Kerala Syllabus 10th Standard Maths Solutions Chapter 11 Statistics

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Kerala State Syllabus 10th Standard Maths Solutions Chapter 11 Statistics

Statistics Textbook Questions & Answers

Textbook Page No. 245

Statistics Class 10 Kerala Syllabus Questions 1.
The distance covered by an athlete in long jump practice are
6.10, 6.20, 6.18, 6.20, 6.25, 6.21, 6.15, 6.10
in meters. Find the mean and median. Why is it that there is not much difference between these?
Answer:
Mean = \(\begin{array}{l}{=\frac{6.10+6.20+6.18+6.20+6.25+6.21+6.15+6.10}{8}} \\ {=\frac{49.39}{8}=6.17}\end{array}\)
If distances are written in ascending order
6.10, 6.15, 6.18, 6.20, 6.21, 6.25
Median = \(\frac{6.18+6.20}{2}=6.19 \mathrm{m}\)
Mean and median are gives the average dis¬tance covered by a person. Hence they will not have much difference..

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Statistics Class 10 Questions 2.
The table below gives the rainfall during one week of September 2015 in various districts of Kerala.

District Rainfall (mm)
Kasaragod 66.7
Kannur 56.9
Kozhikode 33-5
Wayanad 20.5
Malappuram 13-5
Palakkad 56.9
Thrissur 53-4
Ernakulam 70.6
Kottayam 50.3
Idukki 30.5
Pathanamthitta 56.4
Alapuzha 45-5
Kollam 56.3
Thiruvananthapuram 89.0

Calculate the mean and median rainfall in Kerala during this week. Why is the mean less than median?
Answer:
Mean = Total amount of rain / No. of districts
= \(\frac { 700 }{ 14 }\) = 50
In ascending order:
13.5, 20.5, 30.5, 33.5, 45.5, 50.3, 53.4, 56.3, 56.4, 56.9, 56.9, 66.7, 70.6, 89
Median \(=\frac{53.4+56.3}{2}=54.85\)
The mean is less than median because the number contains are far small and large numbers than mean.

10th Statistics Questions 3.
Prove that for a set of numbers arithmetic sequence, the mean and median are equal.
Answer:
Let a, a+d, a+3d, a+4d are the numbers of an arithmetic sequence, then median = \(\frac{a+a+4 d}{2}=\frac{2 a+4 d}{2}=a+2 d\)
Median will be the term which is at center = a + 2d
∴ A set of numbers in arithmetic sequence, the mean and median are equal.

Textbook Page No. 248

Questions 1.
35 households in a neighborhood are sorted according to their monthly income in the table below.

Monthly income (Rs) Number of households
4000 3
5000 7
6000 8
7000 5
8000 5
9000 4
10000 3

Calculate the median income.
Answer:

Monthly income (Rs) Number of households
up to 4000 3
up to5000 10
up to 6000 18
up to 7000 23
up to 8000 28
up to 9000 32
up to10000 35

In the table monthly income up to 18th place be 6000 rupees.
That is 18th place family also includes in the middle of total number of families.
∴ Median of the income = Rs. 6000

Maths Solutions Questions 2.
The table below shows the workers in a factory sorted according to their daily wages.

Daily wages (Rs) Number of workers
400 2
500 4
600 5
700 7
800 5
900 4
1000 3

Calculate the median daily wage.
Answer:

Daily wages (Rs) Number of workers
up to 400 2
up to 500 6
up to 600 11
up to 700 18
up to 800 23
up to 900 27
up to 1000 30

Total number of workers = 30
Half= 15
So median is the wage of 15th worker.
The daily wages between the place 11 and 18 = 700 rupees
Median of daily wages = 700 rupees

Syllabus 10th Class Questions 3.
The table below gives the number of babies born in a hospital during a week, sorted according to their birth weight.

