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# R.D. Sharma solutions Mathematics for Class 9 by R D Sharma (2018-19 Session) chapter 24 Measures of Central Tendency

## Chapter 24 - Measures of Central Tendency

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What do you understand by the word “statistics” in
(i) Singular form
(ii) Plural form?

Describe some fundamental characteristics of statistics.

What is primary data?

What secondary data?

Which of the two – the primary or the secondary data – is more reliable and why?

Why do we group data?

Explain the meaning of the term Variable.

Explain the meaning of the term Class-integral.

Explain the meaning of the term Class-size.

Explain the meaning of the term Class-mark.

Explain the meaning of the term Frequency.

Explain the meaning of the term Class limits.

Explain the meaning of the term True class limits.

The ages of ten students of a group are given below. The ages have been recorded in years
and months:
8 – 6, 9 – 0, 8 – 4, 9 – 3, 7 – 8, 8 – 11,8 – 7, 9 – 2, 7 – 10, 8 – 8
(i) What is the lowest age?
(ii) What is the highest age?
(iii) Determine the range?

The monthly pocket money of six friends is given below: Rs. 45, Rs. 30, Rs. 40, Rs. 50, Rs.
25, Rs. 45.
(i) What is the highest pocket money?
(ii) What is the lowest pocket money?
(iii) What is the range?
(iv) Arrange the amounts of pocket money in ascending order.

Write the class-size in each of the following:
(i) 0 – 4, 5 – 9, 10 – 14
(ii) 10 – 19, 20 – 29, 30 – 39
(iii) 100 – 120, 120 – 140, 160 – 180
(iv) 0 – 0.25, 0.25 – 0.50, 0.50 – 0.75
(v) 5 – 5.01, 5.01 − 5.02, 5.02 – 5.03

The final marks in mathematics of 30 students are as follows:
53, 61, 48, 60, 78, 68, 55, 100,67,90
75,88,77,37,84,58,60,48,62,56
44, 58, 52, 64, 98, 59, 70, 39, 50, 60
(i) Arrange these marks in the ascending order, 30 to 39 one group, 40 to 49 second group etc.
Now answer the following:
(ii) What is the highest score?
(iii) What is the lowest score?
(iv) What is the range?
(v) If 40 is the pass mark how many have failed?
(vi) How many have scored 75 or more?
(vii) Which observations between 50 and 60 have not actually appeared?
(viii) How many have scored less than 50?

The weights of new born babies (in kg) in a hospital on a particular day are as follows:
2.3, 2.2, 2.1, 2.7, 2.6, 3.0, 2.5, 2.9, 2.8, 3.1, 2.5, 2.8, 2.7, 2.9, 2.4
(i) Rearrange the weights in descending order.
(ii) Determine the highest weight.
(iii) Determine the lowest weight.
(iv) Determine the range.
(v) How many babies were born on that day?
(vi) How many babies weigh below 2.5 kg?
(vii) How many babies weigh more than 2.8 kg?
(viii) How many babies weigh 2.8 kg?

The number of runs scored by a cricket. player in 25 innings are as follows:
26, 35, 94, 48, 82, 105, 53, 0, 39, 42, 71, 0, 64, 1.5, 34, 67, 0, 42, 124, 84, 54, 48, 139, 64,47.
(i) Rearrange these runs in ascending order.
(ii) Determine the player, is highest score.
(iii) How many times did the player not score a run?
(iv) How many centuries did he score?
(v) How many times did he score more than 50 runs?

The class size of a distribution is 25 and the first class-interval is 200-224. There are seven
class-intervals.
(i) Write the class-intervals.
(ii) Write the class-marks of each interval.

Write the class size and class limits in each of the following:
(i) 104, 114, 124, 134, 144, 154, and 164
(ii) 47, 52, 57, 62, 67, 72, 77, 82, 87, 92, 97 and 102
(iii) 12.5, 17.5, 22.5, 27.5, 32.5, 37.5, 42.5, 47.5

Following data gives the number of children in 40 families:
1,2,6,5,1,5, 1,3,2,6,2,3,4,2,0,0,4,4,3,2,2,0,0,1,2,2,4,3, 2,1,0,5,1,2,4,3,4,1,6,2,2.
Represent it in the form of a frequency distribution.

