**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

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

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**For complete and clear solutions, please see Joshua Ma's & Calvin's set of solutions.**

MEAN:

ReplyDeleteYears:

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)

Mean

ReplyDeleteConvert 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.

Find the mean age and the median age of the following nine children.

ReplyDeleteMEAN: 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.

This comment has been removed by the author.

ReplyDelete(a)

ReplyDelete12 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.

12 yr 9 mth

ReplyDelete11 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.

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

ReplyDelete12 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(:

This comment has been removed by the author.

ReplyDeletea)

ReplyDeleteMean 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.

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

ReplyDeleteMean: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.

(a)

ReplyDelete12 + 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.