ID : ae-7-data-handling-probability-statistics [1] Grade 7 Data Handling - Probability, Statistics For more such worksheets visit www.edugain.com Answer t he quest ions (1) What is the average of the 11 consecutive integers starting at 17? (2) A group of students f rom a Spanish college were selected f or a study. The color of the eyes of the students were noted as Color of Eyes Number of Students grey 4 black 11 green 8 brown 4 blue 8 What is the probability that the color of a student eye's chosen at random starts with the letter b? (3) What is the average of all possible f ive-digit numbers that can be f ormed by using each of the digits 2, 5, 8, 9, and 1 exactly once? (4) Following f igure shows f ruits in a basket at Gamal's house. Gamal is getting late f or school, and just picks a f ruit f rom the basket without looking at it. Which f ruit is most likely to be picked? (5) A ship docks at the port on 5 dif f erent days at 5:15 AM, 5:00 AM, 10:45 AM, 4:30 AM and 6:45 AM. What is the average time it docks? Choose correct answer(s) f rom given choice (6) In an of f ice, the age of the employees was as f ollows 37, 50, 35, 53, 25, 43, 36, 45, 44, 49, 38, 37 What is the average of their ages? a. 42 b. 38 c. 45 d. 41
(7) Amala tosses a die twice. What is the probability that the sum of the values obtained in the throws is 6? ID : ae-7-data-handling-probability-statistics [2] a. 5 36 b. 6 36 c. 10 36 d. 9 36 (8) The f ollowing table shows prof its of 5 companies in a business group last year. Company Profit Company 1 Dhs 500,000 Company 2 Dhs 250,000 Company 3 Dhs 450,000 Company 4 Dhs 500,000 Company 5 Dhs 250,000 What is the average prof it of the business group? a. Dhs 387900 b. Dhs 391800 c. Dhs 390000 d. Dhs 391100 (9) There are 9 black balls, 11 green balls, and 10 orange balls in a bag. What is the probability of picking up one green ball out of the bag without looking? a. 21 30 c. 11 30 b. 11 20 d. 10 30 (10) There are 40 employees in a company, who works in three shif ts. The f irst group of 7 employees work f rom 9:00 AM to 12 noon. The second group of 19 employees work f rom 10:00 AM to 2:00 PM. And third group of 14 employees work f rom 12 noon to 2:00 PM. If there are only 9 computers, during what time, computers are likely to be used most? a. 12 noon to 2:00 PM b. 10:00 AM to 12 noon c. 10:00 AM to 2:00 PM d. 9:00 AM to 12 noon (11) From a deck of cards, Carna withdraw a card at random. What is the probability that the number on the card is a prime number? a. c. 1 11 4 52 b. 20 52 d. 16 52
(12) A class has 22 students, 8 out of whom are girls. If a teacher picks a student at random, what is the probability that the student picked is a boy? ID : ae-7-data-handling-probability-statistics [3] a. 13 22 b. 8 22 c. 14 22 d. 12 14 Fill in the blanks (13) While doing the science experiment in the physics lab, Karim had to take 7 measurements of the temperature and write the average of those as an answer. If the measurements of the temperature is 2, 0, 1, -2, 2, 1, -2, the f inal answer of his experiment is. (14) The f ollowing are the marks obtained by 33 students in German. Marks T ally Marks Number of students 2 5 3 1 4 1 5 5 6 7 7 4 8 5 9 5 The median of their score is (15) Coman is part of the school cricket team, and this year he has scored an average of 55 runs. He has played 6 innings so f ar, and his scores in 5 of them are 65, 45, 53, 58, 54 His score in the last innings is 2016 Edugain (www.edugain.com). All Rights Reserved Many more such worksheets can be generated at www.edugain.com
Answers ID : ae-7-data-handling-probability-statistics [4] (1) 22 If you look at the question caref ully, you will notice that the 11 consecutive integers starting at 17 = 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27 Sum of 11 consecutive integers = 17 + 18 + 19 + 20 + 21 + 22 + 23 + 24 + 25 + 26 + 27 = 242 Average of 11 consecutive integers starting at 17 = Sum of 11 consecutive integers T otal number of consecutive integers = 242 11 = 22 Now the average of 11 consecutive integers at 17 is 22.
