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2008
Thu
4
Sep
Miss Loi avatar

Miss Loi In Hostage Crisis!

(13)
Tuition given in the topic of E-Maths Tuition Questions from the desk of Miss Loi at 11:56 am (Singapore time)
The sigma better be small!

That σ better be small! *sweats*

While the lucky ones are enjoying life during this busy September term break, Miss Loi gets to ‘enjoy’ the cool night breeze in Novena as she leaves The Temple later & later each day, causing her to miss more & more episodes of the 11pm re-run of a Channel 8 drama involving a villainous cop.

As fate would have it, while she was walking to her car and well on her way to missing tonight’s crucial episode of the Channel 8 drama (where it’s revealed if the villainous cop managed to kill the lead actress), she crucially missed hearing the hurried footsteps of a villainous robber in hot pursuit by the police behind her.

And in an instant, a shell-shocked Miss Loi found herself locked in an utterly unromantic embrace with the burly robber, with his gun pointing at her head.

你们别过来啊!不然我一枪崩了她!(Stay away from me! Or I’ll blow her stupid aunty hairstyle into oblivion!)

… screamed the man in his Mainland Chinese accent.

Unbeknown to the robber, however, a police officer was communicating with her via her geeky bluetooth earpiece hidden behind that humongous aunty hairstyle, for he recognized Miss Loi and had resourcefully found her number earlier from a website known as https://www.exampaper.com.sg.

Don’t worry my Sexy Maths Tutor, our sharpshooters are standing by to take out your captor.

But unfortunately, our 100% bullseye-guaranteed 神枪手 Chief Marksman is still on holiday in Beijing after representing Singapore at the Olympics. And we’re now left with two backup sharpshooters …

The following table shows the results from the last shooting practice of the two sharpshooters:

Distance from center of target (mm)
Sergeant Bobo4791460100
Corporal Pa Jiao323547394045
  1. For each of them, calculate

    1. the mean distance from the center of the target,
    2. the standard deviation.
  2. Who should Miss Loi choose to be her sharpshooter? Explain briefly why.

As I’ve failed EMaths in my O-Levels, please let me know which sharpshooter would you prefer to save you from the robber!

Miss Loi is beginning to hurt from the gun barrel pressing on her forehead …

With the introduction of Standard Deviation to the New EMaths Syllabus this year, it’s almost certain that you’ll get to see a part of your question on Data Analysis that requires you to calculate the mean and standard deviation of two (or more) sets of data and THEN use these values to compare the sets of data with a brief explanation.

For this, besides recalling the right formula to use for the Standard Deviation S i.e.

S = sqrt{{Sigma(x - overline{x})^2}/n}
(for ungrouped data i.e. those without frequencies)

S = sqrt{{Sigma f(x - overline{x})^2}/{Sigma f}} or sqrt{ {Sigma fx^2}/{Sigma f} - ({Sigma fx}/{Sigma f})^2}
(for grouped data i.e. those with frequencies)

it’s important to understand that while the Mean represents the average value of a data set, the Standard Deviation represents the spread and consistency of the data set. In layman terms, you can consider standard deviation as the average deviation of the data set from its mean.

And once you’re convinced that standard deviation questions are pretty straightforward and not as scary as they sound, you can put yourself in a more advantageous position by familiarizing yourself with the SD or STAT MODE of your scientific calculator to cut down your calculation time and lower the risk of careless mistakes.

As all calculators are born unequal with different buttons, please refer to your calculator’s manual and practise how to use buttons like DATA, σn, RCL etc. to solve the above question and save Miss Loi in record time!

P.S. When using the SD/STAT Mode in your calculator, do make a habit of:

  • Clearing your data each time before entering a new set of data!
  • Verifying that you’ve not missed out any data in the set by checking the total number entered i.e. via the n button!

P.P..S. Actual buttons may differ on your calculator model.

頑張って!!!

Revision Exercise

To show that you have understood what Miss Loi just taught you from the centre, you must:

  1. Leave A Comment!
Comments & Reactions

12 Comments

  1. Daniel's Avatar
    Daniel commented in tuition class


    2008
    Sep
    4
    Thu
    6:55pm
     
    1

    Hi Ms Loi, I had such a kick out of reading your blog entry, at first I thought something really happened to you lol.

  2. NAOMI!'s Avatar
    NAOMI! commented in tuition class


    2008
    Sep
    5
    Fri
    12:17am
     
    2

    MISS LOI! My first time commenting!

    1 i) Bobo: 36.8mm
    Pajiao: 39.7mm (all to 3sf)

    ii) Bobo: 36.0mm
    Pajiao: 5.2mm (all also to 3sf)

    2) I think it should be Pajiao right. He has a more consistent record and his SD is lower than Bobo's.

    If I'm wrong, you can shoot me during class 😛

  3. Miss Loi's Avatar
    Miss Loi Friend Miss Loi on Facebook @MissLoi commented in tuition class


    2008
    Sep
    6
    Sat
    12:43am
     
    3

    Daniel: Something really did happened to Miss Loi - she was held hostage at the Omy S'pore Blog Awards Ceremony just now!

