### Chap 16 Data Handling: 6 A.M. QUIZ

Question 1
The median of a set of eight numbers is 4.5.
Given that seven of the numbers are 9, 2, 3, 4, 12, 13 and 1,
find the missing number.
• Arrange the 7 given numbers in ascending order, we get 1, 2, 3, 4, 9, 12, 13
• If there are 8 numbers, the median will be the 'number' betwen the 4th & 5th position.
• Since the median is 4.5, it means the number would be greater than 4 (based on the 7 numbers below).
• 4.5 would be the mean of the numbers in the 4th and 5th position
• Since the number in the 4th position is 4, the number in the 5th position would be 5 so that the mean will result 4.5.
• Hence, missing number is 5
Question 2
The mean of a set of six numbers is 2 and the mean of another set of ten numbers is m.
If the mean of the combined set of sixteen numbers is 7, find the value of m.
• Given that the mean of 6 numbers is 2
• The sum of these 6 numbers would be 6 x 2 = 12
• The mean of another set of 10 numbers is m
• The sum of these 10 numbers would be 10 x m = 10m
• To find the mean of these 16 numbers, we will find the sum of these 16 numbers and then divide by 16
• Sum of these 16 numbers is 12 + 10m
• Also, we are given that the mean of these 16 numbers is 7
• Therefore sum of these 16 numbers is 16 x 7 = 112
• Hence, 12 + 10m = 112
• 10m = 112 - 12
• 10m = 100
• Therefore, m = 10

Question 3
Given that nine numbers are 16, w, 17, 9, x, 2, y, 7 and z have a mean of 11,
find the mean of w, x, y and z.

• Sum of the 9 given numbers is 11 x 9 = 99
• 16 + w + 17 + 9 + x + 2 + y + 7 + z = 99
• w + x + y + z + 51 = 99
• w + x + y + z = 99 - 51
• w + x + y + z = 48
• Therefore mean of w, x, y and z is 48/4 = 12

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The first 3 correct responses shall receive a prize....

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Updated 14 May 2010: ThE QUIZ is now closed... Thank you for your participation... See the complete set of solution below each question.

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2. Question 1:
the median for the 7 no.s is 4.
If the median for the 8 no.s is 4.5, then,
4.5 x 2=9
9-4=5

Question 2
6 x 2=12
the 6 no.s add up to 12.

16 x 7=112
112-12=100
sum of no.s for 10 no.s=100
100÷10=10
m=10

The value of m is 10.

Question 3:
(16+w+17+9+x+2+y+7+z)÷9
=11
16+17+9+2+7=51
9 x 11=99
99-51=48
w+x+y+z=48
48÷4=12
The mean of w,x,y,z is 12.

3. 1) The median for the seven numbers is 4. So if the median for the eight numbers is 4.5, take 4.5 multiply by 2 and subtract 4 is 5.

2) 6x2 = 12 (first set of 6 numbers)
16 x 7 = 112
112-12 = 100
10 numbers = 100
100/10 = 10
M is equal to 10.

3) Average = 11
16+w+17+9+x+2+y+7+z = 99
99-(16+17+9+2+7) = 51
99-51=48
48 = w, x, y, z
Mean of w, x, y, z = 48/4
= 12
The mean of x, x, y, z is 12.

4. 1) The number is 5. If arranged in sequence... 1,2,3,4,9,12,13. The median would hence be 4. If 5 is placed in... 1,2,3,4,5,9,12,13. The median numbers would be 4 and 5. The average of these two numbers is 4.5.
2)6x2=12
10xm=10m
(10m+12)÷16=7
Hence, to find the value of (10m+12)...16x7=112
112-12=100(10m)
100÷10=10(m)
The value of m is 10.
3)11x9=99
16+17+9+2+7=51
99-51=48
48=w+x+y+z
Mean of (w+x+y+z)=48÷4
=12
Hence, the mean of x, y, x and z is 12.

5. 1. The median of the seven numbers are as follows:

1,2,3,4,9,12,13 -> median = 4

median of 8 numbers = 4.5

missing number: 4.5 x 2 = 9
9 - 4 = 5

2. Total value of 6 numbers = 6 x 2 = 12
Total value of 10 numbers = m x 10 = 10m

Total value of the 16 numbers = 7 x 16 = 112

12 + 10m = 112
10m = 100
m = 10

3. Total value of nine numbers = 11 x 9 = 99

16 + w + 17 + 9 + x + 2 + y + 7 + z = 99
w + x + y + z = 99 - 16 - 17 - 9 - 2 - 7
w + x + y + z = 48

mean of w + x + y + z -> 48/4 = 12

6. Q1
The missing number is 5. For the median of the 8 numbers to be 4.5, the average of the middle two numbers should be 4.5. As we can see, in the number sequence: 9, 2, 3, 4, 12, 13 and 1, the middle number is 4. So, in order to allow the median to be 4.5, the number in the middle would be a 5. Any number bigger or smaller will affect the median.

Q2
2 x 6 = 12
10 x m = 10m
16 x 7 = 112
12 + 10m = 112
112 - 12 = 10m
10m = 100
m = 100/10
=10(Ans.)

