Practice the questions of McGraw Hill Math Grade 8 Answer Key PDF Lesson 24.1 Measures of Central Tendency to secure good marks & knowledge in the exams.
McGraw-Hill Math Grade 8 Answer Key Lesson 24.1 Measures of Central Tendency
Exercises
CALCULATE
Round all answers to the hundredths place.
Question 1.
1, 2, 3, 4, 9, 8, 7, 6, 5.
Mean ________
Median ____________
Range __________
Mode __________
Answer:
Mean = 0.05.
Median = 0.05.
Range = 0.08.
Mode = All values appeared just once.
Explanation:
1, 2, 3, 4, 9, 8, 7, 6, 5.
Sum of all numbers given = 1 + 2 + 3 + 4 + 9 + 8 + 7 + 6 + 5Â = 45.
Numbers of numbers given= 9.
Mean = Sum of all numbers given ÷ Numbers of numbers given
= 45 ÷ 9
= 5.
To find the median, list the values of the data set in numerical order and identify which value appears in the middle of the list.
Arrange the digits from least to great:
1,2,3,4,5,6,7,8,9.
Median = 5.
Range = 9 – 1 = 8.
To find the mode, identify which value in the data set occurs most often.
1,2,3,4,5,6,7,8,9.
Mode: There is no mean as no number is repeating.
Hundredth value:
Mean – 6 = 6 ÷ 100 = 0.06.
Median – 5 = 5 ÷ 100 = 0.05.
Mode – 0 = 0÷ 100 = 0.
Range – 1 = 1 ÷ 100 = 0.01.
Question 2.
10, 15, 20, 60, 110, 10, 10, 45
Mean ___________
Median ___________
Range ___________
Mode ___________
Answer:
Mean = 0.35.
Median = 0.175.
Range = 1.
Mode = 0.10.
Explanation:
10, 15, 20, 60, 110, 10, 10, 45
Arranging numbers in numerical order:
10,10,10,15,20,45,60,110.
Sum of all numbers given= 10 + 10 + 10 + 15 + 20 + 45 + 60 + 110 = 280.
Numbers of numbers given = 8.
Mean = Sum of all numbers given÷ Numbers of numbers given
Mean = 280 ÷ 8 = 35.
10,10,10,15,20,45,60,110.
Median = (15 + 20) ÷ 2
= 35 ÷ 2
= 17.5.
10,10,10,15,20,45,60,110.
Mode = 10.(because its repeating thrice)
Range = 110 – 10 = 100.
Hundredth value :
Mean – 35 = 35 ÷ 100 = 0.35.
Median – 17.5 =Â 0.175
Mode – 10 = 10 ÷ 100 = 0.10.
Range – 100 = 100 ÷ 100 = 1.
Question 3.
23, 23, 24, 25, 48, 56, 32, 1, 2
Mean ___________
Median ___________
Range ___________
Mode ___________
Answer:
Mean = 0.26.
Median = 0.24.
Mode = 0.23.
Range = 0.55.
Explanation:
23, 23, 24, 25, 48, 56, 32, 1, 2
Arranging the numbers in numerical order:
1,2,23,23,24,25,32,48,56.
Sum of numbers given = 1 + 2 + 23 + 23 + 24 + 25 + 32 + 48 + 56 = 234
Numbers of numbers given = 9.
Mean = Sum of numbers given ÷ Numbers of numbers given
= 234 ÷ 9
= 26.
1,2,23,23,24,25,32,48,56.
Median = 24.
Mode = 23. (because its repeating twice)
Range = 56 – 1 = 55.
Hundredth value:
Mean – 26 = 26 ÷ 100 = 0.26.
Median – 24 = 24 ÷ 100 = 0.24.
Mode – 23 = 23 ÷ 100 = 0.23.
Range – 55 = 55 ÷ 100 = 0.55.
Question 4.
11, 22, 33, 44, 66, 77, 11, 21
Mean ___________
Median ___________
Range ___________
Mode ___________
Answer:
Mean = 0.35625.
