**1. (a) Find out the arithmetic mean of 5.7,6.6,7.2,9.3,6.2.**

**(b) The weights (in kg) of 8 new born babies are 3,3.2,3.4,3.5,4,3.6,4.1,3.2. Find out the mean weight of the babies.**

**Solution:**

**Mean =**

**(sum of observations)/(number of observations)**

**Mean =(sum of observations)/(number of observations)**

**2. The marks obtained by 15 students in a class test are 12, 14, 07, 09, 23, 11, 08, 13, 11, 19, 16, 24, 17, 03, 20**

**Find out (i) the mean of their marks.**

**(ii) the mean of their marks when the marks of each student are increased by 4.**

**(iii) the mean of their marks when 2 marks are deducted from the marks of each student.**

**(iv) the mean of their marks when the marks of each student are doubled.**

**Solution:-**

**Mean = (sum of observations)/(number of observations)**

**∴ mean=(sum of observations)/(number of observations)**

**∴ mean = sum of marks/number of students**

**∴mean = new sum of marks/number of students**

**3. (a) The mean of the numbers 6,y,7,x,14 is 8. Express y in terms of x.**

**(b) The mean of 9 variates is 11.**

**If eight of them are 7,12,9,14,21,3,8 and 15. Find out the 9th variate.**

**Solution:**

**Mean (sum of observations)/(number of observations)**

**4. (a) The mean age of 33 students of a class is 13 years. If one girl leaves the class, the mean becomes 121516 years. What is the age of the girl ?**

**(b) In a class test, the mean of marks scored by a class of 40 students was calculated as 18.2. Later on, it was detected that marks of one student was wrongly copied as 21 instead of 29. Find out the correct mean.**

**Solution:**

**5. Find out the mean of 25 given numbers when the mean of 10 of them is 13 and the mean of the remaining numbers is 18.**

**Solution:**

**7. The contents of 100 match boxes were checked to determine the number of matches they contained**

**(i) Find out, correct to one decimal place, the mean number of matches per box.**

**(ii) Determine how many extra matches would have to be added to the total contents of the 100 boxes to; bring the mean up to exactly 39 matches.**

**Solution:-**

**9. Six coins were tossed 1000 times, and at each toss the number of heads were counted and the results were recorded as under :**

**21. A class teacher has the following absentee record of 40 students of a class for the whole term. Find out out the mean number of days a student was absent.**

**Exercise 21.2**

**1. A student scored the following marks in 11 questions of a question paper : 3, 4, 7, 2, 5, 6, 1, 8, 2, 5, 7 Find out the median marks.**

**Solution:**

**2. (a) Find out the median of the following set of numbers : 9, 0, 2, 8, 5, 3, 5, 4, 1, 5, 2, 7 (1990) (b)For the following set of numbers, Find out the median: 10, 75, 3, 81, 17, 27, 4, 48, 12, 47, 9, 15.**

**Solution:**

**3. Find out the mean and the median of the numbers : 2, 1, 0, 3, 1, 2, 3, 4, 3, 5**

**Solution:-**

**4. The median of the observations 11, 12, 14, (x – 2), (x + 4), (x + 9), 32, 38, 47 arranged in ascending order is 24. Find out the value of x and hence Find out the mean.**

**Solution:**

**5. The mean of the numbers 1, 7, 5, 3, 4, 4, is m. The numbers 3, 2, 4, 2, 3, 3, p have mean m-1 and median q.**

**Find out**

**(i) p**

**(ii) q**

**(iii) the mean of p and q**

**Solution:**

**10. The daily wages in (rupees of) 19 workers are**

**41,21,38,27,31,45,23,26,29,30,28,25,35,42,47,53,29,31,35.**

**Find out :**

**(i) the median**

**(ii) lower quartile**

**(iii) upper quartile**

**(iv) inter quartile range**

**Solution:**

**11. From the following frequency distribution,**

**Find out :**

**(i) the median**

**(ii) lower quartile**

**(iii) upper quartile**

**(iv) inter quartile range**

**12. For the following frequency distribution,**

**Find out :**

**(i) the median**

**(ii) lower quartile**

**(iii) upper quartile**

**Exercise 21.3**

**1. Find out the mode of the following sets of numbers ;**

**(i) 3, 2, 0, 1, 2, 3, 5, 3**

**(ii) 5, 7, 6, 8, 9, 0, 6, 8, 1, 8**

**(iii) 9, 0, 2, 8, 5, 3, 5, 4, 1, 5, 2, 7**

**Solution:**

**2. Find out the mean, the median and the mode of the numbers : 3, 2, 6, 3, 3, 1, 1, 2**

**Solution:**

**3. Find out the mean, median and mode of the following distribution : 8, 10, 7, 6, 10, 11, 6, 13, 10**

**Solution:**

**4. Find out the mean, the median and the mode of the following numbers : 3, 1, 5, 6, 3, 4, 5, 3, 7, 2**

**Solution:**

**5.The marks of 10 students of a class in an examination arranged in ascending order are as follows: 13,35,43,46,x,x +4,55,61,71,80**

