### Chap 16 Data Handling: 6 A.M. QUIZ (15 May 2010) (I)

(a) Find the mean age and the median age of the following nine children.
• 12 yr 9 mth
• 11 yr 4 mth
• 14 yr 3 mth
• 15 yr 7 mth
• 12 yr 2 mth
• 13 yr 8 mth
• 10 yr 6 mth
• 16 yr 11 mth
• 13 yr 7 mth
(b) The question does not ask for the mode. Why?

Express your thoughts clearly... imagine this question worths 5 marks.

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1. MEAN:
Years:
12+11+14+15+12+13+10+16+13=116 (years)
Months:
9+4+3+7+2+8+6+11+7=57 (months)

57months
= 57÷12
=4.75years
116+4.75=120.75 (years)
120.75÷9=13 5/12 (years)
13 5/12 years=13 years 5 months.

MEAN age is 13 years 5 months.

MEDIAN AGE:
10yr 6mth, 11yr 4mth, 12yr 2mth, 12yr 9mth, 13yr 7mth, 13yr 8mth, 14yr 3mth, 15yr 7mth, 16yr 11mth.

9÷2=4.5 (position 5) |4| ?(position5) |4|

MEDIAN age is position 5, 13yr 7mth.

b) Mode is the number which appears the most number of times in the series of numbers.
The question did not ask for mode as our of all 9 numbers, there is no same number, all numbers are different. Some of them the year is the same, but the months are different, so they cannot be counted as mode age. Thus there is no mode, so there is no answer.

PONDA~ :D (6.41AM)

2. Mean

Convert yrs to months ->

12 + 11 + 14 + 15 + 12 + 13 + 10 + 16 + 13 = 116 years in all

116(12) = 1392 months

Total months -> 1392 + 9 + 4 + 3 + 7 + 2 + 8 + 6 + 11 + 7 = 1449 months

Mean -> 1449 ÷ 9 = 161 months
161 ÷ 12 = 13r5

So 161 mths = 13 yrs 5 mths

Ans: 13 years 5 months

Median

Order of ages from youngest to oldest -> 10 yr 6 mth, 11 yr 4 mth, 12 yr 2 mth, 12 yr 9 mth, 13 yr 7 mth, 13 yr 8 mth, 14 yr 3 mth, 15 yr 7 mth, 16 yr 11 mth

Middle number is the -> 9 ÷ 2 = 4.5
4.5 ≈ 5 (nearest whole number)

the FIFTH number in the order -> 13 yr 7 mth

Ans: 13 years 7 months

(b) The question does not ask for the mode. Why?

The mode of these numbers require one to find out the frequency of which a figure appears in these set of numbers. However in these set of numbers, all of the numbers are different from one another, so there is no need to find out the mode of these numbers.

3. Find the mean age and the median age of the following nine children.
MEAN: 12 yr 9 mth+11 yr 4 mth+14 yr 3 mth+15 yr 7 mth+12 yr 2 mth+13 yr 8 mth+10 yr 6 mth+16 yr 11 mth+13 yr 7 mth= 128 yrs 9mths= 12x12+9+11x12+4+14x12+3+15x12+7+12x12+2+13x12+8+10x12+6+16x12+11+13x12+7=1449 (mths)
1449 ÷ 9 = 161
161 / 12 =13 5 / 12
5/12 x120 = 5
ANS: 13 yrs and 5 mths
10yr 6mth, 11yr 4mth, 12yr 2mth, 12yr 9mth, 13yr 7mth, 13yr 8mth, 14yr 3mth, 15yr 7mth, 16yr 11mth.
9/2 = 4.5
4.5 =5
fifth number : 13 yrs 7 mth
ANS: 13yrs 7 mth
(b) The question does not ask for the mode. Why?
The question does not ask for mode as mode requires similar numbers to find it, however, there is no similar numbers in this quiz , thus the question does not ask for mode.

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5. (a)

12 yr 9 mth + 11 yr 4 mth + 14 yr 3 mth + 15 yr 7 mth + 12 yr 2 mth + 13 yr 8 mth + 10 yr 6 mth + 16 yr 11 mth + 13 yr 7 mth

= 153 mth + 136 mth + 171 mth + 187 mth + 146 mth + 164 mth + 126 mth +203 mth + 163 mth

= 1449 mth

mean = 1449/9

= 161 mth

= 13 yr 5 mth

(b)

10 yr 6 mth
11 yr 4 mth
12 yr 2 mth
12 yr 9 mth
13 yr 7 mth
13 yr 8 mth
14 yr 3 mth
15 yr 7 mth
16 yr 11 mth

9/2 = 4.5

4.5 + 0.5 = 5

median = 13 yr 7 mth

(c) The question does not ask for mode because there are no two or more of the same numbers.

