Organisation Of Data - Class 11 Commerce Economics - Extra Questions

Define arrayed data.

The given data arranged in order- ascending or descending order is called arrayed data.
Example: The marks obtained by $$5$$ students in a English test as given below:
$$45, 55, 70, 80, 100$$
The data are arranged in ascending order is called arrayed data.


Distinguish between raw data and arrayed data.

Raw data
Arrayed data
The data arranged in original form is called raw data.
Example: The marks obtained by $$5$$ students in a Social test as given below:
$$45, 15, 30, 80, 90$$

The data arranged in order-ascending or descending order is called arrayed data.
Example: The marks obtained by $$5$$ students in a Social test as given below:
$$15, 45, 50, 60, 70$$



Fill in the blanks:
Data obtained in the ............... form is called raw data.


According to the definition, Data obtained in the original form is called raw data.


Complete the following cumulative frequency table:
ClassFrequencyLess than type frequency
0-10$$2$$
10-20$$12$$
20-30$$20$$
30-40$$16$$
Total$$50$$

$$Class$$ $$Frequency$$ $$Less\,than\,type\,frequency$$ 
$$0-10$$ $$2$$ $$2$$ 
$$10-20$$ $$12$$ $$2+12=14$$ 
$$20-30$$ $$20$$ $$14+20=34$$ 
$$30-40$$ $$16$$ $$34+16=50$$ 
$$Total$$ $$50$$  


For the following raw data, form a discrete frequency distribution:
$$30, 32, 32, 28, 34, 34, 32, 30, 30, 32, 32, 34, 30, 32, 32, 28, 32, 30, 28, 30, 32, 32, 30, 28$$ and $$30$$

The required frequency table is shown below
Marks Tally marks Frequency
1754471_1823485_ans_65fffc9449a84374aa6351fbcaa0ae61.png


The marks scored by 55 students in a test are given below.
Marks :0 - 55 - 1010 - 1515 - 20 20 - 25 25  - 30 30 - 25
No. of students 2613171142
Prepare a cumulative frequency table.

Marks Cumulative
Frequency
Less then 5  2
Less then 10  8
Less then 15  21
Less then 20 38
Less then 2549
Less then 30               53
Less then 3555


Given below are the cumulative frequencies showing the weights of 685 students of a school. Prepare a frequency distribution table.
Weight (in kg )No. of students 
Below 25  0
Below 3024
Below 3578
Below 40183
Below 45294
Below 50408
Below 55543
Below 60621
Below 65674
Below 70685

Weights No. of students 
25 - 30 24
30 - 35  54
35 - 40                                  105 
40 - 45 111
45 - 50114
50 - 55135
55 - 6078
60 - 6553
65 -7011


The numbers of members in the $$40$$ families in Bhilar are as follows: $$1,\ 6,\ 5,\ 4,\ 3,\ 2,\ 7,\ 2,\ 3,\ 4,\ 5,\ 6,\ 4,\ 6,\ 2,\ 3,\ 2,\ 1,\ 4,\ 5,\ 6,\ 7,\ 3,$$
$$ 4,\ 5,\ 2,\ 4,\ 3,\ 2,\ 3,\ 5,\ 5,\ 4,\ 6,\ 2,\ 3,\ 5,\ 6,\ 4,\ 2$$. Prepare a frequency table and find the mean of members of $$40$$ families. 

$$\textbf{Step 1: Mean of Discrete Frequency Data.}$$

              $$\text{No of members}$$
              $$(x_{i})$$
     $$\text{No. of families}$$
    $$(f_{i})$$
     $$f_{i}x_{i}$$
               $$1$$    $$2$$     $$2$$
               $$2$$    $$8$$     $$16$$
               $$3$$    $$7$$     $$21$$
               $$4$$       $$8$$     $$32$$
               $$5$$    $$7$$     $$35$$
               $$6$$    $$6$$     $$36$$
               $$7$$    $$2$$     $$14$$



$$N = 40$$
$$\sum f_{i}x_{i} = 156$$
             
             $$\text{Mean}= \dfrac {156}{40} = 3.9$$                                                                      $$\left[\because \textbf{Mean} \boldsymbol{= \dfrac {\sum f_{i}x_{i}}{N} }\right]$$ 

$$\textbf{Hence, Mean of members of 40 families is 3.9}$$


Explain the meaning of the following terms: true class limits.

