Class Interval

Q.

What is the lower limit of the modal class of the following frequency distribution?

$\begin{array}{ccccccc}Age\left(inyears\right)& 0-10& 10-20& 20-30& 30-40& 40-50& 50-60\\ Numberofpatients& 16& 13& 6& 11& 27& 18\end{array}$

Q.

In which of the following frequency distributions, the class intervals overlap?

1. Discrete frequency distribution

2. Discontinuous frequency distribution

3. Continuous frequency distribution

4. Both, Continuous frequency distribution as well as Discontinuous frequency distribution

Q.

The relative humidity (in$\%$) of a certain city for a month of $30days$ was as follows: $$\begin{gathered} 98.1,98.6,99.2,90.3,86.5,95.3,92.9,96.3,94.2,95.1,89.2,92.3,97.1,93.5,92.7,95.1,97.2,93.3,95.2, \\ 97.3,96.2,92.1,84.9,90.2,95.7,98.3,97.3,96.1,92.1,89. \end{gathered}$$

(i) Construct a grouped frequency distribution table with classes $84-86,86-88,$ etc.

(ii) Which month or season do you think this data is about?

(iii) What is the range of this data?

Q. Convert the given class intervals in exclusive form.

1. 
2. 
3. 
4. 

Q.

Question 2
The following data gives the information on the observed lifetimes (in hours) of 225 electrical components:

$\begin{array}{ccccccc}\text{Lifetimes(in hours)}& 0-20& 20-40& 40-60& 60-80& 80-100& 100-120\\ \text{Frequency}& 10& 35& 52& 61& 38& 29\end{array}$

Determine the modal lifetimes of the components.

Q. Weight of 60 eggs were recorded as given below:

Weight (in grams)	75−79	80−84	85−89	90−94	95−99	100−104	105−109
Number of eggs	4	9	13	17	12	3	2

Calculate their mean weight to the nearest gram.

Q.

Consider the frequency distribution of the heights of 60 students of a class:

$\begin{array}{ccc}Height\left(incm\right)& No.of.Students& CumulativeFrequency\\ 150-155& 16& 16\\ 155-160& 12& 28\\ 160-165& 9& 37\\ 165-170& 7& 44\\ 170-175& 10& 54\\ 175-180& 6& 60\end{array}$

The sum of the lower limit of the modal class and the upper limit of the median class is :

(a) 310 (b) 315 (c) 320 (d) 330

Q.

Question 5
The given distribution shows the number of runs scored by some top batsmen of the world in one-day international cricket matches.

$\begin{array}{cc}Numberofstudentsperteacher& Numberofstates/U.T\\ 3000-4000& 4\\ 4000-5000& 18\\ 5000-6000& 9\\ 6000-7000& 7\\ 7000-8000& 6\\ 8000-9000& 3\\ 9000-10000& 1\\ 10000-11000& 1\end{array}$

Find the mode of the data.

Q.

In a class interval if only lower limit of the class interval is included in the class limit then that class interval is called ___.

1. Inclusive class interval

2. Exclusive class interval

3. Either of them

4. None of the above

Q.

The width of each of five continuous classes in a frequency distribution is 5 and the lower class limit of the lowest class is 10. The upper limit of the highest class is

1. 40
2. 15
3. 35
4. 25

Q.

Which of the following is true for the histogram ?

1. 20

2. 25

3. 30

4. None of these

Q.

Question 8 (i)
Thirty children were asked about the number of hours they watched TV programmes in the previous week. The results were found as follows:
$\begin{array}{cccccccccc}1& 6& 2& 3& 5& 12& 5& 8& 4& 8\\ 10& 3& 4& 12& 2& 8& 15& 1& 17& 6\\ 3& 2& 8& 5& 9& 6& 8& 7& 14& 12\end{array}$
(i) Make a grouped frequency distribution table for this data, taking class width 5 and one of the class intervals as 5- 10.

Q.

Question 2
The distance (in km) of 40 engineers from their residence to their place of work were found as follows:
$\begin{array}{cccccccccc}5& 3& 10& 20& 25& 11& 13& 7& 12& 31\\ 19& 10& 12& 17& 18& 11& 31& 17& 16& 2\\ 7& 9& 7& 8& 3& 5& 12& 15& 18& 3\\ 12& 14& 2& 9& 6& 15& 15& 7& 6& 12\end{array}$
Construct a grouped frequency distribution table with class size 5 for the data given above taking the first interval as 0-5 (5 not included). What main feature do you observe from this tabular representation?

