SSLC MATHS CHAPTER 11

 

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 = =6.10+6.20+6.18+6.20+6.25+6.21+6.15+6.108=49.398=6.17
If distances are written in ascending order
6.10, 6.15, 6.18, 6.20, 6.21, 6.25
Median = 6.18+6.202=6.19m
Mean and median are gives the average dis¬tance 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.

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
= 70014 = 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+56.32=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+4d2=2a+4d2=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
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

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
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

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
2.500	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

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 – 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

Statistics Class 10 State Syllabus 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 = 510 = 12.
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+53.252=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
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

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 = 24800010 = 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
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

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
140-145	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

Sslc Maths Chapter Statistics Kerala Syllabus  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 = 17840100 = 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.

Answer:

mean = 50
∴ 3480+30a+70b120=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 = 96040 = 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
135-140	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 145 510 cm.
i.e., 145 520 cm.
Similarly, the height of the 15th student is in between 145 510 cm and

Hence height of each child can be increased by 510 cm.
There are 7 children to reach the 21st child from 14th child.
i.e., 14 th term is 145 520 and common difference is 510.
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 = sumoftermsNumberofterms

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.