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.

Following data gives the number of children in 40 families:
1,2,6,5,1,5, 1,3,2,6,2,3,4,2,0,0,4,4,3,2,2,0,0,1,2,2,4,3, 2,1,0,5,1,2,4,3,4,1,6,2,2.
Represent it in the form of a frequency distribution.

The monthly wages of 30 workers in a factory are given below:
83.0, 835, 890, 810, 835, 836, 869, 845, 898, 890, 820, 860, 832, 833, 855, 845, 804, 808,
812, 840, 885, 835, 836, 878, 840, 868, 890, 806, 840, 890.
Represent the data in the form of a frequency distribution with class size 10.

The daily maximum temperatures (in degree celsius) recorded in a certain city during the
month of November are as follows:
25.8, 24.5, 25.6, 20.7, 21.8, 20.5, 20.6, 20.9, 22.3, 22.7, 23.1, 22.8, 22.9, 21.7, 21.3, 20.5,
20.9, 23.1, 22.4, 21.5, 22.7, 22.8, 22.0, 23.9, 24.7, 22.8, 23.8, 24.6, 23.9, 21.1
Represent them as a frequency distribution table with class size 1°C.

Construct a frequency table with equal class intervals from the following data on the monthly
wages (in rupees) of 28 laborers working in a factory, taking one of the class intervals as
210-230 (230 not included):
220, 268, 258, 242, 210, 268, 272, 242, 311, 290, 300, 320, 319, 304, 302, 318, 306, 292,
254, 278, 210, 240, 280, 316, 306, 215, 256, 236.

The daily minimum temperatures in degrees Ce1siu& recorded in a certain Arctic region are
as follows:
−12.5, −10.8, −18.6, −8.4, −10.8, −4.2, −4.8, −6.7, −13.2, −11.8, −2.3, 1.2, 2.6, 0, 2.4,
0, 3.2, 2.7, 3.4, 0, − 2.4, − 2.4, 0, 3.2, 2.7, 3.4, 0, − 2.4, − 5.8, -8.9, 14.6, 12.3, 11.5, 7.8,2.9.
Represent them as frequency distribution table taking − 19.9 to − 15 as the first class
interval.

The blood groups of 30 students of class VIII are recorded as follows:
A, B, O, O, AB, O, A, O, B, A, O, B, A, O, O, A, AB, O, A, A, O, O, AB, B, A, O, B, A, B,O
Represent this data in the form of a frequency distribution table. Find out which is the most Common and which is the rarest blood group among these students.

Three coins were tossed 30 times. Each time the number of head occurring was noted down
as follows:
0        1        2        2        1        2        3        1       3        0
1        3        1        1        2        2        0        1       2        1
3        0        0        1        1        2        3        2       2        0

Thirty children were asked about the number of hours they watched T.V. programmers in the previous week. The results were found as follows:

 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

(i) Make a grouped frequency distribution table for this data, taking class width 5 and one of the class intervals as 5 – 10.
(ii)How many children watched television for 15 or more hours a week?

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Define cumulative frequency distribution.

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

The marks scored by 55 students in a test are given below:

 Marks 0-5 5-10 10-15 15-20 20-25 25-30 30-35 No. of students 2 6 13 17 11 4 2

Prepare a cumulative frequency table:

Following are the ages of360 patients getting medical treatment in a hospital on a day:

 Age (inyears): 10-20 20-30 30-40 40-50 50-60 60-70 No. ofPatients: 90 50 60 80 50 30

Construct a cumulative frequency distribution.

The water bills (in rupees) 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, 59.
Tabulate the data and resent the data as a cumulative frequency table using 70-79 as one of the class intervals.

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, 21.
Prepare a cumulative frequency distribution table using 45-49 as the last class interval.

