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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11 comments:

  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)

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  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.

    ReplyDelete
  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.

    ReplyDelete
  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.

    ReplyDelete
  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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  8. This comment has been removed by the author.

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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.

    ReplyDelete
  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.

    ReplyDelete
  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.

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