RD Sharma - Mathematics

Book: RD Sharma - Mathematics

Chapter: 7. Statistics

Subject: Maths - Class 10th

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Chapter Exercises

Exercise 7.1
Exercise 7.2
Exercise 7.3
Exercise 7.4
Exercise 7.5
Exercise 7.6
CCE - Formative Assessment

Exercise 7.1

1

Calculate the mean for the following distribution:


x :



5



6



7



8



9



y :



4



8



14



11



3
2

Find the mean of the following data:


x:



19



21



23



25



27



29



31



y:



13



15



16



18



16



15



13
3

If the mean of the following data is 20.6. Find the value of p.


x:



10



15



p



25



35



y:



3



10



25



7



5
4

If the mean of the following data is 15, find p.


x :



5



10



15



20



25



y :



6



p



6



10



5
5

Find the value of p for the following distribution whose mean is 16.6


x :



8



12



15



p



20



25



30



y :



12



16



20



24



16



8



4
6

Find the missing value of p for the following distribution whose mean is 12.58


x:



5



8



10



12



p



20



25



y:



2



5



8



22



7



4



2
7

Find the missing frequency (p) for the following distribution whose mean is 7.68.


x:



3



5



7



9



11



13



y:



6



8



15



p



8



4
8

Find the value of p, if the mean of the following distribution is 20.


x:



15



17



19



20+p



23



y:



2



3



4



5p



6
9

The following table gives the number of boys of a particular age in a class of 40 students. Calculate the mean age of the students.


Age (in year):



15



16



17



18



19



20



No. of students:



3



8



10



10



5



4
10

Candidates of four schools appear in a mathematics test. The data were as follows:


Schools



No. of Candidates



Average Score



I



60



75



II



48



80



III



Not available



55



IV



40



50



If the average score of the candidates of all the four schools is 66, find the number of candidates that appeared from school III.
11

Five coins were simultaneously tossed 1000 times and at each toss the numbers of heads were observed. The number of tosses during which 0, 1, 2, 3, 4 and 5 heads were obtained are shown in the table below. Find the mean number of heads per toss.


No. of heads per toss



No. of tosses



0



38



1



144



2



342



3



287



4



164



5



25



Total



1000
12

Find the missing frequencies in the following frequency distribution if it is known that the mean of the distribution 50.


x: 10



30



50



70



90



y: 17



f1



32



f2



19
13

The arithmetic mean of the following data is 14. Find the value of k.


xi:



5



10



15



20



25



yi:



7



k



8



4



5
14

The arithmetic mean of the following data is 25, find the value of k.


xi:



5



15



25



35



45



yi:



3



k



3



6



2



[CBSE 2001]
15

If the mean of the following data is 18.75. Find the value of p.


xi:



10



15



p



25



30



yi:



5



10



7



8



2

Exercise 7.2

1

The number of telephone calls received at an exchange per interval for 250 successive one-minute intervals are given in the following frequency table.


No. of calls (x):



0



1



2



3



4



5



6



No. of intervals (f):



15



24



29



46



54



43



39



Compute the mean number of calls per interval.
2

Five coins were simultaneously tossed 1000 times, and at each toss the number of heads was observed. The number of tosses during which 0, 1, 2, 3, 4 and 5 heads were obtained are shown in the table below. Find the mean number of heads per toss


No. of heads pre toss(x):



0



1



2



3



4



5



No. of tosses (f):



38



144



342



287



164



25
3

The following table gives the number of branches and number of plants in the garden of a school.


No. of branches (x):



2



3



4



5



6



No. of plants (f):



49



43



57



38



13
4

The following table gives the number of children of 150 families in a village


No. of children (x):



0



1



2



3



4



5



No. of families (f):



10



21



55



42



15



7



Find the average number of children per family.
5

The marks obtained out of 50, by 102 students in a Physics test are given in the frequency table below:


Marks (x):



15



20



22



24



25



30



33



38



45



Frequency (f):



5



8



11



20



23



18



13



3



1



Find the average number of marks.
6

The number of students absent in a class were recorded every day for 120 days and the information is given in the following frequency table:


No. of students absent (x):



0



1



2



3



4



5



6



7



No. of days (f):



1



4



10



50



34



15



4



2



Find the mean number of students absent per day.
7

In the first proof reading of a book containing 300 pages the following distribution of misprints was obtained:


No. of misprints per pages (x):



0



1



2



3



4



5



No. of pages (f):



154



95



36



9



5



1



Find the average number of misprints per page.
8

The following distribution gives the number of accidents met by 160 workers in a factory during a month.