Q3
11 x 9 = 99
99 - (16 + 17 + 9 + 2 + 7) = 48
w + x + y + z = 48
Mean: 48/4
=12(Ans.)

JJ(:

7. 1)The missing number is 5.

Reason:

1,2,3,"4",9,12,13 the median is 4

If we add 5 into the number sequence

1,2,3,"4","5",9,12,13

and we take (4+5)/2=4.5

So the missing number is 4.5

2)

2x6= 12 (total value of the six numbers)
7x16= 112 ( total value of the sixteen numbers)
112-12=100 ( total value of m numbers)
100/10= 10 (M)

3)

( 2+7+16+17+w+x+y+z)/9= 11

9x11= 99 ( total value of all 9 numbers)
99-(2+7+16+17)=48 ( total value of the remaining unknown numbers)
48/4= 12 ( mean of the 4 unknowns)

8. 1. 5

2. 10

3.12

solutions:

1： 9，2，，3，4，？，12，13，1

4.5-4=0.5
4.5+0.5=5
ans:5

2: 16x7=112
112-12=100
100divided by10 is 10

ans:10

3: 16+17+2+9+7=51
11x9=99
99-51=48
48divided by4 is 12

ans: 12

9. 1) The median of a set of eight numbers is 4.5.
Given that seven of the numbers are 9, 2, 3, 4, 12, 13 and 1,
find the missing number.

4.5 - 0.5 =4
median of 4 and ? = 4.5
so 4.5+ 0.5 = 5.0

Ans : 5

2)The mean of a set of six numbers is 2 and the mean of another set of ten numbers is m.
If the mean of the combined set of sixteen numbers is 7, find the value of m.

16 x 7= 112
6 x 2= 12
112 - 12 = 100
100 / 10= 10

Ans: 10

3)Given that nine numbers are 16, w, 17, 9, x, 2, y, 7 and z have a mean of 11,
find the mean of w, x, y and z.

9 x 11= 99
99- 16 - 17- 9 - 2- 7 =48
48/4 =12

Ans: 12

10. 1) Median of the 7 given numbers is 4. Median of the 8 numbers is 4.5. Hence the missing number would be (4.5 x 2) - 4, which will be 5.

2) (16 x 7) - (6 x 2) = 100
100 / 10 = 10.
m = 10

3) (11 x 9) - 16 - 17 - 9 - 2 - 7 = 48
48 / 4 = 12
Mean of w, x, y, z is 12

11. Question 1
The median of a set of eight numbers is 4.5.
Given that seven of the numbers are 9, 2, 3, 4, 12, 13 and 1,
find the missing number.

The ascending order is 1,2,3,4,9,12,13.
Median=4.5
4.5x2=9
9-4=5
Missing number=5

Question 2
The mean of a set of six numbers is 2 and the mean of another set of ten numbers is m.
If the mean of the combined set of sixteen numbers is 7, find the value of m.

(16x7)-(6x2)=100
100/10=10
m=10
Question 3
Given that nine numbers are 16, w, 17, 9, x, 2, y, 7 and z have a mean of 11,
find the mean of w, x, y and z.

Total=11x9=99
16+17+9+2+7=51
99-51=48
Mean of w,x,y,z=48/4
=12

12. 1) The median for the seven numbers is 4. So if the median for the eight numbers is 4.5, take 4.5 multiply by 2 and subtract 4 is 5.

2) m=10 because the mean for the 16 numbers is 7 and since there is 16 numbers, 16x7=112
the mean for 6 numbers is 2 and so the total for the 6 numbers is 12. 112-12=100
100 it the total for the 10 numbers. to find the mean, 100/10=10=m
so m=10

3)First find the total value of all numbers. 11x9=99. Then we find the total of all the known values. 16+17+9+2+7=51 Then we minus 51 from 99. 99-51=48. 48 is the total of all the unknowns and since there is 4 unknowns, 48/4=12
12 is the mean.

13. Q1.

Median -> 4 & 5

7 numbers -> 9 , 2, 3, 4, 12, 13 and 1

the eight number -> ?

In order the 7 number -> 1,2,3,4,9,12,13, the median is 4.

If the median is 4.5 of the set of 8 number So we use, 4.5 x 2 - (one of the median) 4 = 5

So the missing number is 5.

Q.2

Mean is sum of the numbers/number of numbers

16 x 7 = 112
2 x 6 = 12
112 - 12 = 100

Mean -> M ->(Sum of numbers) 100 ÷ (number of numbers) 10
= 10

Q.3

11 x 9 = 99
w + x + y + z -> 99 - (16 + 17 + 9 + 2 + 7)
= 48
Mean of w + x + y + z -> 48 ÷ 4
= 12

14. Q1 :
There are eight numbers in the set so the median is the average of the fourth and fifth numbers. The first 4 numbers are 1, 2, 3 and 4 the median is 4.5. The fifth number, the missing one, should be 5 as the average of 4 and 5 is 4.5.

Ans : 5

Q2 :
6 x 2 = 12
10 x m = 10m
16 x 7 = 112
112 - 12= 100
100 ÷ 10 = 10

Ans : m = 10

Q3 :
9 x 11 = 99
99 - 16 - 17 - 9 - 2 - 7 = 48
48 ÷ 4 = 12

Ans : Mean = 12