Statistics Textbook PDF - Data Analysis & Interpretation

FOR ONLINE USE ONLY DO NOT DUPLICATE Chapter Sixteen Statistics Introduction Statistics is the branch of mathematics which deals with the collection...

FOR ONLINE USE ONLY DO NOT DUPLICATE Chapter Sixteen Statistics Introduction Statistics is the branch of mathematics which deals with the collection, LY analysis and interpretation of data. Different types of data can be collected from schools, government agencies, hospitals, business centres and so on. In Standard Four, you learnt how to collect and record as well as drawing N pictorial statistics using the information presented. In this chapter, you will learn how to calculate average using different data, reading and interpreting bar O graphs. This competence will help you to collect different required data and present it systematically as well as providing proper interpretation of data. For SE instance, information about population, harvests, rainfall, health information, financial information, pupils age and the like can be collected and analysed. U Exercise 1: Revision 1. Study carefully the following pictorial statistics which show the daily E sales of cups in one week. N Key: A picture of 1 cup represents 5 cups LI N Days Cups O Monday R Tuesday FO Wednesday 310 MATH std 5.indd 310 30/07/2021 14:50  FOR ONLINE USE ONLY DO NOT DUPLICATE Thursday Friday Saturday LY Sunday Answer the following questions: (i) How many cups were sold on Monday? N (ii) Which day had many sales of cups? O (iii) Which days had the same sales of cups? (iv) How many cups were sold on Sunday? (v) Which day had less sales of cups? SE (vi) What is the difference in the sales of cups between Tuesday and Sunday. U (vii) Which day had less than 25 sales of cups? 3. The following pictorial data shows the number of Standard Three up E to Standard Seven pupils who attended classes on Monday. Study it N carefully and then answer the questions that follow: LI Key: A picture of one pupil represents 10 pupils N Class Students O R Standard three FO 311 MATH std 5.indd 311 30/07/2021 14:50  FOR ONLINE USE ONLY DO NOT DUPLICATE Standard four LY N Standard five O SE U Standard six E N LI N Standard seven O R (i) Which class had the smallest number of pupils? How many pupils FO were they? (ii) Which class had the highest number of pupils? How many pupils were they? 312 MATH std 5.indd 312 30/07/2021 14:50  FOR ONLINE USE ONLY DO NOT DUPLICATE (iii) Which classes had equal number of pupils? How many pupils were they in each class? (iv) How many Standard three pupils attended? (v) How many pupils attended classes on that day? 3. The following table shows the number of books for five subjects taught in Standard Five in one of the primary schools. LY Title of Social Science Mathematics Kiswahili English the book Studies N Number 35 20 30 40 15 of books O (i) Construct a bar chart to show the number of books for different subjects. Vertical scale: 1 cm represents 5 books. SE Horizontal scale: 1 cm represents the width of a bar. (ii) Which subject has the highest number of books? (iii) What is the difference between the number of English books and U Social Studies books? Average E The average is obtained by dividing the sum of the item values by the total N number of items. LI The following examples help to determine the meaning of an average: N (a) Ali had 6 mangoes while Sara had 2 mangoes. In order to have the same number of mangoes, they put all the mangoes in one container and then O divided the total number of mangoes by two. The total number of mangoes is 6 + 2 = 8. Dividing the total by two gives 8 ÷ 2 = 4. Therefore, Ali and R Sara got 4 mangoes each. (b) Five pupils of Msange Primary School were sent to pick maize from the FO school farm. Musa picked 5 maize, Ramadhani 7, Mariamu 3, Neema 9 and Zacharia 6. The teacher asked them to share the maize equally. The pupils followed the following steps in order to get equal number of maize: 313 MATH std 5.indd 313 30/07/2021 14:50  FOR ONLINE USE ONLY DO NOT DUPLICATE 1. The pupils collected all the maize in one container. 2. They counted the maize in the container and found the total: 5 + 7 + 3 + 9 + 6 = 30. 