No. of accidents (x):



0



1



2



3



4



No. of workers (f):



70



52



34



3



1



Find the average number of accidents per worker.
9

Find the mean from the following frequency distribution of marks at a test in statistics:


Marks (x):



5



10



15



20



25



30



35



40



45



50



No. of students (f):



15



50



80



76



72



45



39



9



8



6

Exercise 7.3

1

The following table gives the distribution of total household expenditure (in rupees) of manual workers in a city.


Expenditure (in rupees) (in rupees)



Frequency (f)



Expenditure (in rupees) (x)



Frequency (f)



100-150



24



300-350



30



150-200



40



350-400



22



200-250



33



400-450



16



250-300



28



450-500



7



Find the average expenditure (in rupees) per household.
2

A survey was conducted by a group of students as a part of their environment awareness programme, in which they collected the following data regarding the number of plants in 20 houses in a locality. Find the mean number of plants per house.


Numbers of plants:



0-2



2-4



4-6



6-8



8-10



10-12



12-14



Numbers of houses:



1



2



1



5



6



2



3



Which method did you use for finding the mean, and why?
3

Consider the following distribution of daily wages of 50 workers of a factory.


Daily wages (in Rs):



100-120



120-140



140-160



160-180



180-200



Numbers of workers:



12



14



8



6



10



Find the mean daily wages of the workers of the factory by using an appropriate method.
4

Thirty women were examined in a hospital by a doctor and the number of heart beats per minute recorded and summarized as follows. Find the mean heart beats per minute for these women, choosing a suitable method.


Number of heart beats per minute:



65-68



68-71



71-74



74-77



77-80



80-83



83-86



Number of women:



2



4



3



8



7



4



2



Find the mean of each of the following frequency distributions: (5-14)
5


Class interval:



0-6



6-12



12-18



18-24



24-30



Frequency:



6



8



10



9



7
6


Class interval:



50-70



70-90



90-110



110-130



130-150



150-170



Frequency:



18



12



13



27



8



22
7


Class interval:



0-8



8-16



16-24



24-32



32-40



Frequency:



6



7



10



8



9
8


Class interval:



0-6



6-12



12-18



18-24



24-30



Frequency:



7



5



10



12



6
9


Class interval:



0-10



10-12



20-30



30-40



40-50



Frequency:



9



12



15



10



14
10


Class interval:



0-8



8-16



16-24



24-32



32-40



Frequency:



5



9



10



8



8
11


Class interval:



0-8



8-16



16-24



24-32



32-40



Frequency:



5



6



4



3



2
12


Class interval:



10-30



30-50



50-70



70-90



90-110



110-130



Frequency:



5



8



12



20



3



2
13


Class interval:



25-35



35-45



45-55



55-65



65-75



Frequency:



6



10



8



12



4
14


Classes:



25-29



30-34



35-39



40-44



45-49



50-54



55-59



Frequency:



14



22



16



6



5



3



4
15

For the following distribution, calculate mean using all suitable methods:


Size of items:



1-4



4-9



9-16



16-27



Frequency:



6



12



26



20
16

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 Cost of living



Number of Students



Cost of living Index



Number of students



1400-1500



3



1700-1800



9



1500-1600



10



1800-1900



6



1600-1700



20



1900-2000



2
17

The following table shows the marks scored by 140 students in an examination of a certain paper:


Marks:



0-10



10-20



20-30



30-40



40-50



Number of students:



20



24



40



36



20



Calculate the average marks by using all the three methods: direct method, assumed mean deviation and shortcut method.
18

The mean of the following frequency distribution is 62.8 and the sum of all the frequencies is 50. Compute the missing frequency is 50. Compute the missing frequency.