True class limits:

For example 

$$10 - 20$$
$$30-40$$
$$40-50$$
These class intervals are called inclusive class intervals
and 

$$10-20$$
$$20-30$$
$$30 - 40$$
$$40-50$$
These class intervals are called exclusive class intervals

True class limits are nothing but class boundaries class limits are end numbers of a class interval for instance, we have a class interval $$1-5$$

1 is called the lower limit (LL)
5 is called upper limit (UL)

These numbers define a class


Following are the ages of 360 patients getting medical treatment in a hospital on a day :
Age (in years ) :10 - 2020 - 3030 - 4040 - 50 50 - 60 60 - 70
No. of Patients :905060805030
Construct a cumulative frequency distribution. 

Age in years                                   No. of patients
Less then 2090
Less then 30 140
Less then 40 200
Less then 50 280
Less then 60330
Less then 70360


What is the class mark of the interval $$27-32?$$ 

we know class mark  $$=\dfrac{a+b}{2}$$

Where $$a$$ and $$b$$ are the extreme limits of the class.

class mark of interval $$27-32$$  $$=\dfrac{27+32}{2}$$
                                               $$ =\dfrac{59}{2}$$
                                               $$=29.5$$
Hence class mark is $$29.5$$


Following data gives height in cm(X) and weight in kgs(Y) of $$20$$ boys. Prepare a bivariate frequency table taking class intervals $$150-154$$, $$155-159$$ etc., for X and $$35-39$$, $$40-44$$ etc., Y. Also find conditional frequency distribution of Y when $$155 \leq X\leq 159$$
$$(152, 40)$$ $$(160, 54)$$ $$(163, 52)$$ $$(150, 35)$$
$$(154, 36)$$ $$(160, 49)$$ $$(166, 54)$$ $$(157, 38)$$
$$(159, 43)$$ $$(153, 48)$$ $$(152, 41)$$ $$(158, 51)$$
$$(155, 44)$$ $$(156, 47)$$ $$(156, 43)$$ $$(166, 53)$$
$$(160, 50)$$ $$(151, 39)$$ $$(153, 50)$$ $$(158, 46)$$.


1402617_1672855_ans_aaeb94cd2cb949568fad2608468e500b.jpg


Following table gives income(X) and expenditure(Y) of $$25$$ families.
Find how many families have their income Rs. $$300$$ and more and expenses Rs. $$400$$ and less?

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Following table gives income(X) and expenditure(Y) of $$25$$ families.
Find marginal frequency distribution of income and expenditure.

1672729_d79072c3759c49cb84592d9e03efd08b.PNG


1402302_1672729_ans_ac95316ce75a457e94f6c47e0687bcef.jpg


Following data gives height in cm(X) and weight in kgs(Y) of $$20$$ boys. Prepare a bivariate frequency table taking class intervals $$150-154$$, $$155-159$$… etc., for X and $$35-39$$, $$40-44$$… etc., for Y. Also find marginal frequency distributions.

$$(152, 40)$$ $$(160, 54)$$ $$(163, 52)$$ $$(150, 35)$$
$$(154, 36)$$ $$(160, 49)$$ $$(166, 54)$$ $$(157, 38)$$
$$(159, 43)$$ $$(153, 48)$$ $$(152, 41)$$ $$(158, 51)$$
$$(155, 44)$$ $$(156, 47)$$ $$(156, 43)$$ $$(166, 53)$$
$$(160, 50)$$ $$(151, 39)$$ $$(153, 50)$$ $$(158, 46)$$.


