Most Important Questions CBSE Class 10 Maths Statistics with Solutions

Statistics is a good subject in the Class 10 syllabus, bringing together the power of numbers, data interpretation, and the beauty of mathematical precision. For students aiming to excel in their mathematics exams, working through Statistics Class 10 Important Questions and understanding the theories can make a big difference in the learning of the subject. These extra questions cover concepts of data, measures of central tendency, cumulative frequency, graphical representation, and more, enabling students to build analytical skills essential not only for exams but also for real-life data interpretation.

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Chapter 13 Statistics: Important Questions

1. Consider the frequency distribution of 45 observations.

The upper limit of the median class is:

(a) 20 (b) 10

(c) 30 (d) 40

Sol. c) 30 is the upper limit of the median class

Explanation:

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∴ N/2

= 45/2

=22.5; that lies in the interval 20-30

So, the median class is 20-30 and the upper limit of the median class is 30.

2. The monthly expenditure on milk in 200 families of a Housing Society is given below

Find the value of x and also find the mean expenditure:

Sol. Total number of families= 200

N=200

172+X = 200

X = 200-172

X=28

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Mean Expenditure= f_ix_i / f_i

Mean Expenditure= 532500 / 200

Mean Expenditure= 2662.5

3. The table shows the number of wickets taken by bowlers in a test series match.

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The sum of the lower limits of the median and modal class is:

(a) 15 (b) 25

(c) 30 (d) 35

Sol. b) 25

Explanation:

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∴ N/2

= 66/2

=33

As per the cumulative frequency chart, 33 is somewhat close to 37.

∴  the average class size is between 10 and 15.

The lower limit of the median class =10.

In the given data, the maximum frequency is 20, which falls in the class of 15-20.

∴ , the modal class's lower limit is set to 15.

The sum of the lowest limit of the modal class and median class = 10 + 15 =25.

As a result, 25 is the result of adding the median class and modal class lower limits.

4. If the median and mode of distribution are 7.5 and 6.3 then calculate the mean of the data. Also, justify whether the median class and modal class of grouped data are always different.

Sol. Median = 7.5 and Mode = 6.3

Use the empirical relationship between mean, median, and mode

Mean - Mode = 3(Mean - Median)

Mean - 6.3 = 3(Mean - 7.5)

Mean - 6.3 = 3 Mean - 22.5

- 6.3 + 22.5  = 3 Mean - Mean

16.2 = 2 Mean

Mean = 8.1

The median class and modal class may differ based on data distribution. For example, if the frequencies have been changed so that the highest frequency resides in a different class, the two classes may not coincide. We determine that the median and modal classes of grouped data can be alike depending on the distribution of the data.

5. The median of the following data is 525. Find the values of x and y if the total frequency is 100.

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Sol. 

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76+x+y = 100

x+y = 100-76

⇒ x+y = 24 …(1)

To find cumulative frequency:

N/2= 1000/2 = 500 falls mainly in 400-500 interval

Where lower limit l = 500 , 

class difference h =100,

cumulative frequency c.f = 36+x

Median =  l + ((n/2-cf))/f)xh

Median = 500 + ((50 - (36+x))/20 x 100

525 = 500 + ((50 - (36+x))/20 x 100

525 = 500 + (14 + x)x 5

525 = 500 + (70 + 5x)

525 = 570 + 5x

5x = 570 - 525

5x = 45

x = 9

Putting x=9 in eq 1

9+y = 24

y = 24 - 9

y= 15

6. In statistics, an outlier is a data point that differs significantly from other observations of a data set. If an outlier is included in the following data set, which measure(s) of central tendency would change? 

12, 15, 22, 44, 44, 48, 50, 51

1. only mean
2. only mean and median
3. all mean, median, mode
4. cannot be said without knowing the outlier

Sol. a) only mean

‍Explanation: 

‍An outlier is a data point that differs significantly from other observations of a data set.