Class:



0-20



20-40



40-60



60-80



80-100



100-120



Frequency:



5



f1



10



f2



7



8
19

The following distribution shows the daily pocket allowance given to the children of a multistory building. The average pocket allowance is Rs. 18.00. Find out the missing frequency.


Class interval:



11-13



13-15



15-17



17-19



19-21



21-23



23-25



Frequency:



7



6



9



13



-



5



4
20

If the mean of the following distribution is 27, find the value of p.


Class:



0-10



10-20



20-30



30-40



40-50



Frequency:



8



p



12



13



10
21

In a retail market, fruit vendor were-selling mangoes kept in packing boxes. These boxes contained varying number of mangoes. The following was the distribution of mangoes according to the number of boxes.


Number of mangoes:



50-52



53-55



56-58



59-61



62-64



Number of boxes:



15



110



135



115



25



Find the mean number of mangoes kept in a packing box. Which method of finding the mean did you choose?
22

The table below shows the daily expenditure on food of 25 households in a locality.


Daily expenditure (in Rs):



100-150



150-200



200-250



250-300



300-350



Number of households:



4



5



12



2



2
23

To find out the concentration of SO2 in the air (in parts per million, i.e., ppm), the data was collected for 30 localities in a certain city and is presented below:


Concentration of SO2 (In ppm)



Frequency



0.00-0.04



4



0.04-0.08



9



0.08-0.12



9



0.12-0.16



2



0.16-0.20



4



0.20-0.24



2



Find the mean concentration of SO2 in the air.
24

A class teacher has the following absentee record of 40 students of a class for the whole term. Find the mean number of days a student was absent.


Numbers of days:



0-6



6-10



10-14



14-20



20-28



28-38



38-40



Number of students:



11



10



7



4



4



3



1
25

The following table gives the literacy rate (in percentage) of 35 cities. Find the mean literacy rate.


Literacy rate (in %):



45-55



55-65



65-75



75-85



85-95



Number of cities:



3



10



11



8



3

Exercise 7.4

1

Following are the lives in hours of 15 pieces of the components of aircraft engine. Find the median:

715, 724, 725, 710, 729, 745, 694, 699, 696, 712, 734, 728, 716, 705, 719
2

The following is the distribution of height of students of a certain class in a certain city.


Height (in cms):



160-162



163-165



166-168



169-171



172-174



No. of students:



15



118



142



127



18



Find the median height.
3

Following is the distribution of I.Q of 100 students. Find the median I.Q.


I.Q:



55-64



65-74



75-84



85-94



95-104



105-114



115-124



125-134



135-144



No. of students:



1



2



9



22



33



22



8



2



1
4

Calculate the median from the following data:


Rent (in Rs):



15-25



25-35



35-45



45-55



55-65



65-75



75-85



85-95



No. of Houses:



8



10



15



25



40



20



15



7
5

Calculate the median from the following data:


Marks below:



10



20



30



40



50



60



70



80



No. of students:



15



35



60



84



96



127



198



250
6

An incomplete distribution is given as follows:


Variable:



0-10



10-20



20-30



30-40



40-50



50-60



60-70



Frequency:



10



20



?



40



?



25



15



You are given that the median value is 35 and the sum of all the frequencies is 170. Using the median formula fill up the missing frequency.
7

Calculate the missing frequency form the following distribution, it being given that the median of the distribution is 24.


Age in years:



0-10



10-20



20-30



30-40



40-50



No. of persons:



5



25



?



18



7
8

Find the missing frequencies and the median for the following distribution if the mean is 1.46.


No. of accidents:



0



1



2



3



4



5



Total



Frequency (No. of days):



46



?



?



25



10



5



200
9

An incomplete distribution is given below:


Variable:



10-20



20-30



30-40



40-50



50-60



60-70



70-80



Frequency:



12



30



-



65



-



25



18



You are given that the median value is 46 and the total number of items is 230.


(i) Using the median formula fill up missing frequencies.