6. 12 yr 9 mth
11 yr 4 mth
14 yr 3 mth
15 yr 7 mth
12 yr 2 mth
13 yr 8 mth
10 yr 6 mth
16 yr 11 mth
13 yr 7 mth
Mean: 153+136+171+187+146+164+126+203+163=1449
1449÷9=161months
161months=13years 5 months

The mean is 13 years 5 months.

Median:
10 yr 6 mth
11 yr 4 mth
12 yr 2 mth
12 yr 9 mth
13 yr 7 mth
13 yr 8 mth
14 yr 3 mth
15 yr 7 mth
16 yr 11 mth

9=4+4+1

Median=13 years 7 months

There are no similar numbers in the list.

7. (a) Find the mean age and the median age of the following nine children.
12 yr 9 mth
11 yr 4 mth
14 yr 3 mth
15 yr 7 mth
12 yr 2 mth
13 yr 8 mth
10 yr 6 mth
16 yr 11 mth
13 yr 7 mth

Mean:
12 yr 9 mth + 11 yr 4 mth + 14 yr 3 mth + 15 yr 7 mth + 12 yr 2 mth + 13 yr 8 mth + 10 yr 6 mth + 16 yr 11 mth + 13 yr 7 mth
= 153+136+171+187+146+164+126+203+163=1449(months)
1449months÷9=161months

Median:
9/2=4.5
4.5 round off = 5
5th Number
= Median
= 3 years 7 months

(b) The question does not ask for the mode. Why?
There are no similar number in the list of numbers.

JJ(:

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9. a)
Mean Age :
12 yr 9 mth = 153 mth
11 yr 4 mth = 136 mth
14 yr 3 mth = 171 mth
15 yr 7 mth = 187 mth
12 yr 2 mth = 146 mth
13 yr 8 mth = 164 mth
10 yr 6 mth = 126 mth
16 yr 11 mth = 203 mth
13 yr 7 mth = 163 mth
Total = 1449 mth
Average ( Mean ) = 1449 mth ÷ 9
= 161 mth
= 13 yr 5 mth
Ans : 13 yr 5 mth

Median Age :
In order of magnitude : 10 yr 6 mth, 11 yr 4 mth, 12 yr 2 mth, 12 yr 9 mth, 13 yr 7 mth, 13 yr 8 mth, 14 yr 3 mth, 15 yr 7 mth, 16 yr 11 mth.
The set of numbers contain 9 numbers so the 5th number is the median age.
Ans : 13 yr 7 mth
b) In the set of numbers, there are no two numbers which have the same number of months thus, there cannot be a mode as everything in that set of numbers only occurs once.

10. (a) Find the mean age and the median age of the following nine children.

Mean:Conversion of years into months....
12 yr 9 mth=153 months [(12*12)+9]
11 yr 4 mth=136 months[(11*12)+4]
14 yr 3 mth=171 months[(14*12)+3]
15 yr 7 mth=187 months[(15*12)+7]
12 yr 2 mth=146 months[(12*12)+2]
13 yr 8 mth=164 months[(13*12)+8]
10 yr 6 mth= 126 months[10*12)+6]
16 yr 11 mth=203 months[(16*12)+11]
13 yr 7 mth=163 months[(13*12)+7]

Total age:(153+136+171+187+146+164+126+203+163=1449 months

Mean age= 1449÷ 9
= 161 months
= 13 years and 5 months//

Median age:

Order of magnitude:
10 years 6 months, 11 years 4 months, 12 years 2 months, 12 years 9 months, 13 years 7 months, 13 years 8 months, 14 years 3 months, 15 years 7 months, 16 years 11 months.

There are a total of 9 ages so the median would be number....

9/4≈5

So the median of the set of numbers would be position 5 which is 13 years and 7 months.

(b) The question does not ask for the mode. Why?]

All the numbers in the set are all of different values, thus there would be no replication of any type, thus the mode is not needed as there would be no result as all of those numbers are all different.

11. (a)
12 + 11 + 14 + 15 + 12 + 13 + 10 + 16 + 13 = 116 yr
= 1392 mth
9 + 4 + 3 + 7 + 2 + 8 + 6 + 11 + 7 = 57 mth

Total mth 1392 + 57 = 1449 mth
Mean -> 1449 ÷ 9
= 161 mth
= 13 years 5 months

Order of Magnitude:
10 yr 6 mth, 11 yr 4 mth, 12 yr 2 mth, 12 yr 9 mth, 13 yr 7 mth, 13 yr 8 mth, 14 yr 3 mth, 15 yr 7 mth, 16 yr 11 mth

Median -> Position 5
= 13 years 7 months

(b)

Mode is the replica of the same number in statistic. For this case, there isn't one replica of any number, hence there isn't any use for mode.