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Chapter: 13(Statistics) Formulas used to solve the Assignment on statistics

Range =  Highest value - Lowest value

Class size =  Upper limit - Lower limit

MODE of Data in Statistics

W here l = lower limit of the modal class,

 h = size of the class interval 

  f 1  = frequency of the modal class

f 0  = frequency of the class preceding the modal class,

f 2  = frequency of the class succeeding the modal class.

Median of Data in Statistics

Where l= lower limit of median class                           

N = Sum of all observations

f = frequency of the median class.       

Cf= cumulative frequency of class  preceding the median class

 h= height of  median class

Empirical Formula of Data in Statistics

      Mode= 3 Median  - 2 Mean

Empirical formula does not provide the same result in different situations. So, students should use it only when asked otherwise avoid it.

* If median class is the first class –interval then cumulative frequency (Cf) of the preceding class interval should be taken as zero.

* For finding Mean class interval need not to be continuous.

* For finding Mode and Median class interval should be continuous. 

* For making class interval continuous we should subtract 0.5 from the lower limits and add 0.5 to the upper limits of all class intervals. 

Assignment on Statistics Solve the following questions

Problems based on mean.

Do we use here step-deviation method ? Why or Why not   

No, we cannot use step deviation method here because height of the class intervals are not equal. So we can solve this question either by Direct Method or by Assumed mean method

PROBLEMS BASED ON MODE  

QUESTION 10. For the given data find mean & mode.              

Ans : Mean=26 & Mode=22.85

PROBLEMS BASED ON MEDIAN

QUESTION 15. Find median.         Ans: 40

Ans:  f 1 =35 &  f 2 = 25

MISCELLANEOUS PROBLEMS ON MEAN, MODE, MEDIAN  

QUESTION  21. 

If mode = 24.5 and mean is 29.75 then find median by using empirical formula.    [Ans: 28]

QUESTION 23. Calculate Mean, mode, median.     Ans : Mean = 51.63, Mode = 53.33, Median = 52

Marks no of students more than 0 80 more than 10 76 more than 20 71 more than 30 65 more than 40 57 more than 50 43 more than 60 28 more than 70 15 more than 80 10 more than 90 8 more than 100 0, higher order thinking skills (hots).

Answer:  f 1  = 28,  f 2  = 32 and  f 3  = 24

Solution Hint:   Use direct method to solve this question

For easy calculation use step deviation method and take assume mean (a) in front of f 1

QUESTIONS DELETED FROM CBSE SYLLABUS

QUESTION 25. Find median by using less than ogive & actual calculation.                               

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Statistics Worksheet Class 10 PDF with Answers

These Statistics worksheet PDF can be helpful for both teachers and students. Teachers can track their student’s performance in the chapter Statistics. Students can easily identify their strong points and weak points by solving questions from the worksheet. Accordingly, students can work on both weak points and strong points. 

All students studying in CBSE class 10th, need to practise a lot of questions for the chapter Statistics. Students can easily practise questions from the Statistics problems worksheet PDF. By practising a lot of questions, students can improve their confidence level. With the help of confidence level, students can easily cover all the concepts included in the chapter Statistics. 

Statistics Worksheets with Solutions

Solutions is the written reply for all questions included in the worksheet. With the help of Statistics worksheets with solutions, students can solve all doubts regarding questions. Students can have deep learning in the chapter Statistics by solving all their doubts. By solving doubts, students can also score well in the chapter Statistics. 

Statistics Worksheet PDF

Worksheet is a sheet which includes many questions to solve for class 10th students. The Statistics worksheet PDF provides an opportunity for students to enhance their learning skills. Through these skills, students can easily score well in the chapter Statistics. Students can solve the portable document format (PDF) of the worksheet from their own comfort zone. 

How to Download the Statistics Worksheet PDF? 

To solve questions from the Statistics worksheet PDF, students can easily go through the given steps. Those steps are- 

• Open Selfstudys website.

• Bring the arrow towards CBSE which can be seen in the navigation bar. 

• Drop down menu will appear, select KVS NCERT CBSE Worksheet. 

• A new page will appear, select class 10th from the given list of classes. 
• Select Mathematics from the given list of subjects. Now click the chapter’s name that is Statistics. 

