KSEEB SSLC Class 10 Maths Solutions Chapter 13 Statistics Ex 13.2

KSEEB SSLC Class 10 Maths Solutions Chapter 13 Statistics Ex 13.2 are part of KSEEB SSLC Class 10 Maths Solutions. Here we have given Karnataka SSLC Class 10 Maths Solutions Chapter 13 Statistics Exercise 13.2.

Karnataka SSLC Class 10 Maths Solutions Chapter 13 Statistics Exercise 13.2

Question 1.
The following table shows the ages of the patients admitted in a hospital during a year :
KSEEB SSLC Class 10 Maths Solutions Chapter 13 Statistics Ex 13.2 1
Find the mode and the mean of the data given above. Compare and interpret the two measures of central tendency ?
Solution:
(i) Here the maximum class interval is 35 – 45. This class interval has mode
l = 35, f1 = 23, f0 = 21, f2 = 14, h = 10
KSEEB SSLC Class 10 Maths Solutions Chapter 13 Statistics Ex 13.2 Q 1.1
∴ Mode = 36.8 years

(ii) Mean (\(\overline{X}\)) : Step Deviation Method:
KSEEB SSLC Class 10 Maths Solutions Chapter 13 Statistics Ex 13.2 Q 1.2
Here, a = 30
KSEEB SSLC Class 10 Maths Solutions Chapter 13 Statistics Ex 13.2 Q 1.3
= 30 + 5.37
= 35.37
∴ Mode = 36.8
∴ Mean = 35.37
Hence Age group 36.8 patients are admitted more in number.
Mean age group patients are 35.57

KSEEB Solutions for Class 10 Maths Chapter 15 Surface Areas and Volumes Ex 15.5

Question 2.
The following data gives the information on the observed lifetimes (in hours) of 225 electrical components:
MP Board Class 10th Maths Solutions Chapter 14 Statistics Ex 14.2 4
Determine the modal lifetimes of the components.
Solution:
Here, the highest frequency = 61.
∵ The frequency 61 corresponds to class 60 – 80
∴ The modal class is 60 – 80
∴ We have l = 60, h = 20, f1 = 61, f0 = 52, f2 = 38
KSEEB SSLC Class 10 Maths Solutions Chapter 13 Statistics Ex 13.2 Q2
Thus, the modal lifetimes of the components is 65.625 hours.

KSEEB Solutions for Class 10 Maths Chapter 15 Surface Areas and Volumes Ex 15.5

Question 3.
The following data gives the distribution of total monthly household expenditure of 200 families of a village. Find the modal monthly expenditure of the families. Also. And the mean monthly expenditure :
Solution:
KSEEB SSLC Class 10 Maths Solutions Chapter 13 Statistics Ex 13.2 Q 3
Solution:
(i) Mode is in class interval 1500 – 2000
Here, l = 1500, f1 = 40, f0 = 24, f2 = 33, h = 500
KSEEB SSLC Class 10 Maths Solutions Chapter 13 Statistics Ex 13.2 Q 3.1

(ii) Mean (\(\overline{X}\)): Step Deviation Method:
KSEEB SSLC Class 10 Maths Solutions Chapter 13 Statistics Ex 13.2 Q 3.2
Here, a = 2750
KSEEB SSLC Class 10 Maths Solutions Chapter 13 Statistics Ex 13.2 Q 3.3
KSEEB SSLC Class 10 Maths Solutions Chapter 13 Statistics Ex 13.2 Q 3.4
= 2750 – 87.50
= 2662.5
∴ Modal monthly expenditure = 1847.8
∴ Mean Monthly expenditure = Rs. 2662.5

KSEEB Solutions for Class 10 Maths Chapter 15 Surface Areas and Volumes Ex 15.5

Question 4.
The following distribution gives the state-wise teacher-student ratio in higher secondary schools of India. Find the mode and mean of this data. Interpret the two measures.
MP Board Class 10th Maths Solutions Chapter 14 Statistics Ex 14.2 9
Solution:
Mode : Since greatest frequency i.e., 10 corresponds to class 30 – 35.
∴ Modal class = 30 – 35 and h = 5, l = 30, f1 = 10, f0 = 9, f2 = 3
∴ Mode = l + \(\left[\frac{f_{1}-f_{0}}{2 f_{1}-f_{0}-f_{2}}\right]\) × h
= 30 + \(\left[\frac{10-9}{20-9-3}\right]\) × 5
= 30 + \(\left[\frac{10-9}{20-9-3}\right]\) × 5 = 30 + 0.625 = 30.6 (approx)
Mean: Let the assumed mean, a = 37.5 and class size, h = 5
∴ ui = \(\frac{x_{i}-a}{h}=\frac{x_{i}-37.5}{5}\)
∴ We have the following table:
KSEEB SSLC Class 10 Maths Solutions Chapter 13 Statistics Ex 13.2 Q4
MP Board Class 10th Maths Solutions Chapter 14 Statistics Ex 14.2 11
Interpretation:
The maximum teacher-student ratio is 30.6 while average teacher-student ratio is 29.2

KSEEB Solutions for Class 10 Maths Chapter 15 Surface Areas and Volumes Ex 15.5

Question 5.
The given distribution shows the number of runs scored by some top batsmen of the world in one-day international cricket matches.
KSEEB SSLC Class 10 Maths Solutions Chapter 13 Statistics Ex 13.2 Q 5
Find the mode of the data.
Solution:
Class interval which has mode is = 4000 – 5000
Maximum frequency is
Here, l = 4000, f1 = 18, f0 = 4, f2 = 9, h = 1000
KSEEB SSLC Class 10 Maths Solutions Chapter 13 Statistics Ex 13.2 Q 5.1
= 4000 + 608.7
= 4608.7
∴ Mode = 4608.7 runs.

Question 6.
A student noted the number of cars passing through a spot on a road for 100 periods each of 3 minutes and summarised it in the table given below. Find the mode of the data:
MP Board Class 10th Maths Solutions Chapter 14 Statistics Ex 14.2 14
Solution:
∵ The class 40 – 50 has the maximum frequency i.e., 20
∴ Modal class = 40 – 50
∴ f1 = 20, f0 = 12, f1 = 11 and l = 40. Also, h = 10
MP Board Class 10th Maths Solutions Chapter 14 Statistics Ex 14.2 15
Thus, the required mode is 44.7 cars.

We hope the given KSEEB SSLC Class 10 Maths Solutions Chapter 13 Statistics Ex 13.2 will help you. If you have any query regarding Karnataka SSLC Class 10 Maths Solutions Chapter 13 Statistics Exercise 13.2, drop a comment below and we will get back to you at the earliest.

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