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 30 24 Below 35 78 Below 40 183 Below 45 294 Below 50 408 Below 55 543 Below 60 621 Below 65 674 Below 70 685

The following cumulative frequency distribution table shows the daily electricity consumption (in kW) of 40 factories in an industrial state:

 Consumption (in kW) No. of Factories Below 240 1 Below 270 4 Below 300 8 Below 330 24 Below 360 33 Below 390 38 Below 420 40

(i) Represent this as a frequency distribution table.
(ii) Prepare a cumulative frequency table.

Given below is a cumulative frequency distribution table showing the ages of people living in a locality:

 Ace in years No. of persons Above 108 0 Above 96 1 Above 84 3 Above 72 5 Above 60 20 Above 48 158 Above 36 427 Above 24 809 Above 12 1026 Above 0 1124

Prepare a frequency distribution table

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Read the bar graph shown in Fig. 23.8 and answer the following questions:

(i) What is the information given by the bar graph?
(ii) How many tickets of Assam State Lottery were sold by the agent?
(iii) Of which state, were the maximum number of tickets sold?
(iv) State whether true or false.
The maximum number of tickets sold is three times the minimum number of tickets sold.
(v) Of which state were the minimum number of tickets sold?

Study the bar graph representing the number of persons in various age groups in a town shown in Fig. below. Observe the bar graph and answer the following questions:
(i) What is the percentage of the youngest age-group persons over those in the oldest age
group?
(ii) What is the total population of the town?

(iii) What is the number of persons in the age group 60 - 65?
(iv) How many persons are more in the age-group 10 - 15 than in the age group 30 - 35?
(v) What is the age-group of exactly 1200 persons living in the town?
(vi) What is the total number of persons living in the town in the age-group 50 - 55?
(vii) What is the total number of persons living in the town in the age-groups 10 - 15 and 60 - 65?

(viii) Whether the population in general increases, decreases or remains constant with the
increase in the age-group.

Read the bar graph shown in Fig. 23.10 and answer the following questions
(i) What is the information given by the bar graph?

(ii) What was the number of commercial banks in 1977?
(iii) What is the ratio of the number of commercial banks in 1969 to that in 1980?
(iv) State whether true or false:
The number of commercial banks in 1983 is less than double the number of
commercial banks in 1969.

Given below (Fig. below) is the bar graph indicating the marks obtained out of 50 in mathematics paper by 100 students. Read the bar graph and answer the following questions:

(i) It is decided to distribute work books on mathematics to the students obtaining
less than 20 marks, giving one workbook to each of such students. If a work book
costs Rs 5, what sum is required to buy the work books?
(ii) Every student belonging to the highest mark group is entitled to get a prize of Rs. 10.
How much amount of money is required for distributing the prize money?
(iii) Every student belonging to the lowest mark—group has to solve 5 problems per day.
How many problems, in all, will be solved by the students of this group per day?
(iv) State whether true or false.
a. 17% students have obtained marks ranging from 40 to 49.
b. 59 students have obtained marks ranging from 10 to 29.
(v) What is the number of students getting less than 20 marks?
(vi) What is the number of students getting more than 29 marks?
(vii) What is the number of students getting marks between 9 and 40?
(viii) What is the number of students belonging to the highest mark group?
(ix) What is the number of students obtaining more than 19 marks?

Read the following bar graph (Fig. 23.12) and answer the following questions:
(i) What is the information given by the bar graph?
(ii) State each of the following whether true or false.
a. The number of government companies in 1957 is that of 1982 is 1 :9.
b. The number of government companies have decreased over the year 1957 to
1983.

Read the following bar graph and answer the following questions:

(i) What information is given by the bar graph?
(ii) Which state is the largest producer of rice?
(iii) Which state is the largest producer of wheat?
(iv) Which state has total production of rice and wheat as its maximum?
(v) Which state has the total production of wheat and rice minimum?