1402616_1672853_ans_587eb720b9134d9b8b21b95593fa8c52.jpg


Following table gives income(X) and expenditure(Y) of $$25$$ families.
Find conditional frequency distribution of X when Y is between $$300-400$$.

1672730_fdc71613a9ff496c8450f2b0e32aada9.PNG


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Following data gives the coded price(x) and demand(y) of a commodity.
Price$$5$$$$7$$$$9$$$$8$$$$10$$$$7$$$$9$$$$8$$$$5$$$$11$$$$11$$$$10$$$$2$$$$3$$$$9$$
Demand$$9$$$$15$$$$13$$$$15$$$$14$$$$10$$$$11$$$$14$$$$10$$$$14$$$$6$$$$14$$$$15$$$$11$$$$12$$
Price$$2$$$$4$$$$3$$$$14$$$$6$$$$10$$$$7$$$$15$$$$8$$$$6$$$$5$$$$6$$$$11$$$$14$$$$15$$
Demand$$6$$$$11$$$$8$$$$11$$$$10$$$$15$$$$9$$$$15$$$$13$$$$9$$$$14$$$$10$$$$7$$$$5$$$$6$$
Classify the data by taking classes $$0-4$$, $$5-9$$ etc., for x and $$5-8, 9-12$$ etc., for y. Also find marginal frequency distribution of x and y.


1402755_1672938_ans_ed04ae644bc1457fa307749c2c538ba9.jpg


Two dice are thrown simultaneously $$25$$ times. The following pairs of observations are obtained.
$$(2, 3)$$ $$(2, 5)$$ $$(5, 5)$$ $$(4, 5)$$ $$(6, 4)$$ $$(3, 2)$$ $$(5, 2)$$ $$(4, 1)$$ $$(2, 5)$$ $$(6, 1)$$ $$(3, 1)$$ $$(3, 3)$$ $$(4, 3)$$ $$(4, 5)$$ $$(2, 5)$$ $$(3, 4)$$ $$(2, 5)$$ $$(3, 4)$$ $$(2, 5)$$ $$(4, 3)$$ $$(5, 2)$$ $$(4, 5)$$ $$(4, 3)$$ $$(2, 3)$$ $$(4, 1)$$.
Prepare a bivariate frequency distribution table for the given data. Also obtain the marginal distributions.


1402419_1672763_ans_85e0735738d748cfb7341f037188056e.jpg


Following data gives the age of husbands(X) and age of wives(Y) in years. Construct a bivariate frequency distribution table and find the marginal distributions.
X$$27$$$$25$$$$28$$$$26$$$$29$$$$27$$$$28$$$$26$$$$25$$$$25$$$$27$$
Y$$21$$$$20$$$$20$$$$21$$$$23$$$$22$$$$20$$$$20$$$$19$$$$19$$$$23$$
X$$26$$$$29$$$$25$$$$27$$$$26$$$$25$$$$28$$$$25$$$$27$$$$26$$
Y$$19$$$$23$$$$23$$$$22$$$$21$$$$20$$$$22$$$$23$$$$22$$$$21$$
Find conditional frequency distribution of age of husbands when the age of wife is $$23$$ years.


1402421_1672844_ans_ba08eb2844964bcebf318328f163cbf4.jpg


Construct a bivariate frequency distribution table of the marks obtained by students in English(X) and Statistics(Y).
Marks in Statistics(X)$$37$$$$20$$$$46$$$$28$$$$35$$$$26$$$$41$$$$48$$$$32$$$$23$$$$20$$$$39$$$$47$$$$33$$$$27$$$$26$$
Marks in English(Y)$$30$$$$32$$$$41$$$$33$$$$29$$$$43$$$$30$$$$21$$$$44$$$$38$$$$47$$$$24$$$$32$$$$31$$$$20$$$$21$$
Construct a bivariate frequency distribution table for the given data by taking class intervals $$20-30$$, $$30-40$$, . etc. for both X and Y. Also find the marginal distributions and conditional frequency distribution of Y when X lies between $$30-40$$.


