Samacheer Class 7 Maths Statistics Intext Questions Book Back Answers & Solutions

Q: If the mean is increased by 2, then what happens to the individual observations.

Given number are 3, 6, 9, 12, 15 If mean is increased by 2 then, Sum of observations = 5 × 11 = 55 Difference in sum = 55 – 45 = 10 ∴ Each number is increased by 2 if the mean is increased by 2.

Q: Which average will be most aprropriate for the companies producing the following goods? why? (i) Diaries and notebooks (ii) School bags (iii) Jeans and T-shirts.

for all the above data mode will be more appropriate. Exercise 5.3 Try These (Text book Page No. 106)

Your Progress - Chapter 50% complete

1Book Back Questions50 questions

Q.1Collect the height of students of your class. Organise the data in ascending order.v

Answer:

Height of 15 students in our class.
130cm, 150 cm, 155 cm, 142 cm, 138 cm, 145 cm, 148 cm, 147 cm, 148cm, 143 cm, 141cm, 152 cm, 147 cm, 139 cm, 155 cm.
Ascending order:
130cm, 138cm, 139cm, 141cm, 142cm, 143cm, 145cm, 147cm, 147cm, 148cm, 148 cm, 150cm, 152 cm, 155cm, 155cm.Try These (Text book Page No. 97)
Find the Arithmetic Mean or average of the following data.

Q.1The study time spent by Kathir in a week is 3 hrs, 4 hrs, 5 hrs, 3 hrs, 4 hrs, 3:45 hrs; 4:15 hrs.v

Answer:

mean = 3 : 52 hrs

Q.2The marks scored by Muhil in five subjects are 75, 91, 48, 63, 51.v

Answer:

Arithmetic Mean = 65.6

Q.3Money spent on vegetables for five days is ₹ 120, ₹ 80, ₹ 75, ₹ 95 and ₹ 86.v

Answer:

Arithmetic Mean = 91.2
Think (Text book Page No. 99)
Check the properties of arithmetic mean for the example given below:

Q.1If the mean is increased by 2, then what happens to the individual observations.v

Answer:

Given number are 3, 6, 9, 12, 15If mean is increased by 2 then,Sum of observations = 5 × 11 = 55
Difference in sum = 55 – 45 = 10
∴ Each number is increased by 2 if the mean is increased by 2.

Q.2If first two items are increased by 3 and last two items are reduced by 3, then what will be the new mean?v

Answer:

If the first two items is increased by 3, then the numbers will be 3 + 3, 6 + 3 ⇒ 6, 9.
If last two numbers are decreased by 3, then the numbers will be 12 – 3, 15 – 3 ⇒ 9,12.= \(\frac { 45 }{ 5 } \) = 9
There is no change in the mean.Exercise 5.2
Try These (Text book Page No. 101)

Q.1Find the mode of the following data. 2, 6, 5, 3, 0, 3, 4, 3, 2, 4, 5, 2v

Answer:

Arranging the numbers in ascending order we get 0, 2, 2, 2, 3, 3, 3, 4, 4, 5, 5, 6
Since 2 and 3 occurs the maximum of 3 times. So mode of this data is 2 and 3.

Q.2Find the mode of the following data set. 3, 12, 15, 3, 4, 12, 11, 3, 12, 9, 19.v

Answer:

Arranging the given data in ascending order : 3, 3, 3, 4, 9,11, 12, 12,12, 15, 19.
The data 3 and 12 occurs the maximum of 3 times.
So mode of this data is 3 and 12.

Q.3Find the mode of even numbers within 20.v

Answer:

Even numbers within 20 are 2, 4, 6, 8, 10, 12, 14, 16, 18.
There is no mode for this data.Think (Text book Page No. 102)

Q.1A toy factory making variety of toys for kids, wants to know the most popular toy liked by all the kids. Which average will be the most appropriate for it?v

Answer:

Mode.