Features of the Statistics Worksheet PDF

Before starting to solve questions from the Statistics problems worksheet PDF, students need to know everything about the worksheet. Those features are- 

• Variety of questions are included:  The Statistics Maths Worksheet for Class 10 includes varieties of questions. Those varieties of questions are- one mark questions, two mark questions, three mark questions, etc. 
• Solutions are provided:  Doubts regarding each question can be easily solved through the solutions given. Through solving questions, a student's comprehensive skill can be increased. 
• All concepts are covered:  By solving questions from the Statistics problems worksheet, students can easily cover all the concepts included in the chapter.  
• Created by Expert:  These worksheets are personally created by the subject experts. These Statistics worksheet pdf are created with proper research. 
• Provides plenty of questions:  The Statistics worksheet provides plenty of questions to practise. Through good practice, students can get engaged in the learning process. 

Benefits of the Statistics Worksheet PDF

With the help of Statistics problems worksheet PDF, students can easily track their performance. This is the most crucial benefit, other than this there are more benefits. Those benefits are- 

• Builds a strong foundation:  Regular solving questions from the worksheet can help students to build a strong foundation. Through the strong foundation, students can score well in the chapter Statistics. 
• Improves speed and accuracy:  While solving questions from the chapter Statistics, students need to maintain the speed and accuracy. Speed and accuracy can be easily maintained and improved by solving questions from the Statistics worksheet PDF. 
• Acts as a guide:  Statistics worksheets with solutions acts as guide for both the teachers and students. Through the worksheet, teachers can guide their students according to the answers given by them. Students can also analyse themselves with the help of answers and can improve accordingly. 
• Enhances the learning process:  Regular solving of questions from the worksheet can help students enhance their learning process. According to the learning skills, students can easily understand all topics and concepts included in the chapter Statistics.  
• Improvisation of grades:  Regular solving of questions from the worksheet can help students to improve their marks and grades. With the help of good marks and good grades, students can select their desired field further. 

Tips to Score Good Marks in Statistics Worksheet

Students are requested to follow some tips to score good marks in the Statistics worksheet. Those tips are-

• Complete all the concepts:  First and the most crucial step is to understand all the concepts included in the chapter Statistics.  
• Practise questions:  Next step is to practise questions from the Statistics problems worksheet. Through this students can identify all types of questions: easy, moderate, difficult, etc.  
• Note down the mistakes:  After practising questions, students need to note down the wrong sums that have been done earlier. 
• Rectify the mistakes:  After noting down the mistakes, students need to rectify all the mistakes made. 
• Maintain a positive attitude:  Students are requested to maintain a positive attitude while solving worksheets. By maintaining a positive attitude, students can improve speed and accuracy while solving the worksheets. 
• Remain focused:  Students need to remain focused while solving questions from the Statistics problems worksheet pdf. As it helps students to solve the questions as fast as possible. 

When should a student start solving the Statistics Worksheet PDF?

Students studying in class 10 should start solving worksheets after covering each and every concept included in the chapter. Regular solving questions from the Statistics worksheet PDF, can help students to have a better understanding of the chapter. Better understanding of the chapter Statistics can help students to score well in the class 10th board exam. 

Regular solving questions from the Statistics Worksheet PDF can help students to build a strong foundation for the chapter Statistics. Strong foundation of the chapter Statistics can help students to understand further chapters. 

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Class 10 Mathematics Statistics Assignments

We have provided below free printable Class 10 Mathematics Statistics Assignments for Download in PDF. The Assignments have been designed based on the latest NCERT Book for Class 10 Mathematics Statistics . These Assignments for Grade 10 Mathematics Statistics cover all important topics which can come in your standard 10 tests and examinations. Free printable Assignments for CBSE Class 10 Mathematics Statistics , school and class assignments, and practice test papers have been designed by our highly experienced class 10 faculty. You can free download CBSE NCERT printable Assignments for Mathematics Statistics Class 10 with solutions and answers. All Assignments and test sheets have been prepared by expert teachers as per the latest Syllabus in Mathematics Statistics Class 10. Students can click on the links below and download all Pdf Assignments for Mathematics Statistics class 10 for free. All latest Kendriya Vidyalaya Class 10 Mathematics Statistics Assignments with Answers and test papers are given below.

Mathematics Statistics Class 10 Assignments Pdf Download

We have provided below the biggest collection of free CBSE NCERT KVS Assignments for Class 10 Mathematics Statistics . Students and teachers can download and save all free Mathematics Statistics assignments in Pdf for grade 10th. Our expert faculty have covered Class 10 important questions and answers for Mathematics Statistics as per the latest syllabus for the current academic year. All test papers and question banks for Class 10 Mathematics Statistics and CBSE Assignments for Mathematics Statistics Class 10 will be really helpful for standard 10th students to prepare for the class tests and school examinations. Class 10th students can easily free download in Pdf all printable practice worksheets given below.