1402612_1672852_ans_de8a00bcae1e4a649e8c1732212e7612.jpg


Following table gives income(X) and expenditure(Y) of $$25$$ families.
Find conditional frequency distribution of Y when X is between $$200-300$$.

1672749_c487e3c5857b4582944ffae677ce8d3b.PNG


1402348_1672749_ans_fce7d648aef24a0f9d93a30d9511d9a5.jpg


Following data gives the age in years and marks obtained by $$30$$ students in an intelligence test.
Age$$16$$$$17$$$$22$$$$19$$$$21$$$$16$$
Marks$$16$$$$19$$$$39$$$$50$$$$48$$$$41$$
Age$$21$$$$20$$$$20$$$$23$$$$22$$$$19$$
Marks$$59$$$$44$$$$42$$$$62$$$$37$$$$67$$
Age$$23$$$$20$$$$22$$$$22$$$$23$$$$22$$
Marks$$45$$$$57$$$$35$$$$37$$$$38$$$$56$$
Age$$17$$$$18$$$$16$$$$21$$$$19$$$$20$$
Marks$$54$$$$61$$$$47$$$$67$$$$49$$$$56$$
Age$$17$$$$18$$$$23$$$$21$$$$20$$$$16$$
Marks$$51$$$$42$$$$65$$$$56$$$$52$$$$48$$
Prepare a bivariate frequency distribution by taking class intervals $$16-18$$, $$18-20$$,.... etc., for age and $$10-20, 20-30$$. etc., for marks. Find the marginal frequency distributions.


1402876_1672955_ans_a6833985677443989cfb9775aedda7be.jpg


Following data gives the age in years and marks obtained by $$30$$ students in an intelligence test.
Age$$16$$$$17$$$$22$$$$19$$$$21$$$$16$$
Marks$$16$$$$19$$$$39$$$$50$$$$48$$$$41$$
Age$$21$$$$20$$$$20$$$$23$$$$22$$$$19$$
Marks$$59$$$$44$$$$42$$$$62$$$$37$$$$67$$
Age$$23$$$$20$$$$22$$$$22$$$$23$$$$22$$
Marks$$45$$$$57$$$$35$$$$37$$$$38$$$$56$$
Age$$17$$$$18$$$$16$$$$21$$$$19$$$$20$$
Marks$$54$$$$61$$$$47$$$$67$$$$49$$$$56$$
Age$$17$$$$18$$$$23$$$$21$$$$20$$$$16$$
Marks$$51$$$$42$$$$65$$$$56$$$$52$$$$48$$
Prepare a bivariate frequency distribution by taking class intervals $$16-18$$, $$18-20$$,... etc., for age and $$10-20, 20-30$$… etc., for marks. Find conditional frequency distribution of marks obtained when age of students is between $$20-22$$.


1402911_1672961_ans_ef7a2690c4204b28910fb7a4599867d2.jpg


Find marginal frequency distributions.


1402939_1672977_ans_a30cfa7dc3644829b5b4aadf5d9a29c0.jpg


Conditional frequency distribution of Sales when the advertisement expenditure is between $$64-66$$. (Thousand Rs.)


1402950_1672981_ans_85c354fd20d84db39833c0cecaf462be.jpg


Following data gives the coded price(x) and demand(y) of a commodity.
Price$$5$$$$7$$$$9$$$$8$$$$10$$$$7$$$$9$$$$8$$$$5$$$$11$$$$11$$$$10$$$$2$$$$3$$$$9$$
Demand$$9$$$$15$$$$13$$$$15$$$$14$$$$10$$$$11$$$$14$$$$10$$$$14$$$$6$$$$14$$$$15$$$$11$$$$12$$
Price$$2$$$$4$$$$3$$$$14$$$$6$$$$10$$$$7$$$$15$$$$8$$$$6$$$$5$$$$6$$$$11$$$$14$$$$15$$
Demand$$6$$$$11$$$$8$$$$11$$$$10$$$$15$$$$9$$$$15$$$$13$$$$9$$$$14$$$$10$$$$7$$$$5$$$$6$$
Classify the data by taking classes $$0-4$$, $$5-9$$ etc. for x and $$5-8$$, $$9-12$$ etc. for y.
Also find conditional frequency distribution of y when x is less than $$10$$.