Q.2Is there a mode exists between the odd numbers from 20 to 40? Discuss.v

Answer:

Odd number between 20 to 40 are 21, 23, 25, 27, 29, 31, 33, 35, 37, 39.
As all numbers occurs only once there is no mode for this data.
Think (Text book Page No. 103)

Q.3Which average will be most aprropriate for the companies producing the following goods? why? (i) Diaries and notebooks (ii) School bags (iii) Jeans and T-shirts.v

Answer:

for all the above data mode will be more appropriate.Exercise 5.3
Try These (Text book Page No. 106)

Q.1Find the median of 3, 8, 7, 8,4, 5, 6.v

Answer:

Arranging in ascending order: 3, 4, 5, 6, 7, 8, 8.
Here n = 7, which is odd.Hence the median is 6.

Q.2Find the median: 11, 14, 10, 9, 14, 11, 12, 6, 7, 7.v

Answer:

Arranging in ascending order: 6, 7, 7, 9, 10, 11, 11, 12, 14, 14
Here n = 10, which is even.Think (Text book Page No. 108)
Complete the table given below and observe it to answer the following questions.

Q.1Which are all the series having common mean and median?v

Answer:

A, B and C.

Q.2Why median is same for all the 4 series?v

Answer:

Since the middle value is 100.

Q.3How mean is unchanged in the series A, B and C ?v

Answer:

The difference between the given numbers are equal.

Q.4What change is to be made in the data, so that mean and median of ‘D’ series is equal to other series?v

Answer:

If 99 becomes 0 or 200 becomes 101 then mean becomes 100.
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Q.2Ages of 15 students in 8th standard is 13, 12, 13, 14, 12, 13, 13, 14, 12, 13, 13, 14, 13, 12, 14. Find the mean age of the students.v

Answer:

= \(\frac { 195 }{ 15 } \) = 13
Mean age of the students = 13

Q.3The marks of 14 students in a science test out of 50 are given below. 34, 23, 10, 45, 44, 47, 35, 37, 41, 30, 28, 32, 45, 39 Find (i) the mean mark. (ii) the maximum mark obtained. (iii) the minimum mark obtained.v

Answer:

Mean marks = 35
(ii) Maximum mark obtained = 47
(iii) Minimum mark obtained = 10

Q.4The mean height of 11 students in a group is 150 cm. The heights of the students are 154 cm, 145 cm, Y cm, Y + 4 cm, 160 cm, 151 cm, 149 cm, 149 cm, 150 cm, 144 cm and 140 cm. Find the value of Y and the heights of two students.v

Answer:

150 = \(\frac { 1342+Y+Y+4 }{ 11 } \)
150 = \(\frac { 1346+2Y }{ 11 } \)
150 × 11 = 1346 + 2Y
1650 = 1346 + 2Y
2Y = 1650 – 1346 = 304
Y = \(\frac { 304 }{ 2 } \) = 152
Height of two students are Y and Y + 4
⇒ 152 and 152 + 4
⇒ 152 cm and 156 cm

Q.5The mean of runs scored by a cricket team in the last 10 innings is 276. If the scores are 235, 400, 351, x, 100, 315, 410,165, 260, 284, then find the runs scored in the fourth innings.v

Answer:

Let the runs scored in the fourth innings be x.276 × 10 = 2520 + x
2760 = 2520 + x
x = 2760 – 2520 = 240
∴ Number of runs scored in the fourth innings = 240

Q.6Find the mean of the following data. 5.1, 4.8, 4.3, 4.5, 5.1, 4.7, 4.5, 5.2, 5.4, 5.8, 4.3, 5.6,v

Answer:

Mean = 5

Q.7Arithmetic mean of 10 observations was found to be 22. If one more observation 44 was to be added to the data, what would be the new mean?v

Answer:

Arithmetic mean of 10 observation is 22.= \(\frac { 220+44 }{ 11 } \) = \(\frac { 264 }{ 11 } \) = 24
New mean = 24Objective Type Questions

Q.1________ is a representative value of the entire data. (i) Mean (ii) range (iii) minimum value (iv) maximum valuev

Answer:

(i) Mean

Q.2The mean of first fifteen even numbers is ________ (i) 4 (ii) 16 (iii) 5 (iv) 10v

Answer:

(ii) 16
Hint:

Q.4The mean of the data 12, x, 28 is 18. Find the value of x. (i) 18 (ii) 16 (iii) 14 (iv) 22v

Answer:

(iii) 14
Hint:
\(\frac { 12+x+28 }{ 3 } \) = 18
x + 40 = 54
x = 14
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Q.1Find the mode of the following data. 2, 4, 5, 2, 6, 7, 2, 7, 5,4, 8, 6, 10, 3, 2, 4, 2.v

Answer:

Arranging the given data in ascending order 2, 2, 2, 2, 2, 3, 4, 4, 4, 5, 5, 6, 6, 7, 7, 8, 10.
Here the number 2 occurs 5 times which is the maximum
∴ Mode of this data is 2.