Weight (kg) Number of babies
2.500 4
2.600 6
2.750 8
2.800 10
3.000 12
3-i5o 10
3-250 8
3-300 7
3-5°o 5

Calculate the median birth-weight
Answer:

Weight (kg) Number of babies
up to 2.500 4
up to 2.600 10
up to 2.750 18
up to 2.800 28
up to 3.000 40
up to 3.150 50
up to 3.250 58
up to 3.300 65
up to 3.500 70

Total number of babies = 70
Half =35
So median is the weight of 35th baby.
The weight of 35 111 child be in between 29 and 40 placed child, its weight will be 3 kg.
∴ Median of the weight = 3 kg.

Textbook Page No. 254

Kerala Board Syllabus Questions 1.
The table shows some households sorted according to their usage of electricity:

Electricity usage (units) Number of households
80 – 90 3
90 – 100 6
100 – 110 7
110 – 120 10
120 – 130 9
130 – 140 4

Calculate the median usage of electricity.
Answer:

Usage of electricity (units) Number of households
less than 90 3
less than 100 9
less than 110 16
less than 120 26
less than 130 35
less than 140 39

Half of the number of houses = 20
We have to find the electricity usage of the 20th house. According to this, we can divide

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Standard 10th Standard Question 2.
Answer:

Weight Number
less than 45.5 5
less than 50.5 12
less than 55.5 22
less than 60.5 30
less than 65.5 34

Total number of children = 34
It is an even number, so we will take the half of sum of weight of the children, those are in the 17 and 18 positions. According to this child between 13 and 22 have weight between 50.5 and 55.5. Our required children (between and 17 and 18) are in these positions. Divide 5 years from 50.5 to 55.5 into 10 equal, parts. Let consider each part have one child.

Weight of each part = \(\frac { 5 }{ 10 }\) = \(\frac { 1 }{ 2 }\).
Hence weight of a child in 13th place is in middle of 50.5 and 51. That is 50.75. Further, each student’s weight is increased by 5.
Hence weight of the man in the 17th position
Kerala Syllabus 10th Standard Maths Solutions Chapter 11 Statistics 1
Median \(=\frac{52.75+53.25}{2}=53\)

Question 3.
The workers of a company are arranged as given below. Calculate median

Income (Rs) Number of workers
450 2
500 3
550 5
600 8
650 6
700 5
750 1

Answer:

Income (Rs) Number of workers
up to 450 2
up to 500 5
up to 550 10
up to 600 18
up to 650 24
up to 700 29
up to 750 30

Total number of workers = 30
Half = 15
So median is the wage of 15th worker.
The daily wage between the place 10 and 18 = 600 rupees
Median of daily wage = 600 rupees

Statistics SCERT Questions & Answers

Question 5.
10 households in a neighborhood are sorted according to their monthly income are given below
16500, 21700, 18600, 21050, 19500, 17000, 21000, 18000, 22000, 75000
a. What is the mean income of these 10 families?
b. How many families have monthly incomes less than the mean income? Prove that in such situation this average is suitable or not?
Answer:
a. Mean = \(\frac { sum }{ number }\) = \(\frac { 248000 }{ 10 }\) = 24800
b. 9 families have monthly income less than the mean income. So in this situation this is not a suitable average.

Question 6.
Number of members in 10 families, collected by mathematics club survey are given. Calculate mean; median and explain. Which is the suitable average?.
4, 2, 3, 5, 4, 3, 2, 20, 4, 3
Answer:
a. Mean = 5
b. Median = 3.5
Suitable average median = 3.5

Question 7.
Weekly Wages of 9 persons Working in a factory are given. Find the median 2100; 3500, 2100, 2500, 2800, 4900, 2300, 2200, 3300
Answer:
Write the number in order.
2100, 2100, 2200, 2300, 2500, 2800, 3300, 3300, 3500 (1)

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Median = 2500

10 Standard Statistics Question 8.
The table shows the workers doing different jobs in a factory according to their daily wages.