(2) 23 ID : ae-7-data-handling-probability-statistics [5] 35 If you look at the question caref ully, you will notice that the color of the eyes of the students were noted down as below Color of Eyes Number of Students grey 4 black 11 green 8 brown 4 blue 8 Total number of students = 35 Number of students whose eye's color starts with letter b = (blue + brown + black) = 23 Probability that the color of a student eye's chosen at random starts with the letter b = Number of students whose eye's color starts with letter b T otal number of students = 23 35 Now, probability that the color of a student eye's chosen at random starts with the letter b is 23. 35
(3) 55555 ID : ae-7-data-handling-probability-statistics [6] On creating dif f erent possible f ive-digit numbers, each of the digits 2, 5, 8, 9, and 1 will occur the same number of times at each decimal place. Theref ore the sum of all one's digits of numbers will be the same as the sum of all ten's digits of numbers. This way, the sum of digits of all numbers will be the same at all decimal places. Theref ore the average of the f ace value at each decimal place will be: (2 + 5 + 8 + 9 + 1)/5 = 5 Step 4 Now we know that the averages of f ace values of each decimal place are all equal to 5. The average of the numbers f ormed by such digits will be equal to: (10000 + 1000 + 100 + 10 + 1) (average of f ace value) = 11111 5 = 55555 (4) Apple Probability = Number of f avorable outcomes Number of possible equally-likely outcomes Since there are 9 f ruits in the basket, in which 4 are apples. Theref ore the probability of an apple picked f rom the basket = Number of apple in the basket Total number of f ruits in the basket = 4 9 If you look at the basket caref ully, you will notice that the number of apples in a basket are more as compare to other f ruits. Theref ore the probability of picked an apple f rom the basket is more as compare to other f ruits and hence we can say that the most likely f ruit to be picked f rom the basket is apple.
(5) 6:27 AM ID : ae-7-data-handling-probability-statistics [7] Since all the times are in AM, we can just add the hours in minutes f orm and f ind out the average We take a time as the minutes past midnight So 5:15 AM = 5 x 60 + 15 = 315 5:00 AM = 5 x 60 + 0 = 300 10:45 AM = 10 x 60 + 45 = 645 4:30 AM = 4 x 60 + 30 = 270 6:45 AM = 6 x 60 + 45 = 405 To f ind the average 315 + 300 + 645 + 270 + 405 5 = 1935 5 = 387 To convert it back to the hh:mm f ormat we divide by 60. The quotient is the hours, and the remainder is the minutes 387 = 6R27 60 Average time of docking = 6:27 AM (6) d. 41 If you look at the question caref ully, you will notice that the age of the employees was as f ollows 37, 50, 35, 53, 25, 43, 36, 45, 44, 49, 38, 37 Sum of age of the employees = 37 + 50 + 35 + 53 + 25 + 43 + 36 + 45 + 44 + 49 + 38 + 37 = 492 Total number of employees = 12 Average age of the employees = Sum of age of the employees T otal number of employees = 492 12 = 41 Now the average age of the employees is 41.
(7) a. 5 36 ID : ae-7-data-handling-probability-statistics [8] Let's assume S, E and P are the Sample Space, Event and Probability of getting the sum of the values obtained in the throws is 6 by tossing a die twice respectively. S = { (1,1),(1,2),(1,3),(1,4),(1,5),(1,6), (2,1),(2,2),(2,3),(2,4),(2,5),(2,6), (3,1),(3,2),(3,3),(3,4),(3,5),(3,6), (4,1),(4,2),(4,3),(4,4),(4,5),(4,6), (5,1),(5,2),(5,3),(5,4),(5,5),(5,6), (6,1),(6,2),(6,3),(6,4),(6,5),(6,6) } E = {(1,5),(2,4),(3,3),(4,2),(5,1)} P(E) = n(e) n(s) (Since P(E) is the probability of getting event E, n(e) is the number of elements in the event E and n(s) is the number of elements in the sample space S ) P(E) = 5 36 Now, the probability that the sum of the values obtained in the throws is 6 by tossing a die 5 twice is 36
(8) c. Dhs 390000 ID : ae-7-data-handling-probability-statistics [9] If you look at the question caref ully, you will notice that the table below shows prof its of 5 companies in a business group last year. Company Profit Company 1 Dhs 500,000 Company 2 Dhs 250,000 Company 3 Dhs 450,000 Company 4 Dhs 500,000 Company 5 Dhs 250,000 Total prof its made by the business group = Dhs 500,000 + Dhs 250,000 + Dhs 450,000 + Dhs 500,000 + Dhs 250,000 = Dhs 1950000 Average prof it of the business group = Total prof its made by the business group Number of companies in a group = 1950000 5 = 390000 Now the average prof it of the business group is Dhs 390000.