The following bar graph (Fig. 23. 1 4) represents the heights (in cm) of 50 students of Class
XI of a particular school. Study the graph and answer the following questions:

(i) What percentage of the total number of students have their heights more than 149cm?
(ii) How many students in the class are in the range of maximum height of the class?
(iii) The school wants to provide a particular type of tonic to each student below the height
of 150 cm to improve his height. If the cost of the tonic for each student comes out
to be Rs. 55, how much amount of money is required?
(iv) How many students are in the range of shortest height of the class?
(v) State whether true or false:
a. There are 9 students in the class whose heights are in the range of 155 - 159 cm.
b. Maximum height (in cm) of a student in the class is 17.
c. There are 29 students in the class whose heights are in the range of 145- 154 cm.
d. Minimum height (in cm) of a student is the class is in the range of 140 – 144 cms.
e. The number of students in the class having their heights less than 150 cm is 12.
f. There are 14 students each of whom has height more than 154. cm.

Read the following bar graph(Fig. 23.15)and answer the following questions:
(i) What information is given by the bar graph?
(ii) What was the production of a student in the year 1980 - 81?
(iii) What is the minimum and maximum productions of cement and corresponding years?

The bar graph shown in Fig 23.16 represents the circulation of newspapers in 10 languages. Study the bar graph and answer the following questions:

(i) What is the total number of newspapers published in Hindi, English, Urdu, Punjabi
and Bengali?
(ii) What percent is the number of news papers published in Hindi of the total number of
newspapers?
(iii) Find the excess of the number of newspapers published in English over those
published in Urdu.
(iv) Name two pairs of languages which publish the same number of newspapers.
(v) State the language in which the smallest number of newspapers are published.
(vi) State the language in which the largest number of newspapers are published.
(vii) State the language in which the number of newspapers published is between 2500
and 3500.
(viii) State whether true or false:
a. The number of newspapers published in Malayalam and Marathi together is less
than those published in English.
b. The number of newspapers published in Telugu is more than those published in
Tamil.

Read the bar graph given in Fig. 23.17 and answer the following questions:
(i) What information is given by the bar graph?
(ii) What was the crop-production of rice in 1970 - 71?
(iii) What is the difference between the maximum and minimum production of rice?

i) It gives information regarding the production of rice crop in India in different years
(ii) The crop production of rice in 1970 -71= 42.5 lakh tonnes.
(iii) The difference between the maximum and minimum production of rice = 55 – 22 = 33 lakh tonnes

Read the bar graph given in Fig. below and answer the following questions:

(i) What information does it give?
(ii) In which part the expenditure on education is maximum in 1980?
(iii) In which part the expenditure has gone up from 1980 to 1990?
(iv) In which part the gap between 1980 and 1990 is maximum?

Read the bar graph given in Fig. 23.19 and answer the following questions:
(i) What information is given by the bar graph?

(ii) In which years the areas under the sugarcane crop were the maximum and the minimum?
(iii) State whether true or false:
The area under the sugarcane crop in the year 1982 - 83 is three times that of the year 1950 - 51

Read the bar graph given in Fig. 23.20 and answer the fol1owing questions:

(i) What information is given by the bar graph?
(ii) What was the expenditure on health and family planning in the year 1982-83?
(iii) In which year is the increase in expenditure maximum over the expenditure in
previous year? What is the maximum increase?

Read the bar graph given in Fig. 23.21 and answer the following questions:
(i) What is the information given by the bar graph?
(ii) What is the number of families having 6 members?
(iii) How many members per family are there in the maximum number of families? Also
tell the number of such families.
(iv) What are the number of members per family for which the number of families are
equal? Also, tell the number of such families?

Read the bar graph given in Fig. 23.22 and answer the following questions:

(i) What information is given by the bar graph?
(ii) Which Doordarshan centre covers maximum area? Also tell the covered area.
(iii) What is the difference between the areas covered by the centres at delhi and Bombay?
(iv) Which Doordarshan centres are in U.P State? What are the areas covered by them?

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Explain the reading and interpretation of bar graphs.

