Oh well … the original title of this post was supposed to be something else, something that would guarantee to propel Miss Loi to the very top of Singapore’s Community Meta Blog in the blink of an eye. But this would also subsequently guarantee her eternal banishment from the said meta blog community.

So in the end, it was not meant to be.

As she sadly packs the bikini back into her bag, Miss Loi has to voice out that she’s feeling a little unwell today. As such, no stressful question this time but instead here’s a really simple but vital one that tests your knowledge of your … umm …vital statistics:

After a particularly disasterous exam, some students were interrogated by their form teacher on how many hours they had spent surfing the Internet the night before. The following table shows the results.

No. of hours

0

1

2

3

No. of students

6

4

x

2

Write down the least possible value of x given that the mode is 2.

Write down the greatest possible value of x given that the median is 1.

If it was discovered that an additional two students has each spent 4 hours surfing the Internet on the previous day, find x if the mean is 1.5.

Now stop looking at your waist, hip or ahem!

Regardless on whether the students were lying or not, know your vital statistical definitions i.e. the THREE Ms of AVERAGES: Mode, Median and Mean, and you should be well on your way.

For the benefit of those who still can’t find their textbooks,

The mean of a set of n numbers x_{1}, x_{2} … x_{n} is (DUH!)

For grouped data, the mean is , and you’ll need to make sure you know which row in the table refers to the frequency before you proceed!

The median is the value of the middle term of a set of numbers arranged in order of magnitude. I.e. if there are n numbers, the middle term is the ()^{th} term. When there is an even number of terms, take the average of the two middle terms.

The mode of a set of numbers is the number with the highest frequency. It has no relation to French fashion, and once again, make sure you know which row refers to the frequency before you proceed.

This is one of those must-score Paper One questions! If you can’t even do this, you better see Miss Loi at her office where she’ll interrogate you on how many hours you spent surfing the Internet last night!

Ah kiroii ... at last someone who's focussed on the problem at hand!

1) Yup, the mode is the number/item with the highest frequency. In the table it's obvious frequency refers to the number of students, so in order for the mode to be 2, its frequency (i.e. x) must be at least 7.

2) Yup, to find the greatest x value, the median has to be the last 1 (highlighted below) i.e. the 10^{th} term.

So when you spread out the data:

0 0 0 0 0 0 1 1 1 1 2 ... 2 3 3

So in order for that 1 to be the median term, how many 2s must there be?

Hence solving the median formula (updated in the post),

And you'll get x = 7.

Well done! Now just one more last part to save you from Miss Loi's interrogation session at the office.

Hallo! Hor ny here! Sorry I have being absent for the past 10 years! I report to ur class today! Can or not arr??? Wau laueh! First day report to class & ur question so tought wan arr?? I have taken out my 1 meter ruler to measure whatever ladies is interested to know only to find out that is not the answer to ur question. So I think u have to give me private tuition!!

BTW tq very much for dropping by! Have a very nice day!

Hey Hum Sup Lou, all Jφss Sticks readers are of the purest minds, totally removed from all worldly lusts and temptations ... ain't this true everybody? 😉

A ton of confetti is coming your way Kiroii as you didn't fall into Miss Loi's trap (see the updated definition of mean in red above)!

As you can see this is a set of grouped data, so we cannot use the first formula to calculate your mean.

Since the mean is now , we get

Solving the above you'll get x = 6.

Once again Miss Loi can't emphasize enough the importance of knowing which row in the table refers to your x (the number of hours in this case) and which refers to your frequency (the number of students in this case). Which is probably what led to your careless mistake in your earlier comment 😛

Also many students get confused about the Σf in the bottom of the equation. They ended up (in this example) adding up 0+1+2+3+4 or simply dividing the whole expression by 5!

* Please refer to the relevant Ten-Year Series for the questions of these suggested solutions.

About Miss Loi

Miss Loi is a full-time private tutor in Singapore specializing in O-Level Maths tuition. Her life’s calling is to eradicate the terrifying LMBFH Syndrome off the face of this planet. For over years she has been a savior to countless students … [read more]

Gratitudes

I was confident for the ‘O’ Levels as I knew that Miss Loi had prepared me very well. I ended up achieving A1 for both EMath and AMath … [read more]

## 27 Comments

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OK I failed this one... your office where ah? LOL

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Don't bluff! You didn't even try!

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Got lah! I was thinking about it all the way to my car parked by the highway to on my hazard lights... cannot figure lah

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Hey Miss Loi!