Data set = 12, 15, 22, 44, 44, 48, 50, 51

Median = (44+44)/2 

= (88)/2

= 44

Mean= (12+ 15+ 22+ 44+  44+  48+  50+ 51)/8

= 236/8

= 35.75

Mode = 44

• We calculate the mean by adding all the values in the data set and dividing by the total number of values. An outlier, being significantly different from the other values, can greatly influence the sum, thus pulling the mean toward itself. Therefore, the mean is highly sensitive to outliers. 
• The median is the middle value in a data set when the values are arranged in order. Outliers affect the median less because it only depends on value position, not magnitude. Therefore, the median is less sensitive to outliers than the mean. 
• The mode is the value that appears most frequently in a data set. Outliers generally do not affect the mode unless the outlier itself becomes the most frequent value. Therefore, the mode is usually not affected by outliers. An outlier in the data set would most likely affect the mean.

The median might be affected slightly, but not as much as the mean. The mode would likely remain unchanged unless the outlier becomes the most frequent value.

7. The mean temperature of a particular city for 31 consecutive days was found to be 35.7°C. Further, the mean temperature of the first 8 days was 28.4°C. The mean temperature of the next 12 days was 36.4°C.Find the mean temperature for the rest of the days. Show your work.(Note: Round the numbers to one decimal point.)

Sol. Mean temperature of the city for 31 days = 35.7°C

Mean temperature of first 8 days = 28.4°C

Mean temperature of next 12 days = 36.4°C

We know,

Mean = Sum of all observations/ Number of observations

Therefore, we get:

Sum of temperatures of all the 31 days = 35.7 × 31 

= 1106.7°C

Sum of temperatures of first 8 days = 28.4 × 8 

= 227.2°C

Sum of temperatures of the next 12 days= 36.4×12

= 436.8°C

The number of remaining days= 31-8-12

= 11 days

Then, the sum of temperatures of 11 days = 1106.7 - 227.2 - 436.8 

= 442.7°C.

Hence, the mean temperature of 11 days= 442.711

= 40.2°C

8. In a class test, the mean score of the class is 60. Half the students of the class scored 80 marks or above on the test. Dipti said, "Each of the remaining half of the students would definitely have 40 marks or below in the test for the mean to be 60 marks". Prove or disprove Dipti's statement with a valid example. Answer the questions based on the given information.

Sol. Given,The mean score of the class = 60

alf of the students scored 80 marks or above.

Dipti said, "Each of the remaining half of the students would definitely have 40 marks or below in the test for the mean to be 60 marks".

We know,

Mean = Sum of all observations/Number of observations

Therefore, we have:

For example,

Consider the number of students in the class = 105 students got 80 marks or above.

Let the marks be: 80, 90, 85, 95, 80, 40, 50, 20, 30, 30

Thus, the mean mark= (80+90+85+95+80+40+50+20+30+30)/10

= 6000

= 60 marks.

Here, 5 students got 80 and above and the remaining 5 students got the marks as: 40, 50, 20, 30, 30.That is, one of them from the remaining half got 50 marks, which is above 40 marks as Dipti stated.Hence, Dipti's statement is wrong.

9. Shown below is a table representing the percentage distribution of mental health disorders in Asian countries in 2019.

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(Source of data: https://ourworldindata.org/mental-health.)

Can the median of the above data be more significant than 12.5%? Give a valid reason.

Sol. Median =  l + ((n/2-cf))/f)xh

Here, n/2 = 42/2 = 21, which falls under the range 10-12.5.

Then, l = 10, h = 2.5, cf = 11, and f = 25.

The median cannot be greater than 12.5% because the median class is between 10-12.5%.

Let us find the median of the above data.

Therefore, we get:

Median = 10 + ((21 - 11)/25) × 2.5 

 = 10 + ((21 - 11)/25) × 2.5 

 = 10 + ((10)/25) × 2.5 

= 10+1

= 11%, which is less than 12.5%.

Hence, it is proved that the median of the given data cannot be greater than 12.5%.

10. A survey was conducted on 80 gamers to determine how many games they played in a day. The data is given below.

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Which of the following is the modal class?

1. 1-2
2. 2-3
3. 4-5
4. 7-8

Sol. b) 2-3

To determine the modal class, one has to find the class interval displaying the maximum frequency of gamers. The maximum frequency is 24, relating to the class interval 2–3.

Importance of Extra Questions Statistics Class 10

The purpose of statistics class 10 extra questions is to strengthen students’ knowledge of critical concepts, helping them handle different types of questions that may appear in the exams. By practicing these questions, students develop the ability to apply statistical formulas and interpret data, enhancing both accuracy and speed.