Read the following bar graph and answer the following questions:
(i) What information is given by the bar graph?
(ii) In which year the export is minimum?
(iii)In which year the import is maximum?
(iv)In which year the difference of the values of export and import is maximum?

The following bar graph shows the results of an annual examination in a secondary school. Read the bar graph (Fig. 23.28) and choose the correct alternative in each of the following:

(i) The pair of classes in which the results of boys and girls are inversely proportional are:
(a) VI, VIII (b) VI, IX (c) VIII, IX (d) VIII, X
(ii) The class having the lowest failure rate of girls is
(a) VII (b) X (c) IX (d) VIII
(iii)The class having the lowest pass rate of students is
(a) VI (b) VII (c) VIII (d) IX

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If the heights of 5 persons are 140 cm, 150 cm, 152 cm, 158 cm and 161 cm respectively,
find the mean height.

Find the mean of 994, 996, 998, 1002 and 1000.

Find the mean of first five natural numbers .

Find the mean of all factors of 10.

Find the mean of first 10 even natural numbers.

Find the mean of x, x + 2, x + 4, x +6, x + 8.

Find the mean of first five multiples of 3.

Following are the weights (in kg) of 10 new born babies in a hospital on a particular day:
3.4, 3.6, 4.2, 4.5, 3.9, 4.1, 3.8, 4.5, 4.4, 3.6. Find the mean   x.

The percentage of marks obtained by students of a class in mathematics are : 64, 36, 47, 23,
0, 19, 81, 93, 72, 35, 3, 1. Find their mean.

The numbers of children in 10 families of a locality are:
2, 4, 3, 4, 2, 0, 3, 5, 1, 1, 5. Find the mean number of children per family.

If M is the mean of x1 , x2 , x3 , x4 , x5 and x6, prove that
(x1 − M) + (x2 − M) + (x3 − M) + (x4 − M) + (x5 — M) + (x6 − M) = 0.

Durations of sunshine (in hours) in Amritsar for first 10 days of August 1997 as reported by
the Meteorological Department are given below: 9.6, 5.2, 3.5, 1.5, 1.6, 2.4, 2.6, 8.4, 10.3, 10.9

(i) Find the mean 𝑋 ̅
(ii) Verify that = sum _ ( i = 1)^10(xi - x ) = 0

Explain, by taking a suitable example, how the arithmetic mean alters by

(i) adding a constant k to each term

(ii) subtracting a constant k from each them

(iii) multiplying each term by a constant k and

(iv) dividing each term by a non-zero constant k.

The mean of marks scored by 100 students was found to be 40. Later on it was discovered
that a score of 53 was misread as 83. Find the correct mean.

The traffic police recorded the speed (in kmlhr) of 10 motorists as 47, 53, 49, 60, 39, 42, 55,57, 52, 48. Later on an error in recording instrument was found. Find the correct overagespeed of the motorists if the instrument recorded 5 km/hr less in each case.

The mean of five numbers is 27. If one number is excluded, their mean is 25. Find the
excluded number.

The mean weight per student in a group of 7 students is 55 kg. The individual weights of 6
of them (in kg) are 52, 54, 55, 53, 56 and 54. Find the weight of the seventh student.

The mean weight of 8 numbers is 15. If each number is multiplied by 2, what will be the new mean?

The mean of 5 numbers is 18. If one number is excluded, their mean is 16. Find the excluded number.

The mean of 200 items was 50. Later on, it was discovered that the two items were misread
as 92 and 8 instead of 192 and 88. Find the correct mean.

Find the values of n and X in each of the following cases :

(i)  sum _(i = 1)^n(xi - 12) = - 10 sum _(i = 1)^n(xi - 3) = 62

(ii) sum _(i = 1)^n (xi - 10) = 30  sum _(i = 6)^n (xi - 6) = 150 .

The sums of the deviations of a set of n values 𝑥1, 𝑥2, … . 𝑥11 measured from 15 and −3 are − 90 and 54 respectively. Find the valùe of n and mean.

