Median problem Functional Skills level 2

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Jignesh77

Junior Member
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Dec 8, 2020
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What is the median of the numbers below?
212 244, 221 959, 214 194, 210 344, 221 645, 216 146
214 195
210 344
212 269
215 170
****The answer is 4 — if you put the numbers in order, the middle numbers are 214 194 and 216 146. The median is halfway between these two numbers. 214 194 + 216 146 = 430 340, 430 340 ÷ 2 = 215 170.

Good evening,

I am preparing for the Functional Skills Maths Level 2 as I want to do further studies. I am a matured student and I am struggling with certain topics as I am self-learning. I have uploaded the question image. Please refer to the above question and the given answer.The question is regarding "medians". The correct answer is the option 4( 215 170) but I don't understand at all how to work out the problem ( I don't understand the above explanation given- ****)

146, 194, 210, 212, 214, 216, 221, 221, 244, 344, 645, 959
I did 216 + 221/2 = 218.5
My answer is 218.5
There aren't any questions where the answers are given in pairs as given here: 215 170

I absolutely don't understand how did they worked out the answer:
****The answer is 4 — if you put the numbers in order, the middle numbers are 214 194 and 216 146. The median is halfway between these two numbers. 214 194 + 216 146 = 430 340, 430 340 ÷ 2 = 215 170.
I copied this after clicking review button.
"if you put the numbers in order, the middle numbers are 214 194 and 216 146"
I don't understand this part of the given answer and this explanation.

Please help me to understand this question.

I really appreciate your help.
Have a great weekend!
Kind Regards
Jignesh.
 
I think you are inserting commas where there aren't any. The first number is 212 244 ie 212 thousand, two hundred and 44.

It is usual to write this number with a space instead of a comma. In our younger days we would have written it as 212,244,
 
Harry_the_cat said:
I think you are inserting commas where there aren't any. The first number is 212 244 ie 212 thousand, two hundred and 44.

It is usual to write this number with a space instead of a comma. In our younger days we would have written it as 212,244,
Click to expand...
Thank you so much!
 
I have never seen this notation before. The most brilliant feline in the universe seems to find it quite familiar so I must be showing my provincial ignorance. But it has completely confused our poor student.

@Jignesh77

Here is the idea of a median. It is the number such that there are just as many numbers in the set that are NOT larger as there are NOT smaller.

We have a set of numbers. For example,
75
52
81
77
93

To find the median of that set, we first sort them by magnitude like this

52
75
77
81
93

52, 75, and 77 are each not greater than 77. That is three numbers not larger than 77. And notice that 77, 81, and 93 are each not less than 77. That is three numbers not smaller than 77. Therefore, 77 is the median.

This definition can break down if the number of elements in the set is an even number. For example

135
201
911
266
304
403

First, we sort

135
201
266
304
403
911

Therefore, there are two elements of the set that seem to meet the definition, namely 266 and 304. So we choose the arithmetic mean of those two numbers, namely 285, as the median.

If you think of a set as a sorted list, the median is a number such that half the list precedes the median and half follows it.
 
Harry_the_cat said:
I think you are inserting commas where there aren't any. The first number is 212 244 ie 212 thousand, two hundred and 44.

It is usual to write this number with a space instead of a comma. In our younger days we would have written it as 212,244,
Click to expand...
Yes; for documentation of this (international) fact, see https://en.wikipedia.org/wiki/Decimal_separator#Digit_grouping

Since 2003,[28] the use of spaces as separators (for example: 20 000 and 1 000 000 for "twenty thousand" and "one million") has been officially endorsed by SI/ISO 31-0 standard,[29] as well as by the International Bureau of Weights and Measures and the International Union of Pure and Applied Chemistry (IUPAC),[30][31] the American Medical Association's widely followed AMA Manual of Style, and the Metrication Board, among others.​

I'm guessing that the source is not local to @Jignesh77's country. In America we still use commas predominately, and in other countries even the commas may be used differently, as in India's 2,12,244 where we would write 212,244.

So the numbers are

212 244​
221 959​
214 194​
210 344​
221 645​
216 146​

and put in increasing order, they are

210 344​
212 244​
214 194​
216 146​
221 645​
221 959​

It wasn't immediately obvious to me, either, what it meant -- context is everything.
 
JeffM said:
I have never seen this notation before. The most brilliant feline in the universe seems to find it quite familiar so I must be showing my provincial ignorance. But it has completely confused our poor student.
Click to expand...
Where are you from JeffM? I'm in Australia. A lot of people here still use commas and groups of 3 digits, but as Dr P quotes from Wikipedia, spaces instead of commas are now "officially endorsed".
 
I am in the U.S., was trained as a historian, and worked first as a programmer and then for forty years as a banker.

Financial data in the U.S. is still invariably shown with commas in groups of threes.