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# NCERT Solutions for Class 10 Maths Chapter 14 : Statistics

NCERT Solutions for Class 10 Maths Chapter 14- Statistics are curated by our team of subject experts at Toppr in a detailed manner. NCERT Solutions for statistics class 10 are made strictly in accordance with the CBSE Curriculum and the exam pattern. The NCERT textbook questions are answered in a way to provide you with a better understanding of the concepts in a systematic and step-by-step manner. It also contains the appropriate diagrams to explain the concepts to the students. As Class 10 exams are Board exams, these solutions will not only help the students in preparing for the board exams but also for the Olympiads. NCERT Solutions provided by Toppr are the best study material to excel in the exams. Also, the MCQs and long and short questions are all answered according to the weightage and the exam pattern. With the help of NCERT Statistics Class 10 Solutions you can also test your subject knowledge and analyze your shortcomings and work on them before the exams. These are the best resources designed after proper study and research and study to help the students in scoring good marks.

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## Access NCERT Solutions for Class 10 Maths Chapter 14 : Statistics

Exercise 14.1
Question 3
The following distribution shows the daily pocket allowance of children of a locality. The mean pocket allowance is . Find the missing frequency .
 Daily pocket allowance (in ) Number of children
Medium
Solution
Verified by Toppr

Lets take assumed mean, as
Class interval

Now, we have and

We know that,
Mean,

Hence, the value of missing frequency,
Question 5
Question 6
The table below- shows the daily expenditure on food of households in a locality.
 Daily expenses (in Rs.) 100-150 150-200 200-250 250-300 300-350 No. of households 4 5 12 2 2
Find the mean daily expenses on food by a suitable method

Easy
Solution
Verified by Toppr
 Daily Expense Households (fi) Mid Point (xi) fi xi 100 - 150 4 125 500 150 - 200 5 175 875 200 - 250 12 225 2700 250 - 300 2 275 550 300 - 350 2 325 650 25 5275
Mean
Question 7
To find out the concentration of in the air (in parts per million, i.e., ), the data was collected for localities in certain city and is presented below:
 Concentration of (in ppm) Frequency
Find the mean concentration of in the air.
Medium
Solution
Verified by Toppr
 Concentration of (in ppm) Frequency 0.00-0.04 0.02 4 0.08 0.04-0.08 0.06 9 0.54 0.08-0.12 0.10 9 0.90 0.12-0.16 0.14 2 0.28 0.16-0.20 0.18 4 0.72 0.20-0.24 0.22 2 0.44
Question 8
A class teacher has the following absentee record of students of a class for the whole term. Find the mean number of days a student was absent.
 Number of days: 0-6 6-10 10-14 14-20 20-28 28-38 38-40 Number of students:
Medium
Solution
Verified by Toppr
 No. of days No. of student 0-6 11 3 33 6 - 10 10 8 80 10 - 14 7 12 84 14 - 20 4 17 68 20 - 28 4 24 96 28 - 38 3 33 99 38 - 40 1 39 39
The mean number of days a student was absent

Hence, the mean number of days a student was absent is
Question 9
The following table gives the literacy rate (in percentage) of 35 cities. Find the mean literacy rate.
Medium
Solution
Verified by Toppr
To find the class mark for each interval, using the following relation:

Class size for this data
Taking 70 as assumed mean , calculating :
From the table:

Mean,

Therefore, mean literacy rate is %
Exercise 14.2
Question 1
The following table shows the ages of the patients admitted in a hospital during a year:
 Age (in years) Number of patients
Find the mode and the mean of the data given above. Compare and interpret the two measures of central tendency.
Medium
Solution
Verified by Toppr

Mode: The class which have highest frequency.
In this case, class interval is the modal class.

Now,
Lower limit of modal class,

We know that,
Mode

Mode

Lets take assumed mean, as
Class interval

Hence, Mode years, Mean years.

Maximum number of patients admitted in the hospital are of age group years, while on an average the age of a patient admitted to the hospital is years.
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## NCERT Solutions for Class 10 Maths Chapter 14-  Statistics

Class 10 Chapter 14- Statistics deals with the calculation of the measures of central tendency, namely, mean, median and mode from the grouped data. It also discusses the concept of cumulative frequency, the cumulative frequency distribution and how to draw cumulative frequency curves known as ogives on a graph. This chapter carries a weightage of around 11-12 marks in the board exams. NCERT Solutions for Class 10 Maths Chapter 14-  Statistics will help the students in solving many real-life situations where the fundamentals of statistics are useful to represent a set of data in tabular form or in graphs or in pie charts. The students will learn various methods to calculate the Mean of the grouped data such as the Direct method, step-deviation method and assumed mean method.

### Key Features of NCERT Solutions for Class 10 Maths Chapter 14-  Statistics

• Class 10 NCERT Solutions are provided in a step-by-step manner with appropriate diagrams.
• The solutions provide a better understanding of the subject and concepts.
• These are curated by the experts after thorough research.
• These solutions provide excellent study material for revision.
• They are the best means to evaluate your preparations and overcome your shortcomings.
• The Class 10 NCERT Solutions will help the students in board exams as well as Olympiads.
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### Frequently Asked Questions on NCERT Class 10 Maths Chapter 14 : Statistics

Question 1. State the empirical relationship between the Measures of Central Tendency.

Answer. The empirical relationship between the three measures of central tendency is as follows: 3 Median = Mode + 2 Mean

Question 2. What do you understand by Mean?

Answer. Mean is a measure of the central tendency of a distribution. It refers to the most common or the average value of the given data. There are two types of mean that can be calculated. One is the Arithmetic Mean and the other one is the Geometric Mean. The three methods to calculate the Arithmetic Mean are the direct method, the step-deviation method and the assumed mean method.

Question 3. What do you understand by Median?

Answer. Median refers to the middle number or value of the given set of data when the data is arranged in an ascending or descending order. When the data set contains odd numbers, the median will be the middle value or number that has half of the numbers above it and half of the number below it. However, in the case of even numbers, the median is calculated by adding the two middle numbers and dividing their sum by two. It is also a measure of central tendency.

Question 4. What do you understand by Mode?

Answer. Mode is also a measure of central tendency similar to the Mean and Median. Mode refers to the number or value that is most frequent in a given set of data. In other words, Mode is that value in a given data which occurs the most number of times. Thus, a distribution of data may have only one mode, more than one mode or no mode at all.

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