Median = 0.275.
Mode = 0.11.
Range = 0.66.
Explanation:
11, 22, 33, 44, 66, 77, 11, 21
Arranging the numbers in numerical order:
11,11,21,22,33,44,66,77.
Sum of numbers given = 11 + 11 + 21 + 22 + 33 + 44 + 66 + 77 = 285
Numbers of numbers given = 8.
Mean = Sum of numbers given ÷ Numbers of numbers given
= 285 ÷ 8
= 35.625.
11,11,21,22,33,44,66,77.
Median = (22 + 33) ÷ 2
= 55 ÷ 2
= 27.5.
Mode = 11. (because its repeating twice)
Range = 77 – 11 = 66.
Hundredth value:
Mean – 35.625 = 35.625 ÷ 100 = 0.35625.
Median – 27.5 = 27.5 ÷ 100 = 0.275.
Mode – 11 = 11 ÷ 100 = 0.11.
Range – 66 = 66 ÷ 100 = 0.66.
Question 5.
3, 3, 3, 3, 3, 4, 6, 7, 8
Mean ___________
Median ___________
Range ___________
Mode ___________
Answer:
Mean = 0.44.
Median = 0.03.
Mode = 0.03.
Range = 0.05.
Explanation:
3, 3, 3, 3, 3, 4, 6, 7, 8
Arranging the numbers in numerical order:
3, 3, 3, 3, 3, 4, 6, 7, 8.
Sum of numbers given = 3 + 3 + 3 + 3 + 3 + 4 + 6 + 7 + 8 = 40.
Numbers of numbers given = 9.
Mean = Sum of numbers given ÷ Numbers of numbers given
= 40 ÷ 9
= 4.44.
Median = 3.
Mode = 3.(because its repeating 5 times)
Range = 8 – 3 = 5.
Hundredth value :
Mean – 4.44 = 4.44 ÷ 100 = 0.44.
Median – 3 = 3 ÷ 100 = 0.03.
Mode – 3 = 3 ÷ 100 = 0.03.
Range – 5 = 5 ÷ 100 = 0.05.
Question 6.
4, 5, 6, 8, 9, 21, 22, 23, 24, 21, 5, 27
Mean ___________
Median ___________
Range ___________
Mode ___________
Answer:
Mean = 0.145833.
Median = 0.15.
Mode = 0.05, 0.21.
Range = 0.23.
Explanation:
4, 5, 6, 8, 9, 21, 22, 23, 24, 21, 5, 27
Arranging the numbers in numerical order:
4, 5, 5, 6, 8, 9, 21, 21, 22, 23, 24, 27
Sum of numbers given = 4 + 5 + 5 + 6 + 8 + 9 + 21 + 21 + 22 + 23 + 24 + 27 = 175.
Numbers of numbers given = 12.
Mean = Sum of numbers given ÷ Numbers of numbers given
= 154 ÷ 12
= 14.5833.
Median = (9 + 21) ÷ 2
= 30 ÷ 2
= 15.
Mode = 5, 21 (both are repeating twice)
Range = 27 – 4 = 23.
Hundredth value :
Mean – 14.5833 = 14.5833 ÷ 100 = 0.145833.
Median – 15 = 15 ÷ 100 = 0.15.
Mode – 5,21 = 5 ÷ 100 = 0.05, 21 ÷ 100 = 0.21.
Range – 23 = 23 ÷ 100 = 0.23.
Question 7.
9, 13, 56, 12, 13, 9, 9, 18, 45
Mean ___________
Median ___________
Range ___________
Mode ___________
Answer:
Mean = 0.20444.
Median = 0.13.
Mode = 0.09.
Range = 0.47.
Explanation:
9, 13, 56, 12, 13, 9, 9, 18, 45
Arranging the numbers in numerical order:
9,9,9,12,13,13,18,45,56.
Sum of numbers given = 9 + 9 + 9 + 12+ 13+ 13+ 18 + 45 + 56 = 184.
