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Q1. In a cricket match, the runs scored by 11 players are as follows12, 23, 10, 77, 15, 78, 90, 54, 23, 10, xThe average score is 44 runs. Find the value of x.

Solution

Q2. Find median of the following information:4, 5, 6, 2, 9, 8, 2, 2, 3, 5, 5, 7,1

Solution

The numbers in ascending order:  1, 2, 2, 2, 3, 4, 5, 5, 5, 6, 7, 8,  9Median is the middle most value.So, median = 5

Q3. Read the given table and answer the questions that follow: City Minimum Maximum Delhi 39^oC 38^oC Mumbai 34^oC 35^oC Kolkata 35^oC 38^oC Chennai 38^oC 40^oC Jaipur 39^oC 42^oC (a) Which cities have equal minimum temperature? (b) Which city has the highest maximum temperature?

Solution

(a) Delhi and Jaipur have equal minimum temperature i.e. 39^oC (b) Jaipur has the highest maximum temperature of 42^oC

Q4. Calculate median and mode for following data : 23, 45, 46, 12, 34, 87, 78, 12, 65, 33, 19, 34, 55, 67, 81, 12, 56, 98, 11, 49, 50

Solution

The numbers in ascending order are: 11, 12, 12, 12, 19, 23, 33, 34, 34, 45, 46, 49, 50, 55, 56, 65, 67, 78, 81, 87, 98 As the number of observations (21) are odd, Median = middle observation = 11^th observation = 46 Mode is the observation that appears most often.Here, 12 appears maximum number of times (thrice). So, 12 is the mode.

Q5. Data is arranged in ascending order. The sum of mode and median of the given data is 29. Find the value of y. y - 1, y - 1, y , y + 4, 2y + 5, 3y, 4y

Solution

Mode is observation which appears most often. Mode = y - 1 Median is the middle most value. Median = 4th observation = y + 4 Given, Mode + Median = 29 y - 1 + y + 4 = 29 2y + 3 = 29 2y = 26 y = 13

Q6. If six workers receive daily wages of Rs. 110.10, Rs. 115.32, Rs. 165.52, Rs. 170.18, Rs. 170.92 and Rs. 189.58, what is their median allowance?

Solution

Allowances arranged in ascending order: 110.10, 115.32, 165.52, 170.18, 170.92, 189.58As the number of observations are even,Median = mean of the middle two observations.

Q7. A die is rolled; find the probability of getting an odd number.

Solution

The sample space is S = {1, 2, 3, 4, 5, 6} Let F be the probability of getting an even number. F = {1, 3, 5} n(F) = 3 P(F) =  

Q8. The tale below shows the scores of practice test and test for four different students. Draw a doublr bar graph from this data. Students Naziya Sai Rajyeshree Shweta Practice Test 60 70 55 90 Test 70 90 55 95

Solution

The double bar graph is as shown below:

Q9. Consider the following table and answer the questions that follow. Name of student Weight(kg) Anand 35 Aman 50 Raj 51 Raju 64 Sushma 38 Ritu 35 Sumit 40 Sonu 35 Ravi 30 Rohit 35 (a) Who is the heaviest among all students? (b) What is the most common weight? (c) What is the difference of weight between the heaviest and the lightest student?

Solution

(a) The heaviest weight from the table is 64 kg which belongs to Raju. Thus, Raju is the heaviest among all students. (b) 35 kg is the weight of four students. Thus, 35 kg is the most common weight. (c) Heaviest weight = 64 kg and Lightest weight = 30 kg Thus, Difference of weight = 64 kg - 30 kg = 34 Kg

Q10. The average of 4 quantities is 10. The average of 6 of them is 8. What is the average of the remaining two numbers?

Solution

The average of 4 quantities is 10.Therefore, the sum of the 4 quantities is 4 x 10 = 40.The average of three of these 6 quantities is 8. Therefore, the sum of these three quantities = 6 x 8 = 48Sum of the remaining two quantities = 48 - 40 = 8. Average of these two quantities = 8/2 = 4.

Q11. The median of the given data is 29 arranged in increasing order of value. What is the value of x? x, 20, 2x + 6, 2x + 9, 40, 45, 52

Solution

Median is the middle most value. Median = 4^th observation = 2x + 9 2x + 9 = 29 2x = 20 x = 10

Q12. What is data and what is the need to organize data?

Solution

A collection of numerical facts regarding a particular type of information is called data. It is not easy to understand a raw data. To draw meaningful inferences and work upon it, we need to organize the data systematically.

Q13. Mean of 8 numbers was found to be 50. Later on it was detected that a number 45 was misread as 54. Find the correct mean of the observations.

Solution

Given mean of 8 numbers = 50Sum of 8 numbers = 50 × 8 = 400But 45 was read as 54Correct sum of 7 numbers = 400 - 54 + 45 = 391

Q14. Classify the following data as primary or secondary. (a) Classifying date of birth of different students from class attendance register. (b) Collecting Name, roll number information from each individual.

Solution

(a) This is secondary data as this is the information that someone else has collected. (b) This is primary data as this data is directly collected from each individual.