Q.

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

$\begin{array}{ccccccc}Monthlypocketmoney(inRs.)& 0-50& 50-100& 100-150& 150-200& 200-250& 250-300\\ Numberofstudents& 2& 7& 8& 30& 12& 1\end{array}$

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

Q. What will come in place of the question mark (?) in each of the following series?

17, 52, 158, 477, ?, 4310

1. None of these
2. 1433
3. 1432
4. 1435
5. 1434

Q. The weekly observations on cost of living index in a certain city for the year 2004 − 2005 are given below. Compute the weekly cost of living index.

Cost of living Index	Number of Students	Cost of living Index	Number of Students
1400−1500 1500−1600 1600−1700	5 10 20	1700−1800 1800−1900 1900−2000	9 6 2

Q. Below given is the pulse count of 40 patients.
66, 79, 89, 67, 72, 82, 85, 80, 82, 81, 67, 87, 71, 68, 63, 74, 73, 86, 84, 75, 85, 80, 85, 61, 75, 85, 80, 85, 61, 75, 68, 69, 64, 75, 73, 72, 82, 76, 74, 77.
Group the data first in discontinuous class intervals such that one of the class intervals is 70-74.
Next, group the data in continuous class intervals such that one of the class intervals is 85-90.
Find the second class interval and the corresponding frequency of the class for both the groupings of the data.

Q.

The Mean and Standard Deviation of the heights and weights of 20 persons are given below

Characteristics
Height (in cm) Weight (in kg)	175 70	3.5 2.1

In which characteristics are they more variables?

Q. Question 6
Lipika reads a book for $1\frac{3}{4}$ hours in a day. If she read the entire book in 6 days how many hours did she take to read the book? In how many days will she be able to complete the book if she would have read for $\frac{1}{2}$ hours each day? [3 Marks]

Q. i) Using step-deviation method, calculate the mean marks of the following distribution.
ii) State the modal class.
$\begin{array}{cc}Classinterval& Frequency\\ 50-55& 5\\ 55-60& 20\\ 60-65& 10\\ 65-70& 10\\ 70-75& 9\\ 75-80& 6\\ 80-85& 12\\ 85-90& 8\end{array}$ [4 MARKS]

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. 15-25, 11, 21
2. 35-45, 45, 35
3. 35-45, 35, 45
4. 15-55, 11, 31

Q. Find the mean of each of the following frequency distributions :

Class interval:	50-70	70-90	90-110	110-130	130-150	150-170
Frequency:	18	12	13	27	8	22

Q. Question 95 (v)

Look at the map given below and answer the following question.



Which sector has the maximum number of houses?

Q.

Consider the following frequency distribution:

$\begin{array}{ccccccc}Class& 0-10& 10-20& 20-30& 30-40& 40-50& 50-60\\ Frequency& 3& 9& 15& 30& 18& 5\end{array}$

The modal class is

(a) 10-20 (b)20-30 (c)30-40 (d) 50-60

Q. For a data set, the value of the range is 20. If the smallest value of this data set is 7, find the largest value.

1. 27
2. 17
3. 20
4. 37

Q. What is the class mark of the class interval 10.5 - 15.5?

1. 13
2. 10.5
3. 15.5
4. 26

Q.

Question 2

Shekhar is a famous cricket player. He has so far scored 6980 runs in test matches. He wishes to complete 10, 000 runs. How many more runs does he need?

Q. Question 6
For the following distribution,
$\begin{array}{cccccc}Class& 0-5& 5-10& 10-15& 15-20& 20-25\\ Frequency& 10& 15& 12& 20& 9\end{array}$
the sum of lower limits of the median class and modal class is
(a) 15
(b) 25
(c) 30
(d) 35

Q.

Convert the given frequency distribution into a continuous grouped frequency distribution. In which intervals would $153.5$ and $157.5$ be included?

Class interval	Frequency
$150-153$	$7$
$154-157$	$7$
$158-161$	$15$
$162-165$	$10$
$166-169$	$5$
$170-173$	$6$

Q.

The class mark for a class interval while calculating the mean is its upper limit.

1. True

2. False