1402784_1672948_ans_7332c0e667b7486489d1a13dcbeea1ea.jpg


Prepare a frequency table of the following ages (in years) of 30 students of class VIII in your school:
$$13,14,13,12,14,13,14,15,13,14,13,14,16,12,14$$
$$13,14,15,16,13,14,13,12,17,13,12,13,13,13,14$$

Given $$13,14,13,12,14,13,14,15,13,14,13,14,16,12,14$$
$$13,14,15,16,13,14,13,12,17,13,12,13,13,13,14$$

 Ages (in years):12  13 14 1516  17
 Number of students 4 13 82 2 1 


Following figures relate the weekly wages (in Rs.) of 15 workers in a factory:
$$300,250,200,250,200,150,350,200,250,200,150,300,150,200,250$$
Prepare a frequency table.
Which mark is occurring more frequently?

Given that the weekly wages(in Rs.) of $$15$$ workers in a factory
$$300, 250, 200, 250, 200, 150, 350, 200, 250, 200, 150, 300, 150, 200, 250$$
Frequency table
Wages               Frequency(No. of worke         Tally marks
$$150$$                                $$3$$                                            |||
$$200$$                               $$5$$                                        $$\not{||||}$$
$$250$$                               $$4$$                                            ||||
$$300$$                               $$2$$                                            ||
$$350$$                               $$1$$                                             |
                                              __________
                                               $$15$$
The weekly wage $$200$$ is occurred $$5$$ times so
$$200$$ marks(wage weekly)  occurring more frequently($$5$$ times)
and $$250$$ weekly wage occurring more frequency($$4$$ times)



Construct a bivariate frequency distribution table for the given data by taking classes $$115-125$$, $$125-135$$,... etc., for sales and $$60-62, 62-64$$,... etc., for advertisement expenditure.


1402938_1672973_ans_37fe0ba6eb704eeaa5fa2fb8e0c7e8af.jpg


Conditional frequency distribution of advertisement expenditure when the sales are between $$125-135$$. (lakh Rs.)


1402951_1672984_ans_c66f3b090c9c4b7187c53e7614da0d79.jpg


Fill in the blanks:
Arranging the numerical figures in ascending or descending order is called an .............

Array
According to the definition, arranging the numerical figures of a data in ascending or descending order is called an array.


Define the term Raw data

Raw data: Data obtained in the original form is called raw data.


Define the term Array

Array: Arranging the numerical figures in an ascending or a descending order is called an array.


Define the term:
Array.

An array is a form of representing of data and values.For example the measurement of the heights of the students are as [50cm, 60cm, 64cm] are called array.


Arrange the following as an array (in descending order):
$$0,2,0,3,4,1,2,3,5$$

Descending order $$=5,4,3,3,2,2,1,0$$


Arrange the following as an array (in ascending order):
$$6.3,5.9,9.8,12.3,5.6,4.7$$

Ascending order $$=4.7,5.6,5.9,6.3,9.8,12.3$$


Upper clas limit of $$24-30$$ is _______


1974169_1839483_ans_c9e3856244174a329a7dcae07efac406.jpeg


Fill in the blanks:
Lower class limit of $$15-18$$ is


1974168_1839482_ans_74825f3f5d3c439f8f188257270eb3d0.jpeg


A die is thrown $$25$$ times and the scores were as given below:
$$2, 1, 4, 6, 2, 3, 1, 5, 6, 3, 4, 5, 2, 1, 6, 6, 6, 3, 2, 2, 2, 4, 3, 2, 2$$
Construct data array.