**If the median marks is 48, Find out the value of x. Hence, Find out the mode of the given data.**

**Solution:**

**6. A boy scored the following marks in various class tests during a term each test being marked out of 20: 15, 17, 16, 7, 10, 12, 14, 16, 19, 12, 16**

**(i) What are his modal marks ?**

**(ii) What are his median marks ?**

**(iii) What are his mean marks ?**

**Solution:**

**7. Find out the mean, median and mode of the following marks obtained by 16 students in a class test marked out of 10 marks : 0, 0, 2, 2, 3, 3, 3, 4, 5, 5, 5, 5, 6, 6, 7, 8**

**Solution:**

**8. Find out the mode and median of the following frequency distribution :**

**10. The distribution given below shows the marks obtained by 25 students in an aptitude test. Find out the mean, median and mode of the distribution.**

**12. (i) Using step-deviation method, Find out the mean marks of the following distribution. (ii) State the modal class.**

**13. The following table gives the weekly wages (in Rs.) of workers in a factory :**

**Find out:**

**(i) The mean.**

**(ii) the modal class**

**(iii) the number of workers getting weekly wages below Rs. 80.**

**(iv) the number of workers getting Rs. 65 or more but less than Rs. 85 as weekly wages.**

**Solution:**

**Exercise 21.4**

**1. Draw a histogram for the following frequency distribution and Find out the mode from the graph :**

**5. IQ of 50 students was recorded as follows.**

**Draw a histogram for the above data and estimate the mode.**

**Solution:**

**6. Use a graph paper for this question. The daily pocket expenses of 200 students in a school are given below:**

**Draw a histogram representing the above distribution and estimate the mode from the graph.**

**Solution:**

**7. Draw a histogram for the following distribution :**

**Solution:**

**Exercise 21.5**

**1. Draw an ogive for the following frequency distribution:**

**Solution:-**

**Exercise 21.6**

**1. The following table shows the distribution of the heights of a group of a factory workers.**

**Solution:-**

**3. Use graph paper for this question. The following table shows the weights in gm of a sample of 100**

**potatoes taken from a large consignment:**

**(i) Find out the cumulative frequencies.**

**(ii) Draw the cumulative frequency curve and from it determine the median weight of the potatoes.**

**Solution:**

**4. Attempt this question on graph paper.**

**(i) Construct the ‘less than’ cumulative frequency curve for the above data, using 2 cm = 10 years, on one axis and 2 cm = 10 casualties on the other.**

**(ii) From your graph determine**

**(1) the median and (2) the upper quartile**

**Solution:-**

**5. The weight of 50 workers is given below:**

**Draw an ogive of the given distribution using a graph sheet. Take 2 cm = 10 kg on one axis , and 2 cm = 5 workers along the other axis.**

**Use a graph to estimate the following:**

**(i) the upper and lower quartiles.**

**(ii) if weighing 95 kg and above is considered overweight Find out the number of workers who are overweight.**

**Solution:**

**6. The table shows the distribution of scores obtained by 160 shooters in a shooting competition. Use a graph sheet and draw an ogive for the distribution. (Take 2 cm = 10 scores on the x-axis and 2 cm = 20 shooters on the y-axis)**

**Use your graph to estimate the following:**

**(i) The median.**

**(ii) The interquartile range.**

**(iii) The number of shooters who obtained a score of more than 85%.**

**Solution:**

**7. The daily wages of 80 workers in a project are given below**

**Use a graph paper to draw an ogive for the above distribution. ( a scale of 2 cm = Rs 50 on x- axis and 2 cm = 10 workers on y-axis). your ogive to estimate**

**(i) the median wage of the workers.**

**(ii) the lower quartile wage of the workers.**

**(iii) the number of workers who earn more than Rs 625 daily.**

**Solution:**

**8. Marks obtained by 200 students in an examination are given below**

**Draw an ogive for the given distribution taking 2 cm = 10 marks on one axis and 2 cm = 20 students on the other axis.**

**Using the graph, determine**

**(i) The median marks.**

**(ii) The number of students who failed if minimum marks required to pass is 40.**

**(iii) If scoring 85 and more marks is considered as grade one, Find out the number of students who secured grade one in the examination.**

**Solution:**

**9. The monthly income of a group of 320 employees in a company is given below**

**Draw an ogive of the given distribution on a graph sheet taking 2 cm = Rs. 1000 on one axis and 2 cm = 50 employees on the other axis.**

**From the graph determine**

**(i) the median wage.**

**(ii) the number of employees whose income is below Rs. 8500.**

**(iii) If the salary of a senior employee is above Rs. 11500, Find out the number of senior employees in the company.**

**(iv) the upper quartile.**

**Solution:**

^{320}/

_{4 }

**10. Using a graph paper, draw an ogive for the following distribution which shows a record of the weight in kilograms of 200 students**

