Mode of Continuous Series

Q.

Give the formula for estimating mode in case of continuous series.

Q.

For the following distribution: Marks Number of students Below $103,$ Below $2012,$ Below $3027,$ Below $4057,$ Below $5075,$ Below $6080$. The modal class is

1. $10-20$

2. $20-30$

3. $30-40$

4. $50-60$

Q.

Define Mode. Calculate Mode of the following frequency distribution:

$\begin{array}{cccccccc}\text{Marks}& 10-15& 15-20& 20-25& 25-30& 30-35& 35-40& 40-45\\ \text{No.of Students}& 3& 7& 16& 12& 9& 5& 3\end{array}$

Q.

The modal class for the following distribution is

1. 20 - 30

2. 10 - 20

3. 30 - 40

4. 50 - 60

Q.

Calculate the mean and the median for the following distribution:

Number	$5$	$10$	$15$	$20$	$25$	$30$	$35$
Frequency	$1$	$2$	$5$	$6$	$3$	$2$	$1$

Q. The lifetimes of 100 light bulbs are tabulated below. Find the modal lifetime.

$$\begin{array}{cc}Lifetime\left(inhours\right)& Frequency\\ 0-20& 7\\ 20-40& 13\\ 40-60& 20\\ 60-80& 18\\ 80-100& 16\\ 100-120& 10\\ 120-140& 7\\ 140-160& 9\end{array}$$

1. 70 hours
2. 72 hours
3. 58 hours
4. 84 hours

Q.

The monthly income of $100$ families are given as below : Income$(inRs)$ Number of families $0-5000:85000-10000:2610000-15000:4115000-20000:1620000-25000:325000$-$30000:330000-35000:235000-40000:1$ Calculate the modal income.

Q.

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

$$\begin{array}{cccccc}Ageoffamilymember& 0-20& 20-40& 40-60& 60-80& 80-100\\ Numberofstudents& 7& 8& 2& 2& 1\end{array}$$

Given that modal class is 20-40

1. 21.85

2. 22.85

3. 23.87

4. 24.87

Q.

The following data shows the number of patients admitted in a hospital from different age groups.

$\begin{array}{ccccccc}\text{Age}& 5-15& 15-25& 25-35& 35-45& 45-55& 55-65\\ \text{Frequency}& 6& 11& 21& 23& 14& 5\end{array}$

Identify the modal class for the data

1. 45 - 55

2. 15 - 25

3. 25 - 35

4. 35 - 45

Q.

The following distribution gives the state-wise teacher-student ratio in higher secondary schools of India. Find the mode and mean of this data. Interpret the two measures

No of Students per teacher	Number of states / U.T
$15-20$	$3$
$20-25$	$8$
$25-30$	$9$
$30-35$	$10$
$35-40$	$3$
$40-45$	$0$
$45-50$	$0$
$50-55$	$2$

Q.

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

$\begin{array}{ccccccc}Lifetime\left(inhours\right)& 0-20& 20-40& 40-60& 60-80& 80-100& 100-120\\ Numberofcomponents& 10& 35& 52& 61& 38& 29\end{array}$

Determine the modal lifetimes of the components, given that the modal class is 60-80.

1. 66.21

2. 60.02

3. 65.62

4. 65.69

Q.

Compute mode of the following series:

$\begin{array}{cccccccccc}\text{Mid-values}& 5& 10& 15& 20& 25& 30& 35& 40& 45\\ \text{Frequency}& 7& 13& 19& 24& 32& 28& 17& 8& 6\end{array}$

Q. In a junior football league, the heights of players and the number of goals scored by them are tabulated. Identify the height class which contains the top scorer.

$$\begin{array}{ccccccccc}Height\left(incm\right)& 100-110& 110-120& 120-130& 130-140& 140-150& 150-160& 160-170& 170-180\\ No.ofgoalsscored& 8& 10& 15& 9& 12& 14& 13& 10\end{array}$$

1. 120-130
2. 140-150
3. 150-160
4. 160-170

Q.

Find the mode of the following data

$\begin{array}{cc}Class& Frequency\\ 0-100& 7\\ 100-200& 11\\ 200-300& 15\\ 300-400& 9\\ 400-500& 8\end{array}$

1. 220

2. 240

3. 260

4. 280

Q. Find the modal class of the following distribution.

$\begin{array}{cc}Class& Frequency\\ 0-100& 3\\ 100-200& 13\\ 200-300& 24\\ 300-400& 8\\ 400-500& 16\\ 500-600& 22\\ 600-700& 18\\ 700-800& 9\end{array}$

1. 400-500
2. 500-600
3. 200-300
4. 600-700

Q.

The following data shows monthly savings of 100 families, the difference between modal and mean monthly savings lies between ___. (Given that modal class is the class having the highest frequency)

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

1. 600-700

2. 800 - 900

3. 700-800

4. 900-1000

Q. Jacob was stranded on an island. He was trying to communicate with his friend using a radio transmitter. The quality of communication is measured using a number called Q factor. Jacob tried out different frequency ranges and noted down the Q factors in each range. Identify the frequency with maximum Q factor. Given that the maximum frequency occurs in the range 175-200.

$$\begin{array}{ccccccc}Frequency& 100-125& 125-150& 150-175& 175-200& 200-225& 225-250\\ range\left(inkHz\right)& & & & & & \\ Qfactor\left(in\%\right)& 20& 35& 60& 85& 70& 50\end{array}$$

1. 185.75 kHz
2. 190.625 kHz
3. 200 kHz
4. 212.5 kHz

Q. The following data given the information on the observed life terms (in hours) of $200$ electrical components.

Life times (in hours)	40-60	60-80	80-100	100-120	120-140	140-160
Frequency	$25$	$38$	$65$	$24$	$31$	$17$

Determine the modal lifetimes of the components.

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.

Which of the following expressions is used to determine the mode?

1. 1 + () h

2. 

3. 1 + () h

4. l + () h

Q. Compute the mode from the following series:

Size	45-55	55-65	65-75	75-85	85-95	95-105	105-115
Frequency	7	12	17	30	32	6	10