(ii) Calculate the AM of the completed distribution.
10

The following table gives the frequency distribution of married women by age at marriage


Age (in years)



Frequency



Age (in years)



Frequency



15-19



53



40-44



9



20-24



140



45-49



5



25-29



98



50-54



3



30-34



32



55-59



3



35-39



12



60 and above



2



Calculate the median and interpret the results.
11

If the median of the following frequency distribution is 28.5 find the missing frequencies:


Class interval:



0-10



10-20



20-30



30-40



40-50



50-60



Total



Total Frequency:



5





20



15





5



60
12

The median of the following data is 525. Find he missing frequency, if it is given that there are 100 observations in the data:


Class Interval



Frequency



Class interval



Frequency



0-100



2



500-600



20



100-200



5



600-700



f2



200-300



f1



700-800



9



300-400



12



800-900



7



400-500



17



900-1000



4
13

If the median of the following data is 32.5, find the missing frequencies.


Class interval:



0-10



10-20



20-30



30-40



40-50



50-60



60-70



Total



Frequency:



f1



5



9



12



f2



3



2



40
14

Compute the median for each of the following data


(i) Marks



No. of students



(ii) Marks



No. of students



Less than 10



0



More than150



0



Less than 30



10



More than140



12



Less than 50



25



More than130



27



Less than 70



43



More than120



60



Less than 90



65



More than110



105



Less than 110



87



More than100



124



Less than 130



96



More than90



141



Less than 150



100



More than80



150
15

A survey regarding the height (in cm) of 51 girls of class X of a school was conducted and the following data was obtained:


Height in cm



Number of Girls



Less than 140



4



Less than 145



11



Less than 150



29



Less than 155



40



Less than 160



46



Less than 165



51



Find the median height.
16

A life insurance agent found the following data for distribution of ages of 100 policy holders. Calculate the median age, if policies are only given to persons having age 18 years onwards but less than 60 years.


Age in years



Number of policy holders



Blow 20



2



Blow 25



6



Blow 30



24



Blow 35



45



Blow 40



78



Blow 45



89



Blow 50



92



Blow 55



98



Blow 60



100
17

The lengths of 40 leaves of a plant are measured correct to the nearest millimeter, and the data obtained is represented in the following table:


Length (in mm):



118-126



127-135



136-144



14 5-153



154-162



163-171



172-180



No. of leaves:



3



5



9



12



5



4



2



Find the median life.
18

The following table gives the distribution of the life time of 400 neon lamps:


Light time (in hours)



Number of lamps



1500-2000



14



2000-2500



56



2500-3000



60



3000-3500



86



3500-4000



74



4000-4500



62



4500-5000



48



Find the median life.
19

The distribution below gives the weight of 30 students in a class. Find the median weight of students:


Weight (in kg):



40-45



45-50



50-55



55-60



60-65



65-70



70-75



No. of students:



2



3



8



6



6



3



2

Exercise 7.5

1

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
2

The shirt sizes worn by a group of 200 persons, who bought the shirt from a store, are as follows:


Shirt size:



37



38



39



40



41



42



43



44



Number of persons:



15



25



39



41



36



17



15



12



Find the model shirt size worn by the group.
3

Find the mode of the following distribution.

(i)


Class-interval:



0-10



10-20



20-30



30-40



40-50



50-60



60-70



70-80



Frequency:



5



8



7



12



28



20



10



10



(ii)


Class-interval:



10-15



15-20



20-25



25-30



30-35



35-40



Frequency:



30



45



75



35



25



15



(iii)


Class-interval:



25-30



30-35



35-40



40-45



45-50



50-60



Frequency:



25



34



50



42



38



14
4

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


Age (in years):



16-18



1-20



20-22



22-24



24-26



Group A:



50



78



46



28



23



Group B:



54



89



40



25



17
5

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
6

The following is the distribution of height of students of certain class in a certain city:


Height (in cms):



160-162



163-165



166-168



169-171



172-174



No. of students:



15



118



142



127



18



Find the average height of maximum number of students.
7

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



No. of students:



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.
8

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



No. of components:



10



35



52



61



38



29



Determine the modal lifetimes of the components.
9

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 men monthly expenditure:


Expenditure (in Rs.)