Data array is constructed by writing the scores in the ascending order.
$$1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 4, 4, 4, 5, 5, 6, 6, 6, 6, 6$$


Arrange the following as an array (in descending order):
$$9.1.3.7.5.6.8.3.11.5.10.6$$

Descending order $$=11.5,10.6,9.1,8.3,5.6,3.7$$


Arrange the following as an array (in ascending order):
$$7,5,15,12,10,11,16$$

Ascending order $$=5,7,10,11,12,15,16$$


Uses the table given to find:
The upper and lower limits of the fifth class

The upper and lower limit of the fifth class is 5454 and 5050 respectively.


If the upper limit and the lower limits of a class interval are  $$16$$ and  $$10$$; the class interval is ____


1974171_1839485_ans_9289a29c09fc415488897161e61ea419.jpeg


Upper limit of $$5-12.5$$ is _____


1974170_1839484_ans_f45b637cd18b45f3838623540ca6ee5a.jpeg


Find the actual lower class limits, upper class limits and the mid-values of the classes:
$$10-19,20-29,30-39,$$ and $$40-49$$.

Case $$1$$: frequency $$10-19,$$
The lower class limit is $$10$$
The upper class limit is $$20$$
Mid-value is,
$$\dfrac{10+19}{2}=14.5$$
Case $$2$$: frequency $$20-29,$$
The lower class limit is $$20$$
The upper class limit is $$29$$
Mid-value is,
$$\dfrac{20+29}{2}=24.5$$
Case $$3$$: frequency $$30-39,$$
The lower class limit is $$30$$
The upper class limit is $$39$$
Mid-value is,
$$\dfrac{30+39}{2}=34.5$$
Case $$4$$: frequency $$40-49,$$
The lower class limit is $$40$$
The upper class limit is $$49$$
Mid-value is,
$$\dfrac{40+49}{2}=44.5$$


Fill in the blanks:
In the class interval $$35-46;$$ the lower limit is ....... and the upper limit is.....


1975855_1841269_ans_a637fed9f2934d0b9361ce40641201fd.jpeg


Data personally collected by an investigator is ____________ data.

Data collected by the investigator himself/herself for a specific person is called as primary data. For example, data collected by a student for his/her research project. Hence, correct answer is primary data.


Classification data based on the geographical differences of the data is ________.

Classification data based on the geographical differences of the data is geographical classification.
These data are classified with reference to geographical locations such as countries, states, cities, districts, etc.


Define raw data. What is bivariate and univariate distribution? Explain.

Meaning of raw data: Raw data or primary data are collected directly related to their object of study
Univariate Frequency Distribution:

1. When data is classified on the basis of single variable, the distribution is known as univariate frequency distribution.
2. It aims to make description about the particular variable.
3. It is also known as one-way frequency distribution.
4. For example, height of students in a class.

Bivariate Frequency Distribution:

1. When the data is classified on the basis of two variables, the distribution is known as bivariate frequency distribution.
2. It aims to determine the empirical relationship between the two variables.
3. It is also known as two-way frequency distribution.
4. For example, height and weight of students in a class.



The number of books in different shelves of a library are as follows :
$$ 30, 32, 28, 24, 20, 25, 38, 37, 40, 45, 16, 20 $$
$$ 19, 24, 27, 30, 32, 34, 35, 42, 27, 28, 19, 34, $$ 
$$ 38, 39, 42, 29, 24, 27, 22, 29, 31, 19, 27, 25 $$
$$ 28, 23, 24, 32, 34, 18, 27, 25, 37, 31, 24, 23, $$
$$ 43, 32, 28, 31, 24, 23, 26, 36, 32, 29, 28,$$
Prepare a cumulative frequency distribution table using 45 - 49 as the last class-interval.   

Now we can prepare table cumulative frequency distribution

 Class-interval Frequency Cumulative frequency
$$ 15-19$$
$$20-24$$
$$25-29$$
$$30-34$$
$$35-39$$
$$40-44$$
$$45-49$$		$$ 5$$
$$14$$
$$16$$
$$13$$
$$7$$
$$4$$
$$1$$		$$ 5$$
$$19$$
$$35$$
$$48$$
$$55$$
$$59$$
$$60$$


Explain the difference between a frequency distribution and a cumulative frequency distribution.

