Finding Mode for Ungrouped Data

Q.

What Is advantage and disadvantage of Mode?

Q. The frequency distribution table of agriculture holdings in a village is given below:

Area of land (in hectares): 1-3 3-5 5-7 7-9 9-11 11-13

Number of families: 20 45 80 55 40 12

Find the modal agricultural holdings of the village .

Q.

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.

Expenditure (in Rs)	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

Q. If the mode of the data: 64, 60, 48, x, 43, 48, 43, 34 is 43, then x + 3 =

(a) 44
(b) 45
(c) 46
(d) 48

Q.

The given distribution shows the number of runs scored by some top batsmen of the world in one-day international cricket matches.

Runs scored	Number of batsmen
3000 − 4000	4
4000 − 5000	18
5000 − 6000	9
6000 − 7000	7
7000 − 8000	6
8000 − 9000	3
9000 − 10000	1
10000 − 11000	1

Find the mode of the data.

Q.

Question 6
A student noted the number of cars passing through a spot on a road for 100 periods each of 3 minutes and summarized it in the table given below. Find the mode of the data.

$\begin{array}{ccccccccc}\text{Number of cars}& 0-10& 10-20& 20-30& 30-40& 40-50& 50-60& 60-70& 70-80\\ \text{Frequency}& 7& 14& 13& 12& 20& 11& 15& 8\end{array}$

Q. Compare the modal ages of two groups of students appearing for an entrance test:

Age (in years):	16−18	18−20	20−22	22−24	24−26
Group A:	50	78	46	28	23
Group B:	54	89	40	25	17

Q.

The value of the observation which occurs most frequently in data is called

1. Mean

2. Mode

3. Median

4. Range

Q.

The following table shows the ages of the patients admitted in a hospital during a year:

age (in years)	5 − 15	15 − 25	25 − 35	35 − 45	45 − 55	55 − 65
Number of patients	6	11	21	23	14	5

Find the mode and the mean of the data given above. Compare and interpret the two measures of central tendency.

Q.

Find the mode of the following data:
(i) 3, 5, 7, 4, 5, 3, 5, 6, 8, 9, 5, 3, 5, 3, 6, 9, 7, 4
(ii) 3, 3, 7, 4, 5, 3, 5, 6, 8, 9, 5, 3, 5, 3, 6, 9, 7, 4
(iii) 15, 8, 26, 25, 24, 15, 18, 20, 24, 15, 19, 15

Q. Write the modal class for the following frequency distribution:

Class-interval:	10−15	15−20	20−25	25−30	30−35	35−40
Frequency:	30	35	75	40	30	15

Q. The following data gives the distribution of total monthly household expenditure of 200 families of a villages. Find the modal monthly expenditure of the families. Also, find the mean monthly expenditure:

Expenditure (in Rs.)	Frequency	Expenditure (in Rs.)	Frequency
1000−1500 1500−2000 2000−2500 2500−3000	24 40 33 28	3000−3500 3500−4000 4000−4500 4500−5000	30 22 16 7

Q.

Find the value of x, if the mode of the given data is 15:

15, 20, 18, 25, 14, 15, 25, 15, 18, 16, 20, 25, 20, x, 18

If both 20 and 18 are changed to 25, find the new mode of the data.

Q.

The measure of central tendency that is most suitable to find the average male or female height of the region is

1. Mean and mode

2. Mean

3. Median

4. Mode

Q.

The age wise participation of students in the Annual Function of a school is shown in the following distribution.
$\begin{array}{cccccccc}\text{Age (in years)}& 5-7& 7-9& 9-11& 11-13& 13-15& 15-17& 17-19\\ \text{Number of}& & & & & & & \\ \text{students}& x& 15& 18& 30& 50& 48& x\end{array}$

Find the missing frequencies when the sum of frequencies is 181. Also, find the mode of the data.

Q.

The mode of the given data 1, 7, 2, 4, 5, 9, 8, 3 is

1. 9

2. 5

3. No mode

4. 1

Q. The following data is gives the information on the observed lifetimes (in hours) of 225 electrical components:

Lifetimes (in hours)	0−20	20−40	40−60	60−80	80−100	100−120
No. of components	10	35	52	61	38	29

Determine the modal lifetimes of the components.

Q.

The following data gives the information on the observed lifetimes (in hours) of 225 electrical components:

Lifetimes (in hours)	0 − 20	20 − 40	40 − 60	60 − 80	80 − 100	100 − 120
Frequency	10	35	52	61	38	29

Determine the modal lifetimes of the components.

Q.

For the data 1, 5, 7, + 1, 9, – 2, 3, if the mean is 4. Find the value of . Using this value of , also find mode.

1. x = 2, mode = 3

2. x = 3, mode = 4

3. x = 2, mode = 8

4. x = 4, mode = 6

Q. Question 4
Find the mode of 14, 25, 14, 28, 18, 17, 18, 14, 23, 22, 14, 18.

Q.

Which of the following is the mode of a set of observations?

1. The average value of data set

2. The middle most point of data set

3. Value with maximum frequency

4. Most important datum in data set

Q. The monthly pocket money of 50 students of a class are given in the following distribution:

Monthly pocket money (in ₹)	0−50	50−100	100−150	150−200	200−250	250−300
Number of students	2	7	8	30	12	1

Find the modal class and also give class mark of the modal class.

Q.

Mode is defined as the

1. maximum frequency of a data element

2. maximum frequency of the maximum data element

3. maximum data element

4. datum element having maximum frequency

Q. Write the lower limit of the modal class of the following frequency distribution?

Age (in years)	0−10	10−20	20−30	30−40	40−50	50−60
Number of patients	16	13	6	11	27	18

Q. Consider the following frequency distribution

Class	0-10	10-20	20-30	30-40	40-50	50-60
Frequency	3	9	15	30	18	5

The modal class is
(a) 10-20
(b) 20-30
(c) 30-40
(d) 50-60

Q. The following table show the ages of the patients admitted in a hospital during a year:

Age (in years):	5−15	15−25	25−35	35−45	45−55	55−65
Number of patients:	6	11	21	23	14	5

Find the mode and the mean of the data given above. Compare and interpret the two measures of central tendency.

Q.

The age of the employees in a startup company is shown below.

$\begin{array}{cc}\text{Age}& \text{No. of Employees}\\ 18-26& 30\\ 26-34& 70\\ 34-42& 50\\ 42-50& 30\\ 50-58& 10\\ 58-66& 10\end{array}$

Find the modal age of the employees of the company. [2 MARKS]

Q. Grouped frequency distribution of supply of milk to hotels and the number of hotels is given in the following table. Find the mode of the supply of milk.

Age (years)	Less than 5	5 - 9	10 - 14	15 - 19	20 - 24	25 - 29
No. of patients	38	32	50	36	24	20

Q. The given distribution shows the number of runs scored by some top batsmen of the world in one-day international cricket matches.

Runs scored	Number of batsman	Runs scored	Number of Batsman
3000−4000 4000−5000 5000−6000 6000−7000	4 18 9 7	7000−8000 8000−9000 9000−10000 10000−11000	6 3 1 1

Find the mode of data.

Q.

Which of the following is not a measure of central tendency?

1. Mode

2. Median

3. Range

4. Mean