Topicwise Assignments for Class 10 Mathematics Statistics Download in Pdf

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• As we have the best and largest collection of Mathematics Statistics assignments for Grade 10, you will be able to easily get full list of solved important questions which can come in your examinations.
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NCERT Solutions for Class 10 Maths Ch 14 Statistics

• Exercise 14.1
• Exercise 14.2
• Exercise 14.3
• Exercise 14.4

How many exercises in Chapter 14 Statistics

What are the methods to calculate mean, mode = (...........) − 2 (mean), write the empirical relation between mean, mode and median., contact form.

• Class 10 Maths
• Chapter 14: Statistics

Important Questions For Class 10 Maths Chapter 14- Statistics

Important questions for Class 10 Maths Chapter 14 Statistics are available at BYJU’S, created and designed as per the latest exam pattern by referring to the CBSE board sample papers. Students who are preparing for the CBSE class 10 board exams 2022-23 can practice these Statistics questions to score full marks for the questions from this chapter.

This chapter is important for students from the examination perspective. Most of the long answer questions will come from this chapter for the exam. Students can also refer to the solutions prepared by BYJU’S expert teachers. By solving these Important Questions of Class 10 Maths Chapter 14 Statistics, students will thoroughly revise this chapter and get well versed with the questions expected to be asked in the Maths paper.

Also, check: Class 10 Maths Chapter 14 Statistics MCQs

• Important Questions Class 10 Maths
• Probability and Statistics Concepts
• Statistics Class 10 Notes

Important Questions & Answers For Class 10 Maths Chapter 14 Statistics

The important questions o f the statistics chapter for class 10 are given here in both shor t answer type and long answer type.

Short Answer Type Questions

Q.1. Find the mean of the 32 numbers, such that if the mean of 10 of them is 15 and the mean of 20 of them is 11. The last two numbers are 10.

Solution: The given mean of 10 numbers = 15

So, Mean of 10 numbers = sum of observations/ no. of observations

15 = sum of observations / 10

Sum of observations of 10 numbers = 150

Similarly, Mean of 20 numbers = sum of observations/ no. of observations

11 = sum of observations / 20

Sum of observations of 20 numbers = 220

Hence, Mean of 32 numbers = (sum 10 numbers + sum of 20 numbers + sum of last two numbers)/ no. of observations

Mean of 32 numbers = (150 + 220 + 20 ) / 32 = 390 /32 = 12.188

Q.2. Find the mean of the first 10 natural numbers.

Solution: The first 10 natural numbers are 1, 2, 3, 4, 5, 6, 7, 8, 9, 10

Mean = (1 + 2 +3 + 4 + 5 + 6 + 7 + 8 + 9 + 10) / 10 = 55/10 = 5.5

Q.3 . Find the value of y from the following observations if these are already arranged in ascending order. The Median is 63.

20, 24, 42, y , y + 2, 73, 75, 80, 99

As the number of observations made is odd, so the median will be the middle term, i.e. y + 2.

y = 63 – 2 = 61

Q.4. While checking the value of 20 observations, it was noted that 125 was wrongly noted as 25 while calculating the mean and then the mean was 60. Find the correct mean.

Let y be the sum of observation of 19 (20 – 1) numbers leaving 125.

So, y + 25 = 20 × 60 = 1200 {Mean = (sum of observations/ no. of observations)}

As we know,

x + 25 = 20 × 60 = 1200

x + 125 = 20 × y = 20y

Next, Subtract 125 − 25 = 20y − 1200

Q.5. Find the mode of the following items.

0, 5, 5, 1, 6, 4, 3, 0, 2, 5, 5, 6

Solution: On arranging the items in ascending order, we get:

0, 0, 1, 2, 3, 4, 5, 5, 5, 5, 6, 6

As we can see 5 occurs the maximum number of times.

Therefore, the mode of the given items = 5

Q.6. A student scored the following marks in 6 subjects:

30, 19, 25, 30, 27, 30

Find his modal score.

Solution: If we arrange his marks in ascending order

19, 25, 27, 30, 30, 30

As we can see, 30 occurs a maximum number of times.

Therefore, the modal score of the student = 30

Q.7.The daily minimum steps climbed by a man during a week were as under:

Find the mean of the steps.

Solution: Number of steps climbed in a week: 35, 30, 27, 32, 23, 28.

So, we get,

Mean = sum of observation (steps) / total no of observations

= (35 + 30 + 27 + 32 + 23 + 28) / 6

Q. 8.   If the mean of 4 numbers, 2,6,7 and a is 15 and also the mean of other 5 numbers, 6, 18, 1, a, b is 50. What is the value of b?

