years

4. 15 years

Q.

Question 18
The weight of coffee in 70 packets are shown in the following table

Weight	200-201	201-202	202-203	203-204	204-205	205-206
Number of packets	12	26	20	9	2	1

Determine the model weight.

Q.

Modal class of the following distribution is

1. 20-30

2. 40-50

3. 10-20

4. 30-40

Q.

The modal class in the following frequency distribution is:

1. 30-40

2. 40-50

3. 20-30

4. None of these

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. Compute the modal value for the following frequency distribution
x : - 95 105 115 125 135 145 155 165 175
f : - 4 2 18 22 21 19 10 3 2

Q. What is the cumulative frequency of the modal class of the following distribution?

Class	3−6	6−9	9−12	12−15	15−18	18−21	21−24
Frequency	7	13	10	23	4	21	16

Q.

Find the Mean using Step deviation method if the following table :

$\begin{array}{ccccccccccc}\text{Marks}& \text{Below}10& \text{Below}20& \text{Below}30& \text{Below}40& \text{Below}50& \text{Below}60& \text{Below}70& \text{Below}80& \text{Below}90& \text{Below}100\\ \text{No. of students}& 5& 9& 17& 29& 45& 60& 70& 78& 83& 85\end{array}$

1. 50.25
2. 46.2
3. 52
4. 48.42

Q. Find the mean of the following frequency table by step-deviation method: [3 MARKS]
$\begin{array}{cc}Classinterval& Frequency\\ 10-15& 5\\ 15-20& 6\\ 20-25& 8\\ 25-30& 12\\ 30-35& 6\\ 35-40& 3\end{array}$

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. False

2. True

Q.

For the following distribution the modal class is

1. 20-30

2. 40-50

3. 10-20

4. 30-40

Q. The marks in science of 80 students of class X are given below: Find the mode of the marks obtained by the students in science.

Marks:	0−10	10−20	20−30	30−40	40−50	50−60	60−70	70−80	80−90	90−100
Frequency:	3	5	16	12	13	20	5	4	1	1

Q. Question 04.
Will the median class and modal class of grouped data always be different ? Justify your answer.

Q.

_{^{​​​If the difference of mode and median of a data is 24, then the difference of median and mean is?}}

Q. The weights of 50 apples were recorded as given below. Calculate the mean weight, to the nearest gram, by the Step deviation Method.
$\begin{array}{cc}Weight\left(ing\right)& No.ofapples\\ 80-85& 5\\ 85-90& 8\\ 90-95& 10\\ 95-100& 12\\ 100-105& 8\\ 105-110& 4\\ 110-115& 3\end{array}$ [4 MARKS]

Q.

The age of 18 students of a class is reported below. Their modal age is

10, 17, 14, 10, 11, 12, 12, 13, 17, 13, 14, 14, 15, 16, 17, 15, 17, 16

1. 17 years

2. 22 years

3. 16 years

4. 14 years

Q.

For the following distribution the difference in the upper limit of median and modal class is

1. 20

2. 10

3. 0

4. 40

Q.

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

$$\begin{array}{ccccccc}\text{Warranty period (years)}& 0-1& 1-2& 2-3& 3-4& 4-5& 5-6\\ \text{Number components}& 6& 10& 16& 25& 16& 20\end{array}$$

1. 3
2. 4.5
3. 3.5
4. 3.25

Q. The salary per month of the workers in a factory were as follows:
$\begin{array}{cc}Salary\left(inRs\right)& No.ofworkers\\ 300-400& 52\\ 400-500& 43\\ 500-600& 84\\ 600-700& 142\\ 700-800& 93\\ 800-900& 62\end{array}$
i) Find the modal class of this grouped data
ii) Draw the histogram and locate the mode. [6 MARKS]

Q. Find the mean of the data given in the table using step - deviation method.
$\begin{array}{cc}\text{Class Interval}& \text{Frequency}\\ 0-10& 10\\ 10-20& 12\\ 20-30& 7\\ 30-40& 6\\ 40-50& 5\\ 50-60& 8\end{array}$

Q. Find the mean of the following distribution by step deviation method: [4 MARKS]
$\begin{array}{cc}Classinterval& Frequency\\ 20-30& 10\\ 30-40& 6\\ 40-50& 8\\ 50-60& 12\\ 60-70& 5\\ 70-80& 9\end{array}$

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. 22.85

3. 23.87

4. 24.87

Q. The relationship between Mean, Median and Mode is given by: Mode = .

1. 2 Median + 3 Mean
2. 2 Median - 3 Mean
3. 3 Median - 2 Mean
4. 3 Median + 2 Mean

Q. Calculate the mean of the following distribution using step - deviation method.
$\begin{array}{cc}\text{Class Interval}& \text{Frequency}\\ 50-55& 5\\ 55-60& 20\\ 60-65& 10\\ 65-70& 10\\ 70-75& 9\end{array}$

1. 62.3

Q. Compute the mode from the following data:

Class interval	1-5	6-10	11-15	16-20	21-25	26-30	31-35	36-40	41-45	46-50
Frequency	3	8	13	18	28	20	13	8	6	4