Q.1 – Q.2 , Q.3 – Q.4 Q.5 , Q.6 , Q.7 , Q.9 , Q. 10 , Q. 11 Q.12 , Q.13 , Q. 14 , Q. 15 Q.16 to Q. 19
Answer 1 (a)
Mean = Addition of all numbers/ total Numbers
= ( 61 +62 + 65 + 65 + 65 + 68 + 74 + 74 + 75 + 77)/ 9
= 686 / 10
Mean= 68.6
Median = The Middle Number = (65 + 68)/2
Median = 66.5
Mode = The most repeated number
Mode = 65
Range = Maximum Value – Minimum Value
= 77 – 61
Range = 16
Answer 1 (b)
Each day is warmer by 7 degrees, so every number will be added by 7
New numbers will be : 68 , 70 , 72, 72, 72 , 75 , 81, 81, 82, 84
that means to find mean , just add 7 x 10 = 70 to addition of mean to the above question 1(a)
Mean = (686 + 70) / 10
= 756 / 10
Mean = 75.6
Median = ( 72 + 75 )/2
Median = 73.5
Mode = Most repeated number
Mode = 72
Range = Maximum – Minimum
= 84 – 68
Range = 16
Answer 2
(a).
First arrange the numbers in ascending order
19 , 21 , 22 , 22, 28 , 31 , 33 , 44 , 50
Mean = (19 + 21 + 22 + 22 + 28 + 31 +33 + 44 +50) / 9
= 270/9
Mean = 30
Median = Middle Number
Median = 28
Mode = Most repeated number
Mode = 22
Range = Maimum – Minimum
= 50 – 19
Range = 31
Interquartile Range Q2 = Third Quartile(Q3) – First Quartile(Q1)
Here the list of numbers is odd so take Quartile 1 as below the median 28 and Quartile 3 as the above the median 28.
As 28 is our Median ;
First Quartile will be 19 , 21 , 22 , 22
Median of First Quartile = Q1 = (21 + 22) / 2 = 21.5
Third Quartile will be 31 , 33 , 44 , 50
Median of Third Quartile = Q3 = (33+44)/2 =38.5
Interquartile Range Q 2 = Q3 – Q1
= 38.5 – 21.5
Interquartile Range Q 2= 17
(b).
Passengers in each flight increased 3 times
Mean = (270 x 3) / 9
= 810/9
Mean = 90
After 3 times increase in passengers the list will be
57 , 63 , 66, 66 , 84 , 93 , 99 , 132 , 150
Median = Middle Number
Median = 84
Mode = Most repeated Number
Mode = 66
Range = Maximum – Minimum
= 150 – 57
Range= 93
Interquartile Range Q2 = Q3 – Q1
First Quartile is 57 , 63, 66 , 66
Median of First Quartile = Q1 =( 63 + 66) / 2
= 64.5
Third Quartile is 93 , 99 , 132 , 150
Median of Third Quartile Q3 = (99+132) /2
= 115.5
Interquartile Range Q2 = Q3 – Q1
= 115.5 – 64.5
Interquartile Range Q2 = 51
Standard Deviation of 57 , 63 , 66, 66 , 84 , 93 , 99 , 132 , 150
| Numbers | Mean | ||
| A | B | C = A – B | D = C2 |
| 57 | 90 | -33 | 1089 |
| 63 | 90 | -27 | 729 |
| 66 | 90 | -24 | 576 |
| 66 | 90 | -24 | 576 |
| 84 | 90 | -6 | 36 |
| 93 | 90 | 3 | 9 |
| 99 | 90 | 9 | 81 |
| 132 | 90 | 42 | 1764 |
| 150 | 90 | 60 | 3600 |
| Total Sum of ‘D’ = 8460 |
Average of Squares or column ‘D’ = 8460/9
= 940
Standard Deviation = √940 = 30.65 = Approximately 30.7
( c) .
Each flight had 2 fewer passengers than
List of Passengers will be 17 , 19 , 20 , 20 , 26, 29 , 31 , 42 , 48
Median = 26
First Quartile ; 17 , 19 , 20 , 20 (Consider the Numbers below median 26)
Median of First Quartile Q1 = (19 +20) /2
= 19.5
Third Quartile ; 29 , 31 , 42, 48 (Consider the Numbers above median 26)
Median of Third Quartile Q3 = ( 31+ 42)/2
= 36.5
Interquartile Range Q2 = Q3 – Q1
= 36.5 – 19. 5
Interquartile Range Q2 = 17
Standarad Deviation
Mean = ( 17 + 19 + 20 + 20 + 26 + 29 + 31 + 42 +48 )/9
=252/9
= 28
| Numbers | Mean | ||
| A | B | C = A – B | D = C2 |
| 17 | 28 | -11 | 121 |
| 19 | 28 | -9 | 81 |
| 20 | 28 | -8 | 64 |
| 20 | 28 | -8 | 64 |
| 26 | 28 | -2 | 4 |
| 29 | 28 | 1 | 1 |
| 31 | 28 | 3 | 9 |
| 42 | 28 | 14 | 196 |
| 48 | 28 | 20 | 400 |
| Total Sum of ‘D’ = 940 |
Average of Squares or column ‘D’ = 940 /9
= 104
Standard Deviation = √104
Standard Deviation = 10.198 Approximately = 10.2
Q.1 – Q.2 , Q.3 – Q.4 Q.5 , Q.6 , Q.7 , Q.9 , Q. 10 , Q. 11 Q.12 , Q.13 , Q. 14 , Q. 15 Q.16 to Q. 19
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