Kerala 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 and median are gives the average distance covered by a person. Hence they will not have much difference..

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

DistrictRainfall (mm)
Kasaragod66.7
Kannur56.9
Kozhikode33-5
Wayanad20.5
Malappuram13-5
Palakkad56.9
Thrissur53-4
Ernakulam70.6
Kottayam50.3
Idukki30.5
Pathanamthitta56.4
Alapuzha45-5
Kollam56.3
Thiruvananthapuram89.0

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
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 =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.

Sslc Statistics Solutions Kerala Syllabus 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 = a+a+4d/2=2a+4d/2=a+2d
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

Sslc Maths Statistics Notes Kerala Syllabus  Questions 1.
35 households in a neighborhood are sorted according to their monthly income in the table below.

Monthly income (Rs)Number of households
40003
50007
60008
70005
80005
90004
100003

Calculate the median income.
Answer:

Monthly income (Rs)Number of households
up to 40003
up to500010
up to 600018
up to 700023
up to 800028
up to 900032
up to1000035

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

Sslc Maths Chapter 11 Statistics Kerala Syllabus Questions 2.
The table below shows the workers in a factory sorted according to their daily wages.

Daily wages (Rs)Number of workers
4002
5004
6005
7007
8005
9004
10003

Calculate the median daily wage.
Answer:

Daily wages (Rs)Number of workers
up to 4002
up to 5006
up to 60011
up to 70018
up to 80023
up to 90027
up to 100030

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

Sslc Maths Chapter 11 Kerala Syllabus 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
2.5004
2.6006
2.7508
2.80010
3.00012
3-i5o10
3-2508
3-3007
3-5°o5

Calculate the median birth-weight
Answer:

Weight (kg)Number of babies
up to 2.5004
up to 2.60010
up to 2.75018
up to 2.80028
up to 3.00040
up to 3.15050
up to 3.25058
up to 3.30065
up to 3.50070

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

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

Electricity usage (units)Number of households
80 – 903
90 – 1006
100 – 1107
110 – 12010
120 – 1309
130 – 1404

Calculate the median usage of electricity.
Answer:

Usage of electricity (units)Number of households
less than 903
less than 1009
less than 11016
less than 12026
less than 13035
less than 14039

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

Statistics Class 10 State Syllabus Question 2.
Answer:

WeightNumber
less than 45.55
less than 50.512
less than 55.522
less than 60.530
less than 65.534

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 = 5/10 = 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

Median =52.75+53.25/2=53

Statistics 10th Standard State Syllabus Question 3.
The workers of a company are arranged as given below. Calculate median

Income (Rs)Number of workers
4502
5003
5505
6008
6506
7005
7501

Answer:

Income (Rs)Number of workers
up to 4502
up to 5005
up to 55010
up to 60018
up to 65024
up to 70029
up to 75030

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

Scert Class 10 Maths Statistics Kerala Syllabus 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 = sumnumber = 248000/10 = 24800
b. 9 families have monthly income less than the mean income. So in this situation this is not a suitable average.

Sslc Maths Statistics Questions And Answers Kerala Syllabus 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

Sslc Statistics Questions Kerala Syllabus 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)

Median = 2500

Statistics Class 10 State Board Kerala Syllabus Question 8.
The table shows the workers doing different jobs in a factory according to their daily wages.

Daily wages(Rs)Number of workers
2254
2507
2709
3005
3503
4002

Calculate median of daily wages.

Answer:

Daily wages(Rs)Number of workers
up to 2254
up to 25011
up to 27020
up to 30025
up to 35028
upto40030

The worker in the 12th position to 20th position has daily wage 270 ie, Median

Sslc Maths Chapter 11 Solutions Kerala Syllabus Question 9.
The table below shows the 60 children in a class sorted according to their heights

Height (cm)Number of children’s
140-1455
145-1508
150-15512
155-16016
160-16511
165-1705
170-1753

Find the median height?
Answer:

Height (cm)Number of children’s
Belowl455
Below 15013
Below 15525
Below 16041
Below 16552
Below 17057
Below 17560 1

Sslc Maths Chapter Statistics Kerala Syllabus  Question 10.
Answer:
a. 100
b. 25
c.

Mid value (x)No.of Workers (y)x, y
130162080
150111650
170203400
190285320
210183780
23071610

Mean = 17840/100 = 178.4

Hss Live Guru 10th Maths Kerala Syllabus 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
∴ 3480+30a+70b/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 = 960/40 = 24,
a + 24 = 52
a = 52 – 24 = 28,
∴ a = 28, b = 24

Long Answer Type Questions (Score 5)

10th Standard Maths Statistics Kerala Syllabus Question 21.
The table below shows groups of children in a class according to their heights:

Height (cm)Number of children
135-1405
140-1458
145 – 15010
150-1559
155-1606
160-1653

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 1405
Below 14513
Below 15023
Below 15532
Below 16038
Below 16541

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 5/10 cm.
i.e., 145 5/20 cm.
Similarly, the height of the 15th student is in between 145 5/10 cm and
Kerala Syllabus 10th Standard Maths Solutions Chapter 11 Statistics 6
Hence height of each child can be increased by 5/10 cm.
There are 7 children to reach the 21st child from 14th child.
i.e., 14 th term is 145 5/20 and common difference is 5/10.
Mean is the 21 st term of the arithmetic sequence.

Statistics Menton Map

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

Mean = sumofterms/Numberofterms

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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