Mean = sum of observations / no. of observations

15 = (2 + 6 + 7 +a)/4

15 = (15 + a) / 4

15 x 4 = 15 + a

60 – 15 = a

50 = (18 + 6 + 1 +a + b)/5

50 = (18 + 6 + 1 +45 + b)/5

50 = (70 + b)/5

250 = 70 + b

b = 250 – 70 = 180

So, The value of b = 180.

Q.9: If the mean of first n natural numbers is 15, then find n.

We know that the sum of first n natural numbers = n(n + 1)/2

Mean of the first n natural numbers = Sum of first n natural numbers/n

= [n(n + 1)/2]/ n

= (n + 1)/2

According to the given,

(n + 1)/2 = 15

Q.10: Construct the cumulative frequency distribution of the following distribution : 

The cumulative frequency distribution of the given distribution is given below :

Long Answer Type Questions

Q. 1: Consider the following distribution of daily wages of 50 workers of a factory.

Find the mean daily wages of the workers of the factory by using an appropriate method.

Find the midpoint of the given interval using the formula.

Midpoint (x i ) = (upper limit + lower limit)/2

In this case, the value of mid-point (x i ) is very large, so let us assume the mean value, A = 150 and class interval is h = 20. So, u i  = (x i  – A)/h = u i  = (x i  – 150)/20

Substitute and find the values as follows:

So, the formula to find out the mean is:

Mean = x̄ = A + h (∑f i u i  /∑f i ) =150 + (20 × -12/50) = 150 – 4.8 = 145.20 Therefore, mean daily wage of the workers = Rs. 145.20

Q.2: Thirty women were examined in a hospital by a doctor and the number of heartbeats per minute was recorded and summarised as follows. Find the mean heartbeats per minute for these women, choosing a suitable method.

From the given data, let us assume the mean as A = 75.5

x i  = (Upper limit + Lower limit)/2 Class size (h) = 3 Now, find the u i and f i u i as follows:

Mean = x̄ = A + h∑f i u i  /∑f i

= 75.5 + 3×(4/30)

75.5 + 4/10

= 75.5 + 0.4

= 75.9 Therefore, the mean heartbeats per minute for these women is 75.9

Q. 3: The following data gives the distribution of the total monthly household expenditure of 200 families of a village. Find the modal monthly expenditure of the families. Also, find the mean monthly expenditure :

From the given data:

Modal class = 1500-2000

Frequencies:

f 1  = 24, f< = 33 and

Mode formula:

Substitute the values in the formula, we get;

Mode = 1500 + ((16 x 500)/23)

Mode = 1500+(8000/23) = 1500 + 347.83

Therefore, the modal monthly expenditure of the families= Rupees 1847.83

Calculation for mean:

First find the midpoint using the formula, x i =(upper limit +lower limit)/2

Let us assume a mean, A be 2750

The formula to calculate the mean,

Mean = x̄ = a + (∑f i u i  /∑f i ) х h

Substitute the values in the given formula = 2750 + (-35/200) х 500 = 2750 – 87.50

So, the mean monthly expenditure of the families = Rupees 2662.50

Q. 4: 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:

Modal class = 40 – 50, l = 40,

class width (h) = 10, f m  = 20, f 1  = 12 and f 2  = 11

Substitute the values

Mode = 40 + (80/17) = 40 + 4.7 = 44.7

Thus, the mode of the given data is 44.7 cars

Q. 5: An aircraft has 120 passenger seats. The number of seats occupied during 100  flights are given in the following table :

Determine the mean number of seats occupied over the flights.

∴ Assumed mean, a = 110

Class width, h = 4

And total observations, N = 100

= 110 + (-8/100)

= 110 – 0.08

But we know that the seats cannot be in decimal.

Therefore, the number of seats = 109 (approx).

Q. 6: A survey regarding the heights (in cm) of 51 girls of Class X of a school was conducted and the following data were obtained:

Find the median height.

To calculate the median height, we need to find the class intervals and their corresponding frequencies.

The given distribution is of the less than type, 140, 145, 150,… ., 165 gives the upper limits of the corresponding class intervals.

So, the classes should be below 140, 140 – 145, 145 – 150,… ., 160 – 165.

Observe that from the given distribution, we find that there are 4 girls with height less than 140, i.e., the frequency of class interval below 140 is 4.

Now, there are 11 girls with heights less than 145 and 4 girls with heights less than 140. Therefore, the number of girls with height in the interval of 140 – 145 is 11 – 4 = 7.

