**Exercise 22.1**

**Question 1: What do you understand by the word “statistics” in:**

**(i) Singular form (ii) plural form?**

**Solution:**

**Question 2: Describe some fundamental characteristics of statistics.**

**Solution:**

**Question 3: What are (i) primary data (ii) secondary data? Which of the two—the primary or the secondary data—is more reliable and why?**

**Solution:**

**Question 4: Why do we group data?**

**Solution:**

**Question 5: Explain the meaning of the following terms:**

**(i) Variate**

**(ii) Class-interval**

**(iii) Class-size**

**(iv) Class-mark**

**(v) Frequency**

**(vi) Class limits**

**(vii) True class limits**

**Solution:**

**Question 6: The ages of ten students of a group are given below. The ages have been recorded in years and months:**

**8 – 6, 9 – 0, 8 – 4, 9 – 3, 7 – 8, 8 – 11, 8 – 7, 9 – 2, 7 – 10, 8 – 8**

**(i) What is the lowest age?**

**(ii) What is the highest age?**

**(iii) Determine the range?**

**Solution:**

**Question 7: The monthly pocket money of six friends is given below:**

**Rs. 45, Rs. 30, Rs. 40, Rs. 50, Rs. 25, Rs. 45.**

**(i) What is the highest pocket money?**

**(ii) What is the lowest pocket money?**

**(iii) What is the range?**

**(iv) Arrange the amounts of pocket money in ascending order.**

**Solution:**

**Question 8: Write the class -size in each of the following:**

**(i) 0-4, 5-9, 10-14**

**(ii) 10-19, 20-29, 30-39**

**(iii) 100-120, 120-140, 160-180**

**(iv) 0-0.25, 0.25-00.50, 0.50-0.75**

**(v) 5-5.01, 5.01-5.02, 5.02-5.03.**

**Solution:**

**Question 9: The final marks in mathematics of 30 students are as follows:**

**53, 61, 48, 60, 78, 68, 55, 100, 67, 90, 75, 88, 77, 37, 84, 58, 60, 48, 62, 56, 44, 58, 52, 64, 98, 59, 70, 39, 50, 60.**

**(i) Arrange these marks in ascending order, 30 to 39 one group,40 to 49 second group etc.**

**Now answer the following:**

**(ii) What is the highest score?**

**(iii) What is the lowest score?**

**(iv) What is the range?**

**(v) If 40 is the pass mark how many have failed?**

**(vi) How many have scored 75 or more?**

**(vii) Which observations between 50 and 60 have not actually appeared?**

**(viii) How many have scored less than 50?**

**Solution:**

**Question 10: The weights of new born babies (in kg.) in a hospital on a particular day are as follows:**

**2.3, 2.2, 2.1, 2.7, 2.6, 3.0, 2.5, 2.9, 2.8, 3.1, 2.5, 2.8, 2.7, 2.9, 2.4**

**(i) Rearrange the highest weight.**

**(ii) Determine the highest weight.**

**(iii) Determine the lowest weight.**

**(iv) Determine the range.**

**(v) How many babies were born on that day?**

**(vi) How many babies weight below 2.5 kg?**

**(vii) How many babies weight more than 2.8 kg?**

**(viii) How many babies weigh 2.8 kg?**

**Solution:**

**Question 11: The number of runs scored by a cricket player in 25 innings is as follows:**

**26, 35, 94, 48, 82, 105, 53, 0, 39, 42, 71, 0, 64, 15, 34, 15, 34, 6, 71, 0, 64, 15, 34, 15, 34, 67, 0, 42, 124, 84, 54, 48, 139, 64, 47**

**(i) Rearrange these runs in ascending order.**

**(ii) Determine the player, is highest score.**

**(iii) How many times did the player not score a run?**

**(iv) How many centuries did he score?**

**(v) How many times did he score more than 50 runs?**

**Solution:**

**Question 12: The class size of distribution is 25 and the first class-interval is 200 - 224. There are seven class-intervals.**

**(i) Write the class-intervals.**

**(ii) Write the class marks of each interval.**

**Solution:**

**Question 13: Write the class size and class limits in each of the following:**

**(i) 104, 114, 124, 134, 144, 154 and 164.**

**(ii) 47, 52, 57, 62, 67, 72, 78, 82, 87, 92, 97, 102.**

**(iii) 12.5, 17.5, 22.5, 27.5, 32.5, 37.5, 42.5, 47.5.**

**Solution:**

**Question 14: Following data gives the number of children in 40 families:**

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

**Represent it in the form of a frequency distribution.**

**Solution:**

**Question 15: Marks scored by 40 students of class IX in mathematics are given below:**

**81, 55, 68, 79, 85, 43, 29, 68, 54, 73, 47, 35, 72, 64, 95, 44, 50, 77, 64, 35, 79, 52, 45, 54, 70, 83, 62, 64, 72, 92, 84, 76, 63, 43, 54, 38, 73, 68, 52, 54.**

**Prepare a frequency distribution with class size of 10 marks.**

**Solution:**

**Question 16: Heights (in cm) of 30 students of class IX are given below:**

**155, 158, 154, 158, 160, 148, 149, 150, 153, 159, 161, 148, 157, 153, 157, 162, 159, 151, 154, 156 , 152 , 156 , 160, 152, 147, 155, 163, 155 , 157 , 153.**