Didn't know you are into using such headlines..hahaha..maybe you will become top 10 in ping.sg. Haha

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HighwayBlogger, think you were more worried about TP towing away your car than the vital stats. That's why you couldn't do!

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ignorantsoup,

Miss Loi's sure you'd realize this is just a play on the recent debate on misleading titles.

But unfortunately the strike-through on the title did not appear on Ping.sg. So now high chance this is going to be in top 10!

Die

lah! Think Miss Loi's gonna be banned soon! *begs for mercy*曜

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Hahaha. I can reveal her office for just a tiny sum.

*blackmail*

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oh naughty ms loi!

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1) least possible value of x = 7

2) greatest value of x = 7

3) do tomorrow its after 12midnight-__-

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Now that was a little... distracting. *coughs*

*Goes back to marking test papers... no you idiot that is NOT how you calculate daily temperature range!!!* *GROAN*

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Cris, don't think Miss Loi doesn't know what you think you know.

*Picks up phone to report blackmailing case to police*

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Mr Malique, the strike-through didn't appear in Ping.sg!

Jangan ban Miss Loi! Tolong jangan hate Miss Loi!

After all, you did learn something about statistics in this post didn't you?

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Ah kiroii ... at last someone who's focussed on the problem at hand!

1) Yup, the mode is the number/item with the highest frequency. In the table it's obvious frequency refers to the

number of students, so in order for the mode to be 2, its frequency (i.e.x) must be at least 7.2) Yup, to find the greatest

xvalue, the median has to be thelast1 (highlighted below) i.e. the 10^{th}term.So when you spread out the data:

0 0 0 0 0 0 1 1 1

12 ... 2 3 3So in order for

that1 to be the median term, how many 2s must there be?Hence solving the median formula (updated in the post),

And you'll get

x= 7.Well done! Now just one more last part to save you from Miss Loi's interrogation session at the office.

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not fair!! I was so focused on it! Just dunno the answer mah!

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Hai~Ren, stick to your trance. It helps Miss Loi a lot ... a least when she's driving 🙂

If only we could play those during

joss stickssession ... now that'll be so fun wouldn't it?曜

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Highway Man, you see ... in the exams no one can hear your protestations. The examiner can only see something called your working 🙂

In any case, there's one last part which is not yet solved. But Miss Loi thinks that's probably too simple for most people already.

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Hallo! Hor ny here! Sorry I have being absent for the past 10 years! I report to ur class today! Can or not arr??? Wau laueh! First day report to class & ur question so tought wan arr?? I have taken out my 1 meter ruler to measure whatever ladies is interested to know only to find out that is not the answer to ur question. So I think u have to give me private tuition!!

BTW tq very much for dropping by! Have a very nice day!

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Errr ... HAM, are you at the wrong class? The latest O-Level syllabus didn't mention anything about 1-meter rulers. Tsk.

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Oh I C! Sorry sorry teacher! Enter the wrong class ( I think I even enter the wrong school! ). I should be in pokeing class advance level! He! He!

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OhI Sorry (just saw ur message at myblog) if I 'polluted' ur clean site ( now cleaning it with datol ). Goodbye,cheer & have a nice day!

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Miss Loi..116 pongs already..hahahaha

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eh for de 3rd question is x 1.5 >.< de ans is queer though how can there be 1.5 students>.

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NO crap HALT fer de 3rd question x is 6!~ >.< careless mistake

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Hey Hum Sup Lou, all Jφss Sticks readers are of the purest minds, totally removed from all worldly lusts and temptations ... ain't this true everybody? 😉

曜

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Ignorantsoup, even a sexy Maths tutor can't beat your NUS idiot!

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A ton of confetti is coming your way Kiroii as you didn't fall into Miss Loi's trap (see the updated definition of

meanin red above)!As you can see this is a set of

grouped data, so we cannot use the first formula to calculate your mean.Since the mean is now , we get

Solving the above you'll get

x= 6.Once again Miss Loi can't emphasize enough the importance of knowing which row in the table refers to your

x(the number of hours in this case) and which refers to yourfrequency(the number of students in this case). Which is probably what led to your careless mistake in your earlier comment 😛Also many students get confused about the Σ

fin the bottom of the equation. They ended up (in this example) adding up 0+1+2+3+4 or simply dividing the whole expression by 5!曜

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While we're at this, there's another statistical question back in the days when this blog was relatively quieter.

It requires yet another mean formula that's not listed here (you'll need to

assumesomething).As it is, it's still unsolved so do head over there and try it if you can 😉