Difference between a frequency distribution and a cumulative frequency distribution
The difference between a cumulative frequency distribution and a frequency distribution is that relative frequency rather than simple frequency.
Cumulative relative frequency (also called an give) is the accumulation of the previous relative frequencies. 
Cumulative frequency distribution it is a form of a frequency distribution that represents the sum of a class and all classes.

$$\rightarrow$$ Remember that frequency distribution is an overview of all district values or classes of values and their respective no of occurrences

 Price Range Frequency Cumulative frequency
 0 - 50
50 - 100
100 - 500
500 - 1000
1000 - 1500		 800
1200
700
450
200		 800
2000
2700
3150
3250


The following cumulative frequency distribution table shows the daily electricity consumption (in kW) of 40 factories in an industrial state : Represent this as a frequency distribution table.
Consumption (in kW)No. of Factories
Below 240  1
Below 270  4
Below 300  8
Below 33024
Below 36033
Below 39038
Below 42040


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The marks scored by 40 students of class IX in mathematics are given below:
$$81,55,68,79,85,43,29,68,54,73,47,35,72,64,95,44,50,77,64,35,79,52,45,54,$$
$$70,83,62,64,72,92,84,76,63,43,54,38,73,68,52,54.$$
Prepare a frequency distribution with class size of 10 marks.

Given that the marks scored by $$40$$ students of class IX in mathematics are
$$81,55,68,79,85,43,29,68,54,73,47,35,72,64$$
$$95,44,50,77,64,35,79,52,45,54,70,83,62$$
$$64,72,92,84,76,63,43,54,38,73,68,52,54$$

Class size $$=10$$

 Frequency Distribution Frequency
$$20-30$$
$$30-40$$
$$40-50$$
$$50-60$$
$$60-70$$
$$70-80$$
$$80-90$$
$$90-100$$		$$1$$
$$3$$
$$5$$
$$8$$
$$8$$
$$9$$
$$4$$
$$2$$
 Total$$40$$


Define the following terms: Frequency distribution

Frequency Distributes distribution is a list, table or graph that displays the frequency of various outcomes in a sample. Each entry in the table contains the frequency or count of the occurrences of values within a particular group (or) internal.

Height rangeNumber of students Cumulative numbers 
 1 - 0.525 25 
5 - 5.5  35 60
 5.5 - 6.0 20 80
 6.0 - 6.5 20 100


The heights (in cm) of 30 students of class IX are given below:
$$155,158,154,158,160,148,149,150,153,159,161,148,157,153,157,162,159,151,154,156,$$
$$152,156,160,152,147,155,163,155,157,153.$$
Prepare a frequency distribution table with 160-164 as one of the class intervals.

The heights (in cm) of 30 students of class IX are given below:
$$155,158,154,158,160,148,149,150,153,159,161,148,157,153,157,162,159,151,154,156,$$
$$152,156,160,152,147,155,163,155,157,153.$$

frequency distribution table

 Class interval frequency
$$145-149$$
$$150-154$$
$$155-159$$
$$160-164$$
$$165-169$$		$$4$$
$$8$$
$$13$$
$$5$$
-
  $$30$$


Define the following terms :
True class limits

For example
10 -  20, 30 - 40, 40 - 50
These class intervals are called inclusive class intervals

and
10- 20, 20 - 30, 30 - 40, 40 - 50
These class intervals are called exclusive class intervals

True class limits re nothing but class boundaries
class limits are end numbers of a class interval for instance, we have a class interval 1 - 5
1 is called the lower limit (LL)
5 is called upper limit (UL)
These numbers define a class


The water bills (in RS) of 32 houses in a certain street for the period 1.1.98 to 31.3.98 are given below :$$ 56, 43, 32, 38, 56, 24, 68, 85, 52, 47, 35, 58, 63, 74, 27, 84, 69, 35, 44, 75, 55, 30,  54, 65,$$
$$45, 67, 95, 72, 43, 65, 35,$$ 
Tabulate the data and present the data as a cumulative frequency table using 70 - 79 as one of the class intervals.