(9) c. 11 30 ID : ae-7-data-handling-probability-statistics [10] If you look at the question caref ully, you will notice that there are the f ollowing color balls in the bag Color Number of balls black 9 green 11 orange 10 Total number of balls = 9 + 11 + 10 = 30 Probability of picking up one green ball = Number of green ball Total number of balls = 11 30 Now, the probability of picking up one green ball out of the bag without looking is 11 30. (10) a. 12 noon to 2:00 PM According to question the number of employees work f rom 9:00 AM to 12 noon is = 7 employees and the number of employees work f rom 10:00 AM to 2:00 PM is = 19 employees Theref ore the number of employees work f rom 10:00 AM to 12 noon is = 7 + 19 = 26 employees The number of employees work f rom 12 noon to 2:00 PM is = 14 employees Computers are likely to be used most in that time, in which most number of employees are worked. From 12 noon to 2:00 PM most number of employees are worked and hence the computers are likely to be used most f rom 12 noon to 2:00 PM.
(11) d. 16 52 ID : ae-7-data-handling-probability-statistics [11] If you look at the question caref ully, you will notice that Carna withdraw a card at random f rom a deck of cards. Total number of cards in a deck = 52 cards Prime number cards in a deck of card = {(2, 3, 5, 7) = Clubs, (2, 3, 5, 7) = Diamonds, (2, 3, 5, 7) = Hearts, (2, 3, 5, 7) = Spades } Total prime number cards = 16 Probability that the number on the card is a prime number = Total prime cards in a deck Total number of cards in a deck = 16 52 Now the probability that the number on the card is a prime number = 16 52. (12) c. 14 22 If you look at the question caref ully, you will notice that the Total number of students = 22 Number of girls = 8 Number of boys = (22-8) = 14 Total number of boys Probability that the student picked is a boy = T otal number of students = 14 22 Now, the probability that the student picked a boy is 14 22.
(13) 0.28 ID : ae-7-data-handling-probability-statistics [12] If you look at the question caref ully, you will notice that Karim had to take 7 measurements of the temperature and write the average of those as an answer. Since the measurements of the temperature is 2, 0, 1, -2, 2, 1, -2, theref ore the f inal answer of his experiment = average of 2, 0, 1, -2, 2, 1, -2, Sum of 2, 0, 1, -2, 2, 1, -2, = Number of measurements of the temperature = 2 7 = 0.28
(14) 6 ID : ae-7-data-handling-probability-statistics [13] Marks T ally Marks Number of students 2 5 3 1 4 1 5 5 6 7 7 4 8 5 9 5 If you look at the given table f rom top to bottom caref ully, you will notice that the marks obtained by 33 students in German are arranged in ascending order. Median is the middle marks in a sorted list. Total number of students are 33 which is odd. (n + 1) So, Median = ( ) th 2 (where n is the number of students) =( 33 + 1 ) th 2 = ( 34 ) th 2 = 17 th If you count the number of students in tally marks column of the given table, you will notice that the marks obtained by 17 th student is 6, theref ore Median = 6 Now the median of their scores is 6.
(15) 55 ID : ae-7-data-handling-probability-statistics [14] If you look at the question caref ully, you will notice that Coman has scored an average of 55 runs in 6 innings. Let Coman score in the last inning = x His scores in 5 innings out of 6 innings = 65, 45, 53, 58, 54 Average score = Total score in 6 innings total innings 55 = 65 + 45 + 53 + 58 + 54 + x 6 55 = 275 + x 6 55 6 = 275 + x 330 = 275 + x 275 + x = 330 x = 330-275 x = 55 Theref ore Coman score in the last inning is 55.