Q.2The number of points scored by a Kabaddi team in 20 matches are 36, 35, 27, 28, 29, 31, 32, 31, 35, 38, 38, 31, 28, 31, 34, 33, 34, 31, 30, 29. Find the mode of the points scored by the team.v

Answer:

Arranging the given data in ascending order
27, 28, 28, 29, 29, 30, 31, 31, 31, 31, 31, 32, 33, 34, 34, 35, 35, 36, 38, 38.
Here the number 31 occurs 5 times which is the maximum.
∴ Mode of this data is 31.

Q.3The ages (in years) of 11 cricket players are given below. 25, 36, 39,38 40, 36, 25, 25, 38, o 26,36. Find the mode of the ages.v

Answer:

Arranging the ages is ascending order: 25, 25, 25, 26, 36, 36, 36, 36, 38, 38, 39, 40.
The ages (in years) of 11 cricket players are given below. 25, 36, 39,38 40, 36, 25, 25, 38, o 26,36. Find the mode of the ages.
Arranging the ages is ascending order: 25, 25, 25, 26, 36, 36, 36, 36, 38, 38, 39, 40.
25 and 36 occurs maximum number of times.
∴ Mode is 25 and 36.

Q.4Find the mode of the following data. 12, 14, 12, 16, 15, 13, 14, 18, 19, 12, 14, 15, 16, 15, 16, 16, 15, 17, 13, 16, 16, 15, 15, 13, 15, 17, 15, 14, 15, 13, 15, 14.v

Answer:

Tabulating the given dataThe highest frequency is 10 which corresponds to the value 15.
Hence mode of this data is 15.Objective Type Questions

Q.1The colors used by the six students for drawing is blue, orange, yellow, white, green and blue then the mode is ________ (i) blue (ii) green (iii) white (iv) yellowv

Answer:

(i) blue

Q.2Find the mode of data 3, 6, 9, 12, 15. (i) 1 (ii) 2 (iii) 3 (iv) No modev

Answer:

(iv) No mode

Q.3Find the modes of the data 2, 1, 1, 3, 4, 5, 2. (1) 1 and 5 (2) 2 and 3 (3) 2 and 1 (4) 1 and 4v

Answer:

(3) 2 and 1
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Q.2Find the median of the given data: 35, 25, 34, 36, 45, 18, 28.v

Answer:

Arranging the given data in ascending order 18, 25, 28, 34, 35, 36, 45.
Here the number of observations n = 7, which is odd.Hence Median = 34

Q.3The weekly sale of motor bikes in a showroom for the past 14 weeks given below. 10, 6, 8, 3, 5, 6, 4, 7, 12, 13, 16, 10, 4, 7. Find the median of the data.v

Answer:

Arranging the given data in ascending order 3, 4, 4, 5, 6, 6, 7, 7, 8, 10, 10, 12, 13, 16.
Here number of data n = 14, which is even∴ Median = 7

Q.4Find the median of the 10 observations 36, 33, 45, 28, 39, 45, 54, 23, 56, 25. If another observation 35 is added to the above data, what would be the new median?v

Answer:

Arranging the given 10 observations in ascending order 23, 25, 28, 33, 36, 39, 45, 45, 54, 56.
Here number of data n = 10, which is even∴ Median = 37.5
If 35 is added to the above data then it will be the 5th term then number of data n = 11, odd
∴ Median = (\(\frac { n+1 }{ 2 } \)) th term = (\(\frac { 11+1 }{ 2 } \)) th term
= (\(\frac { 12 }{ 2 } \)) th term = 6th term
New median = 36Objective Type Questions

Q.1If the median of a, 2a, 4a, 6a, 9a is 8, then find the value of a is (i) 8 (ii) 6 (iii) 2 (iv) 10v