Given that the water bills (in Rs) of $$32$$ houses in a certain street for the period 1.1.98 to 31.3.98 are below

$$56,43,32,38,56,24,68,85,52,47,35,58,63,74,27$$
$$84,69,35,44,75,55,30,54,65,45,67,95,72,43,65,35,59$$

Tabulate the data

 Class interval frequency cumulative frequency
20-29
30-39
40-49
50-59
60-69
70-79
80-89
90-99		2
6
5
7
6
3
2
1		2
8
13
20
26
29
31
32


Following figures relate the weekly wages (in Rs.) of 15 workers in a factory:
$$300,250,200,250,200,150,350,200,250,200,150,300,150,200,250$$
Prepare a frequency table.
How many workers are getting the minimum wages?

Given that the weekly wages(in Rs.) of $$15$$ workers in a factory $$300, 250, 200, 250, 200, 150, 350, 200, 250, 200, 150, 300, 150, 200, 250$$
Frequency table
Weekly wages(es)                        No. of workers in factory(frequency)
$$150$$                                                          $$3$$
$$200$$                                                         $$5$$
$$250$$                                                         $$4$$
$$300$$                                                         $$2$$
$$350$$                                                         $$1$$
No. of workers are getting Rs. $$350=1$$
and No. of workers are getting the minimum wages i.e., (Rs. $$150$$)$$=3$$.


Following figures relate the weekly wages (in Rs.) of 15 workers in a factory:
$$300,250,200,250,200,150,350,200,250,200,150,300,150,200,250$$
Prepare a frequency table.
What is the range in wages (in Rs)?

Given that the weekly wages(in Rs.) of $$15$$ workers in a factory $$300, 250, 200, 250, 200, 150, 350, 200, 250, 200, 150, 300, 150, 200, 250$$
Frequency table
Weekly wages                    No. of workers in factory(frequency)
$$150$$                                                   $$3$$
$$200$$                                                  $$5$$
$$250$$                                                  $$4$$
$$300$$                                                  $$2$$
$$350$$                                                   $$1$$
Total $$=15$$
we know Range$$=$$High$$-$$Low
Here
Highest weekly wage$$=350$$
Lowest weekly wage$$=150$$
$$\therefore$$ Range$$=350-150$$
$$=200$$.


Following figures relate the weekly wages (in Rs.) of 15 workers in a factory:
$$300,250,200,250,200,150,350,200,250,200,150,300,150,200,250$$
Prepare a frequency table.
How many Workers are getting Rs 350?

Given that the weekly wages(in Rs.) of $$15$$ workers in a factory $$300, 250, 200, 250, 200, 150, 350, 200, 250, 200, 150, 300, 150, 200, 250$$
Frequency table
Weekly wages(e's)                             No. of workers in factory(frequency)
$$150$$                                                               $$3$$
$$200$$                                                              $$5$$
$$250$$                                                              $$4$$
$$300$$                                                              $$2$$
$$350$$                                                              $$1$$
No of workers are getting Rs. $$350=1$$.


Following figures relate the weekly wages (in Rs.) of 15 workers in a factory:
$$300,250,200,250,200,150,350,200,250,200,150,300,150,200,250$$
Prepare a frequency table.
What is the highest mark?

Given that the weekly wages(in Rs.) of $$15$$ workers in a factory
$$300,250, 200, 250, 200, 150, 350, 200, 250, 200, 150, 300, 150, 200, 250$$
Frequency table
Weekly wages                             No. of workers in factory(frequency)
$$150$$                                                          $$3$$
$$200$$                                                         $$5$$
$$250$$                                                         $$4$$
$$300$$                                                         $$2$$
$$350$$                                                         $$1$$
We know Range$$=$$High$$-$$Low
Here
Highest weekly wage$$=350$$
Lowest weekly wage$$=150$$.


Class 11 Commerce Economics Extra Questions