Daily wages(Rs) Number of workers
225 4
250 7
270 9
300 5
350 3
400 2

Calculate median of daily wages.

Answer:

Daily wages(Rs) Number of workers
up to 225 4
up to 250 11
up to 270 20
up to 300 25
up to 350 28
upto400 30

The worker in the 12th position to 20th position has daily wage 270 ie, Median
Kerala Syllabus 10th Standard Maths Solutions Chapter 11 Statistics 2

Question 9.
The table below shows the 60 children in a class sorted according to their heights

Height (cm) Number of children’s
140-145 5
145-150 8
150-155 12
155-160 16
160-165 11
165-170 5
170-175 3

Find the median height?
Answer:

Height (cm) Number of children’s
Belowl45 5
Below 150 13
Below 155 25
Below 160 41
Below 165 52
Below 170 57
Below 175 60 1

Kerala Syllabus 10th Standard Maths Solutions Chapter 11 Statistics 3

Question 10.
Answer:
a. 100
b. 25
c.

Mid value (x) No.of Workers (y) x, y
130 16 2080
150 11 1650
170 20 3400
190 28 5320
210 18 3780
230 7 1610

Mean = \(\frac { 17840 }{ 100 }\) = 178.4

Question 11.
The mean of the frequency table given below is 50. Then find out the values of a and b.
Kerala Syllabus 10th Standard Maths Solutions Chapter 11 Statistics 4
Answer:
Kerala Syllabus 10th Standard Maths Solutions Chapter 11 Statistics 5
mean = 50
∴ \(\frac{3480+30 a+70 b}{120}=50\)
30a + 70b = 6000 – 3480
30a + 70b = 2520 (1)
17 + 32 + 19 + a + b = 120
68 + a + b = 120,
a + b = 52 (2)
(2) x 30 => 30a + 30b = 1560
30a + 70b = 2520,
30a + 30b = 1560,
40b = 960,
b = \(\frac { 960 }{ 40 }\) = 24,
a + 24 = 52
a = 52 – 24 = 28,
∴ a = 28, b = 24

Long Answer Type Questions (Score 5)

Question 21.
The table below shows groups of children in a class according to their heights:

Height (cm) Number of children
135-140 5
140-145 8
145 – 150 10
150-155 9
155-160 6
160-165 3

a. If the children are lined up according to their heights, the median is the height of the child in which position?
b. According to the table, the height of this child is between what limits?
c. What are the assumptions used to compute the median?
d. What is the median height according to these assumptions?
Answer:

Height (cm) Number of children
Below 140 5
Below 145 13
Below 150 23
Below 155 32
Below 160 38
Below 165 41

a. Height of the 21st child is the median height.
b. Height of the 21st child is between 145 cm and 150 cm.
c. Methods to find the median are.
1. Divide 5cm in between 145 cm and 150 cm into 10 equal sections.
2. Consider that the height of each sub-group is exactly on the midpoint of the subgroup.
Height of the 14th child is in between 145 cm and 145 \(\frac { 5 }{ 10 }\) cm.
i.e., 145 \(\frac { 5 }{ 20 }\) cm.
Similarly, the height of the 15th student is in between 145 \(\frac { 5 }{ 10 }\) cm and
Kerala Syllabus 10th Standard Maths Solutions Chapter 11 Statistics 6
Hence height of each child can be increased by \(\frac { 5 }{ 10 }\) cm.
There are 7 children to reach the 21st child from 14th child.
i.e., 14 th term is 145 \(\frac { 5 }{ 20 }\) and common difference is \(\frac { 5 }{ 10 }\).
Mean is the 21 st term of the arithmetic sequence.
Kerala Syllabus 10th Standard Maths Solutions Chapter 11 Statistics 7

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Statistics Menton Map

Arithmetic mean is the sum divided by the number of terms.

Mean = \(\frac { sum of terms }{ Number of terms }\)

When the numbers are arranged in a ascending order, then the middle term is the median.
i.e., half of the total frequency will give the median.

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