Q15. Given below are the marks (out of 100) in mathematics obtained by 20 students of a class in an annual examination: 23, 75, 56, 42, 70, 84, 92, 51, 40, 63, 87, 58, 35, 80, 14, 63, 49, 72, 66, 61 Arrange the above data in ascending order and find: (i) The lowest marks obtained (ii) The highest marks obtained (iii) The range of the given data.

Solution

Arranging the given data in ascending order we get: 14, 23, 35, 40, 42, 49, 51, 56, 58, 61, 63, 63, 66, 70, 72, 75, 80, 84, 87, 92 i) Lowest marks obtained = 14 ii) Highest marks obtained = 92 iii) Range of the given data = (92 - 14) = 78

Q16. Make a list of 4 common pieces of data that can be organized from real life.

Solution

1. What is the population of major cities in world like Delhi, Kolkata and Chennai? 2. How much should a healthy baby weigh at each month of age?3. How many calories are there in food we eat every day?4. What is the healthy blood pressure for a person my age?

Q17. Classify the following data as primary or secondary. (a) Classifying date of birth of different students from class attendance register. (b) Collecting Name, roll number information from each individual.

Solution

(a) Secondary (b) Primary

Q18. The average (mean) of a list of 6 numbers is 20. If we remove one of the numbers, the average of the remaining numbers is 15. Find the number that was removed.

Solution

The removed number could be obtained by difference between the sum of original 6 numbers and the sum of remaining 5 numbers i.e.     = sum of original 6 numbers - sum of remaining 5 numbers Using the formula- Sum of terms = mean x number of terms Sum of original 6 numbers = 20 × 6 = 120 Sum of remaining 5 numbers = 15 × 5 = 75   Number removed = sum of original 6 numbers - sum of remaining 5 numbers                           = 120 - 75 = 45 The number removed is 45.

Q19. Classify the following data as primary or secondary.(a) Classifying the items on the basis of their expiry date from stock register.(b) Entering item name, item number information, expiry date of each item.

Solution

(a) This is secondary data as this is the information that someone else has collected.(b) This is primary data as this data is directly collected from each individual item.

Q20. Find the mode of the given data. Heights of basketball players (in.) 75 72 79 75 78 78

Solution

Mode is the observation that appears most often.In the given data, there are two values 75 and 78 which occur twice and hence, Mode = 75, 78

Q21. Consider table given below to answer the following questions: City Minimum Maximum Delhi 39^oC 38^oC Mumbai 34^oC 35^oC Kolkata 35^oC 38^oC Chennai 38^oC 40^oC Jaipur 39^oC 42^oC (a) What are the number of rows and columns in the table? (b) What information is given in the table?

Solution

(a) Number of Rows = 5  and Number of Columns = 3 (b) The table shows the minimum and maximum temperature data of five cities in the form of rows and columns.

Q22. A coin is tossed three times. Write the sample space ‘S’.

Solution

The sample space is S={HHH, HHT, HTT, HTH, THH, TTH, THT, TTT}

Q23. Consider the following table: City Minimum Maximum Delhi 39^o 38^oc Mumbai 34^oc 35^oc Kolkata 35^oc 38^oc Chennai 38^oc 40^oc Jaipur 39^oc 42^oc What information is given in the table?

Solution

The table shows the minimum and maximum temperature data of five cities in the form of row and column.

Q24. Find median and mode of the following information: 2, 2, 3, 5, 5, 7, 8

Solution

The numbers in ascending order: 2, 2, 3, 5, 5, 7, 8 Median is the middle most value. So, median = 5 Mode is the observation which appears most often. Here 2 and 5 appears twice. So, there are two modal values, 2 and 5.

Q25. A die is rolled; find the probability of getting an even number.

Solution

The sample space is S = {1, 2, 3, 4, 5, 6} Let E be the probability of getting an even number. E = {2, 4, 6} n(E) = 3 P(E) =

Q26. Mean of 5 numbers is 35. One number 8 is excluded. Find the new mean.

Solution

Mean of 5 numbers = 35 Thus, Sum of 5 numbers is 35 x 5 = 175 Excluded number = 8 Thus, Sum of the remaining 4 numbers = 175 - 8 = 167Numbers left now = 5 - 1 = 4

Q27. Find mode of the following information:2, 2, 3, 5, 5, 4, 9,9,9,9,9

Solution

Mode is the observation which appears most often.Here 9 appears five times.So, there are two mode is 9.

Q28. The given data is arranged in ascending order. The sum of mode and median of the given data is 15. Find the value of y. y - 1, y - 1, y + 1, y + 4, 2y + 1, 3y, 4y

Solution

Mode is observation which appears most often. Mode = y - 1 Median is the middle most value. Median = 4^th observation = y + 4 Given, Mode + Median = 15 y - 1 + y + 4 = 15 2y + 3 = 15 2y = 12 y = 6

Q29. What is the mean of first four odd natural numbers?

Solution

First four odd natural numbers are 1, 3, 5, 7. Their mean = (1 + 3 + 5 + 7) / 4 = 16/4 = 4

Q30. A coin is tossed three times. Then find the event of getting at least one head.

Solution

The sample space is S = {HHH, TTH, HHT, THT, HTH, TTT} Let G be the event of getting at least one head. H = {TTH, HHT, THT, HTH, TTT} n(H) = 5 P(H)=