3. They divided the total number of maize by the total number of pupils, that is, 30 ÷ 5 = 6. Thus, each pupil got 6 maize. LY Sum  of  the  item  values _________________ Therefore, ​Average   =  ​       ​​. Number  of  items N Example 1 O The ages of four standard three pupils at Mwenge Primary School were as SE follows: Selina was 9 years old, Ashura 8 years old, Emmanuel 10 years old, and Hassan 9 years old. Find the average of their ages. U Solution 1. Add the ages of all pupils: 9 years + 8 years + 10 years + 9 years = 36 years. E 2. The number of pupils is 4. N Total number of ages _______________ ​ verage   =  ​    3. A     ​​ LI Number  of pupils 36 _ = ​​   ​​ years N 4 O = 9 years. Therefore, the average age of the four pupils is 9 years. R FO Example 2 Find the average of 5, 10, 15, 25 and 20. 314 MATH std 5.indd 314 30/07/2021 14:50  FOR ONLINE USE ONLY DO NOT DUPLICATE Solution There are 5 numbers. Total of the numbers: 5 + 10 + 15 + 25 + 20 = 75. Sum of numbers _____________ 75    ​ = ​ _ ​ = 15.​ ​Average   =  ​    Number  of values 5 Therefore, the average of the numbers is 15. LY Exercise 2 N Answer the following questions: O 1. Kulwa bought crates of tomatoes from the market as follows: On the first day, she bought 5 crates, on the second day 3 crates, and SE 4 crates on the third day. Find the average number of tomato crates bought per day? U 2. A businessman sold motor cycles on six consecutive days as follows: Monday 5, Tuesday 4, Wednesday 7, Thursday 11, Friday 12 and Saturday 15. Find the daily average number of motor cycles that were sold. E N 3. The class attendance of standard five pupils in a week was as follows: LI Day Monday Tuesday Wednesday Thursday Friday Attendance 33 45 48 45 39 N Find the daily average attendance of pupils during the week. O 4. The following table shows school attendance of pupils in five days: R Day Monday Tuesday Wednesday Thursday Friday FO Attendance 330 350 340 300 280 (a) Find the daily average attendance of pupils during the week. (b) On which days was the attendance above the average? 315 MATH std 5.indd 315 30/07/2021 14:50  FOR ONLINE USE ONLY DO NOT DUPLICATE 5. Find the average of 28 000 shillings, 32 000 shillings and 96 000 shillings. 6. If seven lorries are loaded with bags of maize weighing the following kilograms: 1 050 kg, 600 kg, 800 kg, 940 kg, 900 kg, 850 kg and 600 kg. What is the average weight of maize in a lorry? LY 7. The weights of seven people are: 50 kg, 59 kg, 72 kg, 45 kg, 80 kg, 52 kg and 48 kg. What is their average weight? N O 8. Four cows produce milk as follows: 8 litres, 15 litres, 7 litres and 14 litres. Find the average of the litres of milk. SE 9. Find the average of the following lengths: 36 cm, 54 cm, 44 cm, 50 cm and 66 cm. U 10. The following table gives information on five children. Use this information to answer the questions that follow: E N Name Weight in kg Height in cm Kisuda 35 140 LI Amani 32 135 Furaha 28 142 N Musa 28 128 O Salimu 25 125 (a) Find the average weight of the children in kilograms. R (b) Find the average height of the children in metres. FO (c) How many children have their weights above the average? (d) How many children have their heights above the average? 316 MATH std 5.indd 316 30/07/2021 14:50  FOR ONLINE USE ONLY DO NOT DUPLICATE Bar graphs A bar graph is a chart that uses bars to show comparisons between categories of data. It can be either horizontal or vertical. The heights of bars represent the total number of items for a given category. Example 1 Study carefully the following bar graph which represents the number of LY chickens sold in five days of the week and answer the questions that follow: N Chicken sold in five days O 700 600 Number of chickens 500 400 SE 300 U 200 100 0 E Monday Tuesday Wednesday Thursday Friday N LI Questions (a) Which day had the lowest sales of chickens? How many chickens N were sold on that day? O (b) Which day had the highest sales of chickens? How many chickens were sold on that day? (c) Which days had the same sales of chickens? How many chickens R were sold on those days? FO (d) How many chickens were sold on Tuesday? (e) How many more chickens were sold on Tuesday compared to Monday? 