Numbers of numbers given = 9.
Mean = Sum of numbers given ÷ Numbers of numbers given
= 184 ÷ 9
= 20.444.
Median = 13.
Mode = 9 (because its repeating thrice)
Range = 56 – 9 = 47.
Hundredth value :
Mean – 20.444 = 20.444÷ 100 = 0.20444.
Median – 13 = 13 ÷ 100 = 0.13.
Mode – 9 = 9 ÷ 100 = 0.09.
Range – 47= 47÷ 100 = 0.47.
Question 8.
-3, -10, -10, 14, 16, 22, 21, 30
Mean ___________
Median ___________
Range ___________
Mode ___________
Answer:
Mean = 0.10.
Median = 0.15.
Mode = – 0.10.
Range = 0.40.
Explanation:
-3, -10, -10, 14, 16, 22, 21, 30
Arranging the numbers in numerical order:
-10, -10, -3, 14, 16, 21, 22, 30
Sum of numbers given = -3 – 10 – 10 + 14 + 16 + 21 + 22 + 30 = – 23 + 103 = 80.
Numbers of numbers given = 8.
Mean = Sum of numbers given ÷ Numbers of numbers given
= 80 ÷ 8
= 10.
Median = (14 + 16) ÷ 2
= 30 ÷ 2
= 15.
Mode = – 10. (because its repeating twice)
Range = 30 – (-10) = 30 + 10 = 40.
Hundredth value :
Mean – 10= 10÷ 100 = 0.10.
Median – 15 = 15 ÷ 100 = 0.15.
Mode – (-10) = (-10) ÷ 100 = – 0.10.
Range – 40 = 40÷ 100 = 0.40.
Question 9.
-1, -1, -5, -6, -7, 10, 1, 14, 27
Mean ___________
Median ___________
Range ___________
Mode ___________
Answer:
Mean = 0.03555.
Median = – 0.01.
Mode = – 0.01.
Range = 0.34.
Explanation:
-1, -1, -5, -6, -7, 10, 1, 14, 27
Arranging the numbers in numerical order:
-7, -6, -5, -1, -1, 1, 10, 14, 27
Sum of numbers given = – 1 – 1 – 5 – 6 – 7 + 10 + 1 + 14 + 27 = – 20 + 52 = 32.
Numbers of numbers given = 9.
Mean = Sum of numbers given ÷ Numbers of numbers given
= 32 ÷ 9
= 3.555.
Median = -1.
Mode = – 1. (because its repeating twice)
Range = 27 – (7) = 27 + 7 = 34.
Hundredth value :
Mean – 3.555 = 3.555 ÷ 100 = 0.03555.
Median – (-1) = – 1÷ 100 = – 0.01.
Mode – (-1) = -1 ÷ 100 = – 0.01.
Range – 34= 34 ÷ 100 = 0.34.
Question 10.
-10, -20, -20, 0, 10, 20, 20
Mean ___________
Median ___________
Range ___________
Mode ___________
Answer:
Mean = 0.00.
Median = 0.00.
Mode = – 0.20 and 0.20.
Range = 0.40.
Explanation:
-10, -20, -20, 0, 10, 20, 20
Arranging the numbers in numerical order:
-20, -20, -10, 0, 10, 20, 20.
Sum of numbers given = – 20 – 20 – 10 + 0 + 10 + 20 + 20 = – 50 + 50 = 0.
Numbers of numbers given = 7.
Mean = Sum of numbers given ÷ Numbers of numbers given
= 0 ÷ 7
= 0.
Median = 0.
Mode = – 20, 20. (because both are repeating twice)
Range = 20 – (-20) = 20 + 20 = 40.
Hundredth value :
Mean – 0 = 0 ÷ 100 = 0.00.
Median – 0 = 0 ÷ 100 = 0.00.
Mode – (-20, 20) = -20 ÷ 100 = – 0.20 and 20 ÷ 100 = 0.20.
Range – 40 = 40 ÷ 100 = 0.40.