Hey there! Sign in to join this conversationNew here? Join for free
    • Thread Starter
    Offline

    11
    ReputationRep:
    Apples are Normally distributed by mass. M~N(110, 15^2)

    A medium sized apple is:

    90 <= x < 120

    Question is:

    Find the median mass of a medium size apple

    My attempt was:

    (120 + 90) / 2 = 105g

    Seemed reasonable.

    But in fact answer is 107g. Why and how?
    Offline

    16
    ReputationRep:
    (Original post by acomber)
    Apples are Normally distributed by mass. M~N(110, 15^2)

    A medium sized apple is:

    90 <= x <= 120

    Question is:

    Find the median mass of a medium size apple

    My attempt was:

    (120 + 90) / 2 = 105g

    Seemed reasonable.

    But in fact answer is 107g. Why and how?
    Why would that be correct

    Your working assumes an even distribution between 90 and 120 but that is not the case
    • Thread Starter
    Offline

    11
    ReputationRep:
    (Original post by TenOfThem)
    Why would that be correct

    Your working assumes an even distribution between 90 and 120 but that is not the case
    But I thought the median was the middle value?
    Offline

    16
    ReputationRep:
    (Original post by acomber)
    But I thought the median was the middle value?
    Yes, it is, but you do not just have 2 apples

    Is the median of 1,2,2,7,7,8,8,8,9 the same as (1+9)/2
    • Study Helper
    • Welcome Squad
    Offline

    18
    ReputationRep:
    Study Helper
    Welcome Squad
    (Original post by acomber)
    But I thought the median was the middle value?
    Yes, but if you have: 12, 12, 15, 24. What's the median?
    • Thread Starter
    Offline

    11
    ReputationRep:
    (Original post by TenOfThem)
    Yes, it is, but you do not just have 2 apples

    Is the median of 1,2,2,7,7,8,8,8,9 the same as (1+9)/2
    I see...

    Can you give me a hint on how to calculate then?
    • Thread Starter
    Offline

    11
    ReputationRep:
    (Original post by Andy98)
    Yes, but if you have: 12, 12, 15, 24. What's the median?
    (12+15)/2 = 13.5.

    So I have to find out roughly the middle in the distribution? How do I do that?
    Offline

    16
    ReputationRep:
    (Original post by acomber)
    I see...

    Can you give me a hint on how to calculate then?
    I am sure there is an annoying formula somewhere
    Offline

    21
    ReputationRep:
    (Original post by acomber)
    (12+15)/2 = 13.5.

    So I have to find out roughly the middle in the distribution? How do I do that?
    You first have to find the area between when x=120 and x=90 then the median will lie at half that area from both x=90 and x=120 use z=(x-mean)/standard deviation to calculate the areas using tables and then you will have to work backwards to find value of x when that area is the area at x=120 -half the area between x=120 and x=90 and then rearrange for x.
    • Thread Starter
    Offline

    11
    ReputationRep:
    (Original post by Dalek1099)
    You first have to find the area between when x=120 and x=90 then the median will lie at half that area from both x=90 and x=120 use z=(x-mean)/standard deviation to calculate the areas using tables and then you will have to work backwards to find value of x when that area is the area at x=120 -half the area between x=120 and x=90 and then rearrange for x.
    OK got it.

    Area up to 90 = 0.0913
    Area under 90 to 120 = 0.6564

    Half area between 90 to 120 is median value = 0.6564/2 = 0.3282

    0.0913 + 0.3282 = 0.4195

    We now just find the z value for 0.4195

    phi(z) = 0.4195

    tables only give +ve z so lookup for 1-0.4195=0.5805, that z = 0.2045

    Therefore, z for our area = -0.2045

    -0.2045 = (x - 110)/15 x = 106.93 ~ 107.

    Perfect.

    Thanks.
 
 
 
  • See more of what you like on The Student Room

    You can personalise what you see on TSR. Tell us a little about yourself to get started.

  • Poll
    Has a teacher ever helped you cheat?
    Useful resources

    Make your revision easier

    Maths

    Maths Forum posting guidelines

    Not sure where to post? Read the updated guidelines here

    Equations

    How to use LaTex

    Writing equations the easy way

    Student revising

    Study habits of A* students

    Top tips from students who have already aced their exams

    Study Planner

    Create your own Study Planner

    Never miss a deadline again

    Polling station sign

    Thinking about a maths degree?

    Chat with other maths applicants

    Can you help? Study help unanswered threads

    Groups associated with this forum:

    View associated groups
  • See more of what you like on The Student Room

    You can personalise what you see on TSR. Tell us a little about yourself to get started.

  • The Student Room, Get Revising and Marked by Teachers are trading names of The Student Room Group Ltd.

    Register Number: 04666380 (England and Wales), VAT No. 806 8067 22 Registered Office: International House, Queens Road, Brighton, BN1 3XE

    Write a reply...
    Reply
    Hide
    Reputation gems: You get these gems as you gain rep from other members for making good contributions and giving helpful advice.