Frequency



1000-1500



24



1500-2000



40



2000-2500



33



2500-3000



28



3000-3500



30



3500-4000



22



4000-4500



16



4500-5000



7
10

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:


Number 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



50-95



2
11

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



3000-4000



4



4000-5000



18



5000-6000



9



6000-7000



7



7000-8000



6



8000-9000



3



9000-10000



1



10000-10000



1



Find the mode of the data.
12

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:


Number of cars:



0-10



10-20



20-30



30-40



40-50



50-60



60-70



70-80



Frequency:



7



14



13



12



20



11



15



8
13

The following frequency distribution gives the monthly consumption of electricity of the consumers of a locality. Find the median, mean and mode of the data and compare them.


Monthly consumption (in units):



65-85



85-105



105-125



125-145



145-165



165-185



185-205



No. of consumers:



4



5



13



20



14



8



4
14

100 surnames were randomly picked up from a local telephone directly and the frequency distribution of the number of letters in the English alphabets in the surnames was obtained as follows:


Numbers of letters:



1-4



4-7



7-10



10-13



13-16



16-19



Number surnames:



6



30



40



16



4



4



Determine the median number of letters in the surnames. Find the mean number of letters in the surnames. Also, find the modal size of the surnames.
15

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


Classes:



0-20



20-40



40-60



60-80



80-100



100-120



120-140



Frequency:



6



8



10



12



6



5



3
16

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
17

The following table gives the daily income of 50 workers of a factory:


Daily income (in Rs):



100-120



120-140



140-160



160-180



180-200



Number of workers:



12



14



8



6



10

Exercise 7.6

1

Draw an ogive by less than method for the following data:


No. of rooms:



1



2



3



4



5



6



7



8



9



10



No. of houses:



4



9



22



28



24



12



8



6



5



2
2

The marks scored by 750 students in an examination are given in the form of a frequency distribution table:


Marks



No. of Students



600-400



16



640-680



45



680-720



156



720-760



284



760-800



172



800-840



59



840-880



18



Prepare a cumulative frequency table by less than method and draw an ogive.
3

Draw an ogive to represent the following frequency distribution:


Class-interval:



0-4



5-9



10-14



15-19



20-24



No. of students:



2



6



10



5



3
4

The monthly profits (in Rs.) of 100 shops are distributed as follows:


Profits per shop:



0-50



50-100



100-150



150-200



200-250



250-300



No. of shops:



12



18



27



20



17



6



Draw the frequency polygon for it.
5

The following table gives the height of trees:


Height



No. of trees



Less than 7



26



Less than 14



57



Less than 21



92



Less than 28



134



Less than 35



216



Less than 42



287



Less than 49



341



Less than 56



360



Draw ‘less than’ ogive and ‘more than’ ogive.
6

The annual profits earned by 30 shops of a shopping complex in a locality give rise to the following distribution:


Profit (in lakhs in Rs.)



Number of shops (frequency)



More than or equal to 5



30



More than or equal to 10



28



More than or equal to 15



16



More than or equal to 20



14



More than or equal to 25



10



More than or equal to 30



7



More than or equal to 35



3



Draw both ogives for the above data and hence obtain the median.
7

The following distribution gives the daily income of 50 workers of a factory:


Daily income (in Rs.):



100-120



120-140



140-160



160-180



180-200



Number of workers:



12



14



8



6



10



Convert the above distribution to a less than type cumulative frequency distribution and draw its ogive.
8

The following table gives production yield per hectare of wheat of 100 farms of a village:


Number of farms:



50-55



55-60



60-65



65-70



70-75



75-80 in kg per hectare



Number of farms:



2



8



12



24



38



16



Draw ‘less than’ ogive and ‘more than’ ogive.
9

During the medical check-up of 35 students of a class, their weights were recorded as follows:


Weight (in kg)



Number of students



Less than 38



0



Less than 40



3



Less than 42



5



Less than 44



9



Less than 46



14



Less than 48



28



Less than 50



32



Less than 52



35



Draw a less than type ogive for the given data. Hence, obtain the median weight from the graph and verify the result by using the formula.