Core concepts and theories in statistics

A solid understanding of core statistical measures like mean, median, and mode is essential for Class 10 students. Most statistics problems rely on these concepts, which also frequently appear in extra and important questions.

The mean, defined as the average of a data set, provides a measure of central tendency. Students in Class 10 are taught various methods to determine the mean, such as

• The Direct Method is suitable for small data sets where the calculation is straightforward.
• The Assumed Mean Method is useful for larger data sets as it simplifies the computation.
• Step-Deviation Method: This approach further simplifies calculations for larger or more complex data sets.

Understanding these methods and when to use each one is important for students as they approach statistics class 10th extra questions.

Median: The median is the middle value of an ordered data set, providing insight into data distribution. It is especially useful for understanding data sets. Students must be adept at organising data and applying the formula for cumulative frequency to find the median accurately.

Mode: The mode is the most frequently occurring value in a data set. When dealing with categorical data, it's particularly helpful to identify the most common data points in a distribution. In practice, the mode can provide immediate insights into trends within data, making it a valuable measure of central tendency for statistical analysis.

Frequency Distribution Tables

A frequency distribution table organizes data into classes and shows the frequency of each class, simplifying large data sets for easier interpretation. Students in class 10 learn how to construct these tables, which is an essential skill when addressing important statistics questions that involve data handling.

Cumulative Frequency and Its Applications

Cumulative frequency is a progressive summing of frequencies, allowing students to understand data distribution over intervals. This concept is essential for calculating percentiles, medians, and quartiles—all of which provide additional layers of insight into the data. 

Graphical Representation of Data

A visual representation of data helps understand trends and patterns at a glance.  Students in Class 10 are taught various types of graphical representation, such as:

• Histograms are useful for displaying the distribution of continuous data.
• Ogives are helpful for cumulative frequency data, making it easy to identify the median and quartiles.
• Frequency polygons are used to compare two or more distributions.

The ability to interpret and create these graphs is essential for effectively addressing the extra questions in class 10 statistics.

Understanding Probability with Statistics (Class 10)

Although not directly related to statistics, we introduce probability concepts in tandem, providing students with a preliminary understanding of chance events. These ideas are crucial for students as they prepare for more advanced studies in probability and statistics.

Statistical Data in Real Life

Statistical literacy allows students to make informed decisions based on data in everyday situations. For instance, understanding the mean helps in determining average marks, while median and mode are relevant in analyzing income levels or demographic data.

Challenges Faced by Class 10 Students in Statistics

Many students find statistics challenging due to its nature and the need for logical reasoning. Extra questions, especially those designated as statistics class 10 imp questions, require critical thinking and a step-by-step approach to solve.

Tips for Handling Statistics (Class 10 Extra Questions)

Extra questions often push students to go beyond rote learning and apply statistical methods creatively. Here are some tips:

• Ensure clarity on the basic formulas and concepts.
• Work on varied problems to strengthen comprehension.
• Draw graphs to get a visual sense of the data distribution.

Benefits of Practicing Statistics: Class 10: Important Questions

By practicing statistics with 10 important questions, students gain confidence and enhance their problem-solving abilities. This targeted practice can help them perform well in exams, especially in questions involving complex data interpretations.

Why Focus on Statistics Class 10th Important Questions?

Exams frequently cover certain topics within statistics that have high-scoring potential. Important questions in Statistics Class 10th often involve calculating the mean, median, or mode for grouped data, drawing frequency polygons, and constructing cumulative frequency tables. These topics are crucial for scoring well.

Strategies to Maximize Scores in Statistics

Here are some proven strategies to help students maximize their scores:

• Formulas for mean, median, mode, and cumulative frequency are fundamental.
• These provide structure to data and make analysis easier.
• Statistics can involve lengthy calculations; practice managing time to complete all questions.
• Set aside time each day for solving statistics problems.
• Regularly go over core concepts and formulas.
• Engage with additional class 10 statistics questions that cover diverse scenarios to ensure comprehensive preparation.

By working through the statistics class's 10 extra questions, students improve their understanding of statistical principles and sharpen the skills necessary for handling exam questions with confidence. This subject not only prepares students for exams but also equips them with skills that will be useful in higher studies and daily life. Focusing on statistics in class 10 and developing a strong understanding of data analysis can lead to opportunities in various fields.