**Prepare a frequency distribution table with 160 - 164 as one of the class intervals.**

**Solution:**

**Question 17: The daily maximum temperatures (in degree Celsius) recorded in a certain city during the month of November are as follows:**

**25.8, 24.5, 25.6, 20.7, 21.8, 20.5, 20.6, 20.9, 22.3, 22.7, 23.1, 22.8, 22.9, 21.7, 21.3, 20.5, 20.9, 23.1, 22.4, 21.5, 22.7, 22.8, 22.0, 23.9, 24.7, 22.8, 23.8, 24.6, 23.9, 21.1.**

**Represent the data in the form of a frequency distribution table with class size 11°C.**

**Solution:**

**Question 18: Construct a frequency table with equal class intervals from the following data on the monthly wages (in rupees) of 28 laborers working in a factory, taking one of the class intervals as 210 – 230 (230 not included).**

**220, 268, 258, 242, 210, 268, 272, 242, 311, 290, 300, 320, 319, 304, 302, 218, 306, 292, 254, 278, 210, 240, 280, 316, 306, 215, 256, 236.**

**Solution:**

**Question 19: The daily minimum temperatures in degree Celsius recorded in a certain arctic region are as follows:**

**-12.5, -10.8, -18.6, -8.4-10.8, -4.2, -4.8, -6.7, -13.2, -11.8, -2.3, -1.2,**

**-2.6, 0, 2.4, 0, 3.2, 2.7, 3.4, 0, -2.4, -2.4, 0, 3.2, 2.7, 3.4, 0, -2.4, -5.8, -8.9, -14.6, -12.3,**

**-11.5, -7.8, -2.9.**

**Represent them as frequency distribution table taking -19.9 to -15 as the first class interval.**

**Solution:**

**Question 20: The blood groups of 30 students of class VIII are recorded as follows:**

**A, B, O, O, AB, O, A, O, B, A, O, B, A, O, O, A, AB, O, A, A, O, O, AB, B, A, O, B, A, B, O**

**Represent this data in the form of a frequency distribution table .Find out which is the most common and which is the rarest blood group among these students.**

**Solution:**

**Question 21 : Three coins were tossed 30 times. Each time the number of heads occurring was noted down as follows:**

**0, 1, 2, 2, 1, 2, 3, 1, 3, 0**

**1, 3, 1, 1, 2, 2, 0, 1, 2, 1**

**3, 0, 1, 1, 2, 3, 2, 2, 0**

**Prepare a frequency distribution table for the data given above.**

**Solution:**

**Question 22: Thirty children were asked about the number of hours they watched TV programes in the previous week. The results were found as follows:**

**1, 6, 2, 3, 5, 12, 5, 8, 4, 8**

**10, 3, 4, 12, 2, 8, 15, 1, 17, 6**

**3, 2, 8, 5, 9, 6, 8, 7, 14, 2.**

**(i) Make a frequency distribution table for this data, taking class width 5 and one of the class intervals as 5 - 10.**

**(ii) How many children watched television for 15 or more hours a week.**

**Solution:**

**Exercise 22.2**

**Question 1: Define cumulative frequency distribution.**

**Solution:**

**Question 2: Explain the difference between a frequency distribution and a cumulative frequency distribution.**

**Solution:**

**Question 3: The marks scored by 55 students in a test are given below:**

**Prepare a cumulative frequency table**

**Solution:**

**Question 4: Following are the ages of 360 patients getting medical treatment in a hospital on a day.**

**Construct a cumulative frequency table.**

**Solution:**

**Question 5: The water bills (in rupees) of 32 houses in a certain street for the period 1.198 to 31.398 are given below:**

**56, 43, 32, 38, 56, 24, 68, 85, 52, 47, 35, 58, 63, 74, 27, 84, 69, 35, 44, 75, 55, 30, 54, 65, 45, 67, 95, 72, 43, 65, 35, 69.**

**Tabulate the data and present the data as a cumulative frequency table using 70-79 as one of the class intervals.**

**Solution:**

**Question 6: The number of books in different shelves of a library is as follows:**

**30, 32, 28, 24, 20, 25, 38, 37, 40, 45, 16, 20**

**19, 24, 27, 30, 32, 34, 35, 42, 27, 28, 19, 34**

**38, 39, 42, 29, 24, 27, 22, 29, 31, 19, 27, 25**

**28, 23, 24, 32, 34, 18, 27, 25, 37, 31, 24, 23**

**43, 32, 28, 31, 24, 23, 26, 36, 32, 29, 28, 21.**

**Prepare a cumulative frequency distribution table using 45 – 49 as the last class-interval.**

**Solution:**

**Question 7: Given below are the cumulative frequencies showing the weights of 685 students of a school. Prepare a frequency distribution table.**

**Solution:**

**Question 8: The following cumulative frequency distribution table shows the daily electricity consumption (in KW) of 40 factories in an industrial state.**

**(1) Represent this as a frequency distribution table.**

**(2) Prepare a cumulative frequency table.**

**Solution:**

**Question 9: Given below is a cumulative frequency distribution table showing ages of the people living in a locality:**

**Prepare a frequency distribution table.**

**Solution:**