Find the sum of the deviations of the variate values 3, 4, 6, 7, 8, 14 from their mean.

If x is the mean of the ten natural numbers x_1, x_2 , x_3+....... + x_10 show that (x1 -x) + (x2 - x) +.........+ (x10 - x)` = 0

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Calculate the mean for the following distribution:

 x : 5 6 7 8 9 f : 4 8 14 11 3

Find the mean of the following data:

 x : 19 21 23 25 27 29 31 f : 13 15 16 18 16 15 13

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

 x : 10 15 p 25 35 f : 3 10 25 7 5

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

 x: 5 10 15 20 25 f : 6 p 6 10 5

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

 x: 8 12 15 p 20 25 30 f : 12 16 20 24 16 8 4

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

 x 5 8 10 12 p 20 25 f 2 5 8 22 7 4 2

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

 x 3 5 7 9 11 13 f 6 8 15 p 8 4

Find the mean of the following distribution:

 x : 10 12 20 25 35 F : 3 10 15 7 5

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

 Schools No. of candidates Average score 1 60 75 2 48 80 3 N A 55 4 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 3.

Five coins were simultaneously tossed 1000 times and at each toss the number of heads wereobserved. 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

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

 x 10 30 50 70 90 f 17 f1 32 f2 19 Total =120

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Find the median of the following data (1-8)

83, 37, 70, 29, 45, 63, 41, 70, 34, 54

Find the median of the following data (1-8)

133, 73, 89, 108, 94, 1O4, 94, 85, 100, 120

Find the median of the following data (1-8)

31 , 38, 27, 28, 36, 25, 35, 40

Find the median of the following data (1-8)

15, 6, 16, 8, 22, 21, 9, 18, 25

Find the median of the following data (1-8)

41, 43, 127, 99, 71, 92, 71, 58, 57

Find the median of the following data (1-8)

25, 34, 31, 23, 22, 26, 35, 29, 20, 32

Find the median of the following data (1-8)

12, 17, 3, 14, 5, 8, 7, 15

Find the median of the following data (1-8)

92, 35, 67, 85, 72, 81, 56, 51, 42, 69

Numbers 50, 42, 35, 2x + 10, 2x − 8, 12, 11, 8 are written in descending order and their
median is 25, find x.

Find the median of the following observations : 46, 64, 87, 41, 58, 77, 35, 90, 55, 92, 33. If 92 is replaced by 99 and 41 by 43 in the above data, find the new median?

Find the median of the following data : 41, 43, 127, 99, 61, 92, 71, 58, 57 If 58 is replaced
by 85, what will be the new median.

The weights (in kg) of 15 students are: 31, 35, 27, 29, 32, 43, 37, 41, 34, 28, 36, 44, 45, 42,30. Find the median. If the weight 44 kg is replaced by 46 kg and 27 kg by 25 kg, find the new median.

The following observations have been arranged in ascending order. If the median of the data is 63, find the value of x: 29, 32, 48, 50, x, x + 2, 72, 78, 84, 95

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Find out the mode of the following marks obtained by 15 students in a class:
Marks : 4, 6, 5, 7, 9, 8, 10, 4, 7, 6, 5, 9, 8, 7, 7.

Find the mode from the following data:

125, 175, 225, 125, 225, 175, 325, 125, 375, 225, 125

Find the mode for the following series :
7.5, 7.3, 7.2, 7.2, 7.4, 7.7, 7.7,7.5, 7.3, 7.2, 7.6, 7.2

Find the mode of the following data :
14, 25, 14, 28, 18, 17, 18, 14, 23, 22, 14, 18

Find the mode of the following data :
7, 9, 12, 13, 7, 12, 15, 7, 12, 7, 25, 18, 7

The demand of different shirt sizes, as obtained by a survey, is given below:

 Size: 38 39 40 41 42 43 44 Total No of persons(wearing it) 26 39 20 15 13 7 5 125

Find the modal shirt sizes, as observed from the survey.

S