# Class 10 Maths Chapter 13 Question Answers - Statistics

Q1. In the following distribution:

 Monthly expenditure Number of families Expenditure more than Rs 10,000 100 Expenditure more than Rs 13,000 85 Expenditure more than Rs 16,000 69 Expenditure more than Rs 19,000 50 Expenditure more than Rs 22,000 33 Expenditure more than Rs 25,000 15

The number of families having expenditure range in (Rs) 16000–19000 is:

(i) 15
(ii) 16
(iii)17
(iv) 19

Sol. (iv)1 9 [∵ 69 − 50 = 19]

Q2.  Construction of a cumulative frequency table is useful in determining the (i) mean (ii) mode (iii) median (iv) all the above

(i) mean
(ii) mode
(iii) median
(iv) all the above

Sol. (iii) median

Q3. The abscissa of the point of interaction of the ‘less than type’ and of the ‘more than type’ comutative frequency curve of grouped data gives its:

(i) mode
(ii) mean
(iii) median
(iv) All the three above

Sol. (iii) median.

Q4. For the following distribution:

 Marks Number of Students Below 10 3 Below 20 12 Below 30 27 Below 40 57 Below 50 75 Below 60 80

The modal class is

(i) 15−60
(ii) 30−40
(iii) 20−30
(iv) 10−20

Sol. (ii) 30−40

Q5. The formula   is used to determine:

(i) mean
(ii) mode
(iii) median
(iv) all the three above of grouped data.

Sol. (i) mean

Q6. Consider the following distribution:

 Marks obtained Number of students More than or equal to 0 63 More than or equal to 10 58 More than or equal to 20 55 More than or equal to 30 51 More than or equal to 40 48 More than or equal to 50 42

The frequency of the class 30−40 is:

(i) 51
(ii) 48
(iii) 4
(iv) 3

Sol. (iv) 3

Q7. Fill in the blank:

Mode = (..................) − 2 (Mean)

Sol. Mode = 3 (median) − 2 (Mean)

Q8. What is the modal class of the following frequency distribution?

 Classes 0-10 10-20 20-30 30-40 40-50 50-60 Frequencies 5 8 13 38 30 4

Sol. The Highest frequency 38 corresponds to 30−40.
∴ The modal class is 30–40.

Q9. Write the empirical relation between mean, mode and median.

Sol. The three measures i.e., mean, mode and median are connected by the following empirical relation:

Mode = 3 Median – 2 Mean

Q10. Write the median class of the following distribution:

 Class Frequency 0-10 4 10-20 4 20-30 8 30-40 10 40-50 12 50-60 8 60-70 4

Sol. We have:

 Class Frequency CumulativeFrequency 0-10 4 4 + 0 = 4 10-20 4 4 + 4 = 8 20-30 8 8 + 8 = 16 30-40 10 16 + 10 = 26 40-50 12 26 + 12 = 38 50-60 8 38 + 8 = 44 60-70 4 46 + 4 = 50

Here,

∵ 25 is cumulative frequency corresponding to the class 30−40.
∴ Median class is 30−40.

Q11. What is the modal class of the following frequency distribution?

 Age (in years) 0 -10 10 - 20 20 - 30 30 - 40 40 - 50 50 - 60 Number of Patients 16 13 6 11 27 18

Sol. Here, the maximum class frequency is 27 and the class corresponding to this frequency is 40−50.
∴ The modal class is 40−50.

Q12. Find the median class of the following data:

 Marks 0 -10 10 - 20 20 - 30 30 - 40 40 - 50 50 - 60 Frequency 8 10 12 22 30 18

Sol. We have:

 Marks obtained Frequency Cumulative Frequency 0-10 8 8 + 0 = 8 10-20 10 8 + 10 = 18 20-30 12 18 + 12 = 30 30-40 22 30 + 22 = 52 40-50 30 52 + 30 = 82 50-60 18 82 + 18 = 100

Here,

∴ The median class is 30−40

Q13. Find the class marks of classes 10− 25 and 35− 55.

Sol.

The document Class 10 Maths Chapter 13 Question Answers - Statistics is a part of the Class 10 Course Mathematics (Maths) Class 10.
All you need of Class 10 at this link: Class 10

## Mathematics (Maths) Class 10

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## FAQs on Class 10 Maths Chapter 13 Question Answers - Statistics

 1. What is statistics?
Statistics is a branch of mathematics that deals with the collection, analysis, interpretation, presentation, and organization of data. It involves the study of data patterns, trends, and probabilities to make informed decisions or draw conclusions about a population based on a sample.
 2. What are the different types of data?
There are two main types of data: qualitative and quantitative. Qualitative data refers to non-numerical information, such as categories or labels, while quantitative data consists of numerical values. Quantitative data can further be categorized as discrete or continuous, depending on whether it can take on only specific values or any value within a range, respectively.
 3. What is the importance of statistics in everyday life?
Statistics plays a crucial role in various aspects of everyday life. It helps in making informed decisions, understanding trends and patterns, evaluating risks, predicting future outcomes, and solving real-world problems. From analyzing market trends to determining the effectiveness of medical treatments, statistics provides valuable insights and helps us make evidence-based choices.
 4. What is the difference between a population and a sample?
In statistics, a population refers to the entire set of individuals, objects, or events that we are interested in studying. On the other hand, a sample is a smaller subset of the population that is selected to represent the whole. Collecting data from a sample is often more feasible and cost-effective than studying the entire population. By analyzing the sample, we can make inferences about the population.
 5. How do we measure central tendency in statistics?
Central tendency measures are used to describe the central or typical value of a data set. The three commonly used measures of central tendency are the mean, median, and mode. The mean is calculated by summing all the values and dividing by the total number of data points. The median is the middle value when the data is arranged in ascending or descending order. The mode is the value that appears most frequently in the data set.

## Mathematics (Maths) Class 10

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