CCE - Formative Assessment

1

Define mean.
2

What is the algebraic sum o5f deviations of a frequency distribution about its mean?
3

Which measure of central tendency is given by the x-coordinate of the point of intersection of the ‘more than’ ogive and ‘less than’ ogive?
4

What is the value of the median of the data using the graph in the following figure of less than ogive and more than ogive?
5

Write the empirical relation between mean, mode and median.
6

Which measure of central tendency can be determined graphically?
7

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
8

A student draws a cumulative frequency curve for the marks obtained by 40 students of a class as shown below. Find the median marks obtained by the students of the class.
9

Write the median class for the following frequency distribution:


Class-interval:



0-10



10-20



20-30



30-40



40-50



50-60



60-70



70-80



Frequency:



5



8



7



12



28



20



10



10
10

In the graphical representation of a frequency distribution, if the distance between mode and mean is k times the distance between median and mean, then write the value of k.
11

Find the class marks of classes 10-25 and 35-55
12

Write the median class of the following distribution:


Classes:



0-10



10-20



20-30



30-40



40-50



50-60



60-70



Frequency:



4



4



8



10



12



8



4
1

Which of the following is not a measure of central tendency?
2

The algebraic sum of the deviations of a frequency distribution from its mean is
3

The arithmetic mean of 1, 2, 3, ..., n is
4

For a frequency distribution, mean, median and mode are connected by the relation
5

Which of the following cannot be determined graphically?
6

The median of a given frequency distribution is found graphically with the help of
7

The mode of a frequency distribution can be determined graphically from
8

Mode is
9

The mean of n observations is . If the first item is increased by 1, second by 2 and so on, then the new mean is
10

One of the methods of determining mode is
11

If the mean of the following distribution is 2.6, then the value of y is


Variable (x):



1



2



3



4



5



Frequency:



4



5



y



1



2
12

The relationship between mean, median and mode for a moderately skewed distribution is
13

The mean of a discrete frequency distribution xi/fi; i = 1, 2, ..., n is given by
14

If the arithmetic mean of x, x + 3, x + 6, x + 9, and x + 12 is 10, the x =
15

If the median of the data: 24, 25, 26, x + 2, x + 3, 30, 31, 34 is 27.5, then x =
16

If the median of the data: 6, 7, x − 2, x, 17, 20, written in ascending order, is 16. Then x =
17

The median of first 10 prime numbers is
18

If the mode of the data: 64, 60, 48, x, 43, 48, 43, 34 is 43, then x + 3 =
19

If the mode of the data: 16, 15, 17, 16, 15, x, 19, 17, 14 is 15, then x =
20

The mean of 1, 3, 4, 5, 7, 4 is m. The numbers 3, 2, 2, 4, 3, 3, p have mean m − 1 and median q. Then, p + q =
21

If the mean of a frequency distribution is 8.1 and Σfixi = 132 + 5k, Σfi = 20, then k =
22

If the mean of 6, 7, x, 8, y, 14 is 9, then
23

The mean of n observation is . If the first observation is increased by 1, the second by 2, the third by 3, and so on, then the new mean is
24

If the mean of first n natural numbers is , then n =
25

The arithmetic mean and mode of a data are 24 and 12 respectively, then its median is
26

The mean of first n odd natural number is
27

The mean of first n odd natural numbers is , then n =
28

If the difference of mode and median of a data is 24, then the difference of medina and mean is
29

If the arithmetic mean of 7, 8, x, 11, 14 is x, then x =
30

If mode of a series exceeds its mean by 12, then mode exceeds the median by
31

If the mean of first n natural number is 15, then n =
32

If the mean observations x1, x2, ..., xn is , then the means of x1 + a, x2 + a, ..., xn + a is
33

Mean of a certain number of observations is . If each observation is divided by m(m ≠ 0) and increased by n, then the mean of new observation is
34

If , then =
35

If 35 is removed from the data: 30, 34, 35, 36, 37, 38, 39, 40, then the median increases by