Similarly, the frequency of 145 – 150 is 29 – 11 = 18, for 150 – 155, it is 40 – 29 = 11, and so on. So, our frequency distribution table with the given cumulative frequencies becomes:

Now n = 51. So, n/2 = 51/2 =25.5

This observation lies in class 145 – 150.

Then, l (the lower limit) = 145,

cf (the cumulative frequency of the class preceding 145 – 150) = 11,

f (the frequency of the median class 145 – 150) = 18,

h (the class size) = 5.

Using the formula,

= 145 + 72.5/18 = 149.03.

So, the median height of the girls is 149.03 cm.

This means that the height of about 50% of the girls is less than this height, and 50% are taller than this height.

Q. 7: The lengths of 40 leaves of a plant are measured correct to the nearest millimetre, and the data obtained is represented in the following table :

Find the median length of leaves.  

( Hint : The data needs to be converted to continuous classes for finding the median since the formula assumes continuous classes. The classes then change to 117.5 – 126.5, 126.5 – 135.5, . . ., 171.5 – 180.5.)

Since the data are not continuous reduce 0.5 in the lower limit and add 0.5 in the upper limit.

From the above tab

n = 40 and n/2 = 20

Median class = 144.5-153.5

then, l = 144.5,

cf = 17, f = 12 & h = 9

=144.5+(9/4)

Therefore, the median length of the leaves = 146.75 mm.

Q. 8: If the median of a distribution given below is 28.5 then, find the value of an x &y.

From the given data,

Median of the given data = 28.5

Where, n/2 = 30

Median class is 20 – 30 with a cumulative frequency = 25 + x

Lower limit of median class = 20,

Cf = 5 + x ,

f = 20 & h = 10

28.5=20+10(30−5−x)/20)

8.5 =(25-x)/2

Therefore, x =8

Now, from cumulative frequency, we can identify the value of x + y as follows:

60=5+20+15+5+x+y

Now, substitute the value of x, to find y

60 = 5+20+15+5+8+y

Therefore, the value of x = 8 and y = 7

Q. 9: The annual profits earned by 30 shops of a shopping complex in a locality give rise to the following distribution :

Draw both Ogives for the above data. Hence obtain the median profit.

We first draw the coordinate axes, with lower limits of the profit along the horizontal axis, and the cumulative frequency along the vertical axes.

Then, we plot the points (5, 30), (10, 28), (15, 16), (20, 14), (25, 10), (30, 7) and (35, 3). We

join these points with a smooth curve to get the ‘more than’ ogive, as shown in the below figure.

Now, let us obtain the classes, their frequencies and the cumulative frequency from the given table.

Using these values, we plot the points (10, 2), (15, 14), (20, 16), (25, 20), (30, 23), (35, 27), (40, 30) on the same axes as in the above figure, to get the ‘less than’ ogive, as shown below.

The abscissa of their point of intersection is nearly 17.5, which is the median. This can also be verified by using the formula.

Hence, the median profit (in lakhs) is Rs. 17.5.

Q. 10: The following tables give the production yield per hectare of wheat of 100 farms of a village.

Change the distribution to a more than type distribution and draw its ogive.

Converting the given distribution to a more than type distribution, we get

From the table obtained draw the ogive by plotting the corresponding points where the upper limits in x-axis and the frequencies obtained in the y-axis are (50, 100), (55, 98), (60, 90), (65, 78), (70, 54) and (75, 16) on this graph paper.

The graph obtained is known as more than type ogive curve.

Practice Questions for Class 10 Maths Chapter 14 Statistics

• Consider the data : Class65-8585-105105-125125-145145-165165-185185-205Frequency4513201474 (1) The difference of the upper limit of the median class and the lower limit of the modal class is (A) 0 (B) 19 (C) 20 (D) 38 (2) In the formula x = a + h(f i u i /f i ), for finding the mean of grouped frequency distribution, u i = (A) (x i +a)/h (B) h (x i – a) (C) (x i –a)/h (D) (a – x i )/h
• In a continuous frequency distribution, the median of the data is 21. If each observation is increased by 5, then find the new median.
• The average score of boys in the examination of a school is 71 and that of the girls is 73. The average score of the school in the examination is 71.8. Find the ratio of the number of boys to the number of girls who appeared in the examination.

The Important Questions & Answers For Class 10 Maths Chapter 14 Statistics must have helped students in their Class 10 Maths exam preparation. They must keep practising the questions and stay tuned to BYJU’S for the latest update on CBSE/ICSE/State Board/Competitive Exams.

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