  4. Kenny's Avatar
    Kenny  commented in tuition class


    2008
    Sep
    6
    Sat
    1:17am
  5. Miss Loi's Avatar
    Miss Loi Friend Miss Loi on Facebook @MissLoi commented in tuition class


    2008
    Sep
    6
    Sat
    1:24am
     
    5

    Alright Naomi, time to 'shoot' you now since there wasn't time in class just now 🙂

    You answers are spot-on but how did you arrive at your answers? Did you do it the old-fashioned way i.e.

    Bobo's Mean overline{x}_1 = {47+9+1+4+60+100}/6 = 36.8mm

    Pa jiao's Mean overline{x}_2 = {32+35+47+39+40+45}/6 = 39.7mm

    For the standard deviations, you plot out the good o' table and calculate the values one by one:

    BoBoPa Jiao
    x1(x_1 - overline{x}_1)^2x2(x_2 - overline{x}_2)^2
    47103.45258.8
    9774.73521.8
    112844753.8
    41078390.444
    60546.7400.111
    10039904528.4
    Sigma (x_1 - overline{x}_1)^2 =7766.83Sigma (x_2 - overline{x}_2)^2 =163.33

    ∴ Bobo's standard deviation σ1
    = sqrt{{Sigma (x_1 - overline{x}_1)^2}/n} = sqrt{7766.83/6} = 36.0mm

    ∴ Pa Jiao's standard deviation σ2
    = sqrt{{Sigma (x_2 - overline{x}_2)^2}/n} = sqrt{163.33/6} = 5.2mm

    OR

    You simply set your super duper calculator to SD MODE and for BoBo:

    47 DATA
    9 DATA
    1 DATA
    4 DATA
    60 DATA
    100 DATA

    To get Bobo's mean you press x (the one with the overline{x}) on your calculator.
    To get Bobo's standard deviation you press σn on your calculator.

    SCR CLEAR your data before repeating the above steps for Pa Jiao.

    Which method do you think is faster and safer - especially for straightforward non-grouped (i.e. no frequencies) data like the ones in this question?

    N.B. Once again, actual buttons might differ in your specific calculator model.

  6. Miss Loi's Avatar
    Miss Loi Friend Miss Loi on Facebook @MissLoi commented in tuition class


    2008
    Sep
    6
    Sat
    1:39am
     
    6

    Lastly, even though Bobo has a slightly lower mean (i.e. better accuracy but not by much) than Pa Jiao, Bobo's much higher standard deviation means that his shooting consistency is abysmal i.e. he probably has trembling hands and his shots are all over the place.

    Miss Loi would rather trust Pa Jiao's relatively steadier hands!

    *Signals to Corporal Pa Jiao and quickly ducks head down by ~40mm*

    *Bullet is fired and burnt a hole straight through Miss Loi's big aunty hairstyle to hit the robber's gun off his hand*

    Miss Loi has been saved by Pa Jiao's shot!

    劇終
  7. ignorantsoup's Avatar
    ignorantsoup commented in tuition class


    2008
    Sep
    6
    Sat
    12:12pm
     
    7

    Miss Loi!! You're on the news again for the Omy blog awards..lol.. congrats, btw, abit slow but better late than never!

  8. Daniel's Avatar
    Daniel commented in tuition class


    2008
    Sep
    6
    Sat
    7:08pm
     
    8

    Congratulations Ms Loi on the Omy S'pore Blog Awards 🙂

  9. eastcoastlife's Avatar
    eastcoastlife commented in tuition class


    2008
    Sep
    6
    Sat
    7:32pm
  10. clarion-x's Avatar
    clarion-x commented in tuition class


    2008
    Sep
    7
    Sun
    12:14pm
     
    10

    wow. err... very honoured to be mentioned in your post.

  11. Miss Loi's Avatar
    Miss Loi Friend Miss Loi on Facebook @MissLoi commented in tuition class


    2008
    Sep
    7
    Sun
    11:43pm
     
    11

    Kenny: Bright spotlights and camera flashes make me dizzy 😛

    Thanks Soupie + Daniel + ECL. Finally finished the write-up on Friday's event. A pity they held it on one of Miss Loi's busiest weekends of the entire year *tired*

    Clarion: Good things in life must share mah 😉 Hope you didn't enjoy until you've forgotten all your formulae when school re-opens tomorrow!

  12. clarion-x's Avatar
    clarion-x commented in tuition class


    2008
    Sep
    9
    Tue
    7:24pm
     
    12

    Heheh... No lah. Full marks for EM trigo! XD

    (however the same feat could, unfortunately, not be repeated for AM. le sigh...)

One Reaction

  1.  
    13

    [...] that you know which buttons (e.g. DATA, σn etc.) to use in YOUR calculator for mean and standard deviation [...]

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