**Use your ogive to estimate the following:**

**(i) The percentage of students weighing 55 kg or more.**

**(ii) The weight above which the heaviest 30% of the students fall,**

**(iii) The number of students who are : 1. under-weight and 2. over-weight, if 55.70 kg is considered as standard weight**

**Solution:**

**11. The marks obtained by 100 students in a Mathematics test are given below**

**Draw an ogive on a graph sheet and from it determine the :**

**(i) median**

**(ii) lower quartile**

**(iii) number of students who obtained more than 85% marks in the test.**

**(iv) number of students who did not pass in the test if the pass percentage was 35.**

**Solution:**

**12. The marks obtained by 120 students in a Mathematics test are-given below**

**Draw an ogive for the given distribution on a graph sheet. Use a suitable scale for ogive to estimate the following:**

**(i) the median**

**(ii) the lower quartile**

**(iii) the number of students who obtained more than 75% marks in the test.**

**(iv) the number of students who did not pass in the test if the pass percentage was 40.**

**Solution:**

**13. The following distribution represents the height of 160 students of a school.**

**Height140-145145-150150-155155-160160-165165-170170-175175-180**

**Draw an ogive for the given distribution taking 2 cm = 5 cm of height on one axis and 2 cm = 20 students on the other axis.**

**Using the graph, determine :**

**(i)The median height.**

**(ii)The inter quartile range.**

**(iii) The number of students whose height is above 172 cm.**

**Solution:**

**14. 100 pupils in a school have heights as tabulated below**

**Draw the ogive for the above data and from it determine the median (use graph paper).**

**Solution:**

**Chapter Test**

**1. Arun scored 36 marks in English, 44 marks in Civics, 75 marks in Mathematics and x marks in Science. If he has scored an average of 50 marks, Find out x.**

**Solution:**

**2. The mean of 20 numbers is 18. If 3 is added to each of the first ten numbers, Find out the mean of new set of 20 numbers.**

**Solution:**

**3. The average height of 30 students is 150 cm. It was detected later that one value of 165 cm was wrongly copied as 135 cm for computation of mean. Find out the correct mean.**

**Solution:**

**4. There are 50 students in a class of which 40 are boys and the rest girls. The average weight of the students in the class is 44 kg and average weight of the girls is 40 kg. Find out the average weight of boys.**

**Solution:**

**5. The contents of 50 boxes of matches were counted giving the following results.**

**Find out the mean number of matches per box.**

**Solution:**

**6. The heights of 50 children were measured (correct to the nearest cm) giving the following results**

**Find out the mean height for this distribution correct to one place of decimal.**

**Solution:**

**7. Find out the value of p for the following distribution whose mean is 20.6.**

**Solution:-**

**8. Find out the value of p if the mean of the following distribution is 18.**

**Solution:-**

^{2}+10p-15 = 0

^{2}+2p-3 = 0

**9. Find out the mean age in years from the frequency distribution given below:**

**Solution:**

**10. Find out the Arithmetic mean, correct to one decimal place, for the following frequency**

**Solution:**

**11. The mean of the following frequency distribution is 62.8. Find out the value of p.**

**Solution:-**

**12. The daily expenditure of 100 families are given below. Find out f1, and f2, if the mean daily expenditure is Rs 188.**

**Solution:**

**13. The measures of the diameter of the heads of 150 screw is given in the following table. If the mean diameter of the heads of the screws is 51.2 mm, Find out the values of p and q .**

**Solution:**

**15. If the median of 5, 9, 11, 3, 4, x, 8 is 6, Find out the value of x.**

**Solution:**

**16. Find out the median of: 17, 26, 60, 45, 33, 32, 29, 34, 56 . If 26 is replaced by 62, Find out the new median.**

**Solution:**

**17. The marks scored by 16 students in a class test are : 3, 6, 8, 13, 15, 5, 21, 23, 17, 10, 9, 1, 20, 21, 18, 12 Find out**

**(i) the median**

**(ii) lower quartile**

**(iii) upper quartile**

**Solution:**

**18. Find out the median and mode for the set of numbers: 2, 2, 3, 5, 5, 5, 6, 8, 9**

**Solution:**

**19. Find out the mean, the median and the mode of the following distribution.**

**Solution:**

**20. The daily wages of 30 employees in an establishment are distributed as follows:**

**Estimate the modal daily wages for this distribution by a graphical method.**

**Solution:**

**Estimate the modal daily wages for this distribution by a graphical method.**

**Solution:**

**21. Using the data given below, construct the cumulative frequency table and draw the ogive. From the ogive, estimate :**

**(i) the median**

**(ii) the inter quartile range.**

**Also state the median class**

**Solution:**

**22. Draw a cumulative frequency curve for the following data :**

**(i) the median**

**(ii) the pass marks if 85% of the students pass.**

**(iii) the marks which 45% of the students exceed.**

**Solution:-**