Answer:

(iii) 2
Hint:Median = 4a = 8
a = 2

Q.2The median of the data 24, 29, 34, 38, 35 and 30, is ________ (i) 29 (ii) 30 (iii) 34 (iv) 32v

Answer:

(iv) 32
Hint:Median = \(\frac { 30+34 }{ 2 } \)
= \(\frac { 64 }{ 2 } \)
= 32

Q.3The median first 6 odd natural numbers is (i) 6 (ii) 7 (iii) 8 (iv) 14v

Answer:

(i) 6
Hint:Median = \(\frac { 5+7 }{ 2 } \)
= \(\frac { 12 }{ 2 } \)
= 6
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Q.1Arithmetic mean of 15 observations was calculated as 85. In doing so an observation was wrongly taken as 73 for 28. What would be correct mean?v

Answer:

85 × 15 = sum of 15 observations
1275 = sum of 15 observations
Wrong observation = 73
Correct observation = 28Correct mean = 82

Q.2The median of 25,16,15,10, 8, 30.v

Answer:

Arranging is ascending order : 8, 10, 15, 16, 25, 30
Here n = 6, even∴ Median = 15.5

Q.3Find the mode of 2, 5, 5, 1, 3, 2, 2, 1, 3, 5, 3.v

Answer:

Arranging the data in ascending order: 1, 1, 2, 2, 2, 3, 3, 3, 5, 5, 5
Here 2, 3 and 5 occurs 3 times each.
Which is the maximum number of times.
∴ Mode is 2, 3 and 5.

Q.4The marks scored by the students in social test out of 20 marks are as follows. 12, 10, 8, 18, 14, 16. Find the mean and the median?v

Answer:

Arranging the given data in ascending order: 8, 10, 12, 14, 16, 18.There are n = 6 observations, which is even

Q.5The number of goals scored by a football team is given below. Find the mode and median for the data of 2 ,3, 2, 4, 6, 1, 3, 2, 4, 1, 6.v

Answer:

Arranging the given data in ascending order: 1, 1, 2, 2, 2, 3, 3, 4, 4, 6, 6
Clearly 2 occurs at the maximum of 3 times and so mode = 2
Here number of data of data n = 11, odd.
∴ Median = (\(\frac { n+1 }{ 2 } \)) th term
= (\(\frac { 11+1 }{ 2 } \)) th
term = (\(\frac { 12 }{ 2 } \)) th term
= 6 th term
Median = 3

Q.6Find the mean and mode of 6, 11, 13, 12, 4, 2.v

Answer:

Arranging is ascending order : 2, 4, 6, 11, 12, 13Mean = \(\frac { 48 }{ 6 } \) = 8
All observation occurs only once and so there is no mode for this date.Challenge Problems

Q.1The average marks of six students is 8. One more student mark is added and the mean is still 8. Find the student mark that has been added.v

Answer:

Sum of observation = 6 × 8 = 48
If one more mark is added then number of observations = 6 + 1 = 7
Let the number be x
Still average = 8
∴ 8 = \(\frac { 48+x }{ 7 } \)
48 + x = 7 × 8
48 + x = 56
48 + x = 56 – 48
x = 8
∴ The number that is added = 8

Q.2Calculate the mean, mode and median for the following data: 22, 15, 10, 10, 24, 21.v

Answer:

Arranging in ascending order: 10, 10, 15, 21, 22, 24Here n = 6, even∴ Median = 18
Clearly the data 10 occurs maximum number of times and so 10 is the mode.
∴ Mode = 10

Q.3Find the median of the given data: 14, -3, 0, -2, -8, 13, -1, 7.v

Answer:

Arranging the data is ascending order: -8, -3, -2, -1, 0, 7, 13, 14
Here number of data n = 8, even
∴ Median∴ Median = – 0.5

Q.4Find the mean of first 10 prime numbers and first 10 composite numbers.v

Answer:

First 10 prime numbers are 2, 3, 5, 7, 11, 13, 17, 19, 23, 29Mean = 12.9
Mean of first 10 prime numbers = 12.9
First 10 composite numbers are 4, 6, 8, 9, 10, 12, 14, 15, 16, 18Mean of first 10 composite numbers = 11.2
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