317 MATH std 5.indd 317 30/07/2021 14:50  FOR ONLINE USE ONLY DO NOT DUPLICATE Solution (a) The shortest bar shows that Wednesday had the lowest sales of chickens. Thus, 200 chickens were sold on that day. (b) The tallest bar shows that Thursday had the highest sales of chickens. Thus, 700 chickens were sold on that day. (c) By comparing the columns, it shows that the bars on Monday and Friday had equal heights, which means that the same number of chickens were sold on both days. So, 400 chickens were sold on each of the LY two days. (d) By looking at the bar for the sales on Tuesday, you observe that 600 N chickens were sold. (e) Since 600 chickens were sold on Tuesday and 400 chickens were O sold on Monday, then, the difference between the two sales was 200. Therefore, 200 more chickens were sold on Tuesday compared to Monday. SE U Example 2 The following bar graph shows the amount of rainfall in millimetres in five E regions. Study the graph and answer questions that follow: N Rainfall distribution for one day LI 80 Amount of rainfall (mm) 70 N 60 50 O 40 30 R 20 10 FO 0 Tabora Singida Mwanza Mbeya Tanga Regions 318 MATH std 5.indd 318 30/07/2021 14:50  FOR ONLINE USE ONLY DO NOT DUPLICATE (a) Which regions recorded the same amount of rainfall? How many millimetres of rainfall were recorded in each of these regions? (b) Which region had the lowest amount of rainfall on that day? What was the recorded amount of rainfall in that region? (c) Find the difference in the amount of rainfall recorded in Mwanza and Mbeya. (d) Find the total amount of rainfall recorded in all the five regions. LY Solution N (a) By comparing the bars, the bars which have the same height represent the same amount of rainfall. Therefore, Tabora and Tanga regions O recorded the same amount of rainfall, which was 80 millimetres. (b) By comparing the bars, the shortest bar represents the lowest amount SE of rainfall. The region which recorded the lowest amount of rainfall was Singida, with 20 millimetres. (c) By comparing the bars it shows that, the difference in the amount of U rainfall in Mwanza and Mbeya was: 60 mm ‒ 40 mm = 20 mm. (d) The total amount of rainfall in all five regions is obtained by adding all the records of rainfall: E Total amount of rainfall = 80 mm + 20 mm + 60 mm + 40 mm + 80 mm N = 280 mm. LI Therefore, the total amount of rainfall recorded in all five regions was 280 mm. N O Exercise 3 Answer the following questions: R 1. If a total number of Standard One registered pupils at Bukongwa, FO Mkolani, Nyasubi, Nyegezi and Ibanda primary schools is as shown in the following bar graph, study it and then, answer the questions that follow: 319 MATH std 5.indd 319 30/07/2021 14:50  FOR ONLINE USE ONLY DO NOT DUPLICATE Number of registered pupils in five schools 1000 900 Number of pupils 800 700 600 LY 500 400 300 N 200 100 O 0 Bukongwa Mkolani Nyasubi Nyegezi Ibanda SE Schools (a) Which school registered the largest number of pupils? How many U pupils were they? (b) Which schools had equal number of registered pupils? (c) Find the difference between the pupils registered at Bukongwa and E Ibanda primary schools. N (d) What is the total number of the pupils registered in all schools? LI 2. The following pictorial representation of data shows the number of pineapples harvested by Baraka from his farm in seven consecutive N days. Study the pictorial and then answer the questions that follow: O Key: 1 picture of a pineapple represents 100 pineapples. R Days Number of pineapples FO Saturday 320 MATH std 5.indd 320 30/07/2021 14:50  FOR ONLINE USE ONLY DO NOT DUPLICATE Sunday Monday Tuesday LY Wednesday N O Thursday Friday SE U (a) Construct a bar graph to represent the data given above. Vertical scale: 1 cm represents 100 pineapples. Horizontal scale: 1 cm represents the width of each bar. E (b) Which day did he harvest a largest number of pineapples? How N many pineapples were harvested on that day? (c) Which days did he harvest the same number of pineapples? How LI many pineapples were harvested in each of those days? N (d) Find the average number of pineapples harvested in all seven days. O 3. The following table shows a number of malaria patients at Mgori Health Center. Study it and answer the questions that follow: R Month January February March April May June FO Number 160 180 120 200 200 100 of malaria patients 321 MATH std 5.indd 321 30/07/2021 14:50  FOR ONLINE USE ONLY DO NOT DUPLICATE (a) Construct a bar graph to represent the data given in the table. Vertical scale: 1 cm represents 20 patients. Horizontal scale: 1 cm represents the width of each bar. (b) Which month recorded the highest number of patients? What was the number of patients? (c) Find the average number of patients who reported at the Health Center from January to June. LY (d) By how many patients was the number of patients in June less than the average? N 4. Msunga bought bananas for five consecutive weeks as shown in the O following table. Study the table and answer the questions that follow: Week Number of First week 350 Second week 250 SE Third week 450 Fourth week 350 Fifth week 150 bananas U (a) Construct a bar graph to represent the data given in the table. Vertical scale: 1 cm represents 50 bananas. E Horizontal scale: 1 cm represents the width of each bar. N (b) In which weeks did Msunga buy the same number of bananas? (c) Find the difference between the number of bananas bought during LI the third and fifth weeks. (d) Find the average of the bought bananas in a week. N (e) How many bananas did Msunga buy in the second week? O Exercise 4 R Answer the following questions: FO 1. Find the average of the following measurements: (a) 20 km, 80 km, 40 km, and 60 km (b) 35 litres, 50 litres, 45 litres, and 30 litres 322 MATH std 5.indd 322 30/07/2021 14:50  FOR ONLINE USE ONLY DO NOT DUPLICATE 2. Anna scored 45 marks in science, 50 marks in mathematics and 55 marks in Kiswahili. What was the average score of Anna in all three subjects? 3. Paul is 11 years old, Juma is 9 years old and Aisha is 7 years old. What is the average age of the three children? 4. The weights of 6 people in kilograms are 80 kg, 70 kg, 65 kg, 90 kg, 55 kg and 60 kg. Find their average weight in kilograms. LY 5. If five bags of maize weigh 100 kg, 90 kg, 110 kg, 95 kg and 105 kg. N What is the average weight of the five bags of maize? O 6. Mr. Jombwe’s sales of milk for seven consecutive days were as follows: 46 litres, 41 litres, 40 litres, 50 litres, 58 litres, 60 litres and 34 litres. What was Mr. Jombwe’s average sale of milk in a day? SE 7. The harvests of coconuts on 8 different occasions were: 10 coconuts, 15 coconuts, 5 coconuts, 7 coconuts, 3 coconuts, 4 coconuts, 4 U coconuts and 24 coconuts. What was the average harvest of coconuts on one occasion? E 8. The following bar graph shows the kilograms of beans eaten by students in seven days. Study the graph and answer the questions that follow: N Kilograms of beans eaten in seven days LI 90 80 N Kilograms of beans 70 60 O 50 40 30 R 20 FO 10 0 First Second Third Forth Fifth Sixth Seventh day day day day day day day Days 323 MATH std 5.indd 323 30/07/2021 14:50  FOR ONLINE USE ONLY DO NOT DUPLICATE (a) On which day was the largest number of kilograms of beans used? (b) On which days was the same number of kilograms of beans used? (c) Find the total number of kilograms of beans used during all seven days. (d) On average, how many kilograms of beans were used in one day? 9. The number of cows sold at Songambele auction mart in 6 weeks were as in the following table: LY Week First Second Third Fourth Fifth Six week week week week week week N Number of 90 40 20 25 50 75 O cows (a) Construct a bar graph to represent the data given in the table. Vertical scale: 1 cm represents 5 cows. SE Horizontal scale: 1 cm represents the width of each bar. (b) Which week recorded the lowest sales of cows? (c) What is the total number of cows sold during the 6 weeks? U (d) Which week recorded the highest sales of cows? (e) Find the average number of cows sold in a week. E 10. A health centre recorded the number of patients with eye problems N for six consecutive days as shown in the following table: LI Day Monday Tuesday Wednesday Thursday Friday Saturday Number 450 310 340 520 424 356 N of patients O (a) Construct a bar graph to represent the data given in the table. Vertical scale: 1 cm represents 5 patients. R Horizontal scale: 1 cm represents the width of each bar. FO (b) Which day recorded the largest number of patients? How many were they? (c) Find the average number of patients recorded in the six days. 324 MATH std 5.indd 324 30/07/2021 14:50  FOR ONLINE USE ONLY DO NOT DUPLICATE Summary 1. Bar charts are used to represent and compare information or data. 2. Bar charts can be drawn using vertical or horizontal bars. 3. The average is calculated using the formula: Sum of the item values ____________ Average = ​​       ​​. Number of items LY 4. The choice of a scale in constructing a bar graph depends on the size of the given data. N O SE U E N LI N O R FO 325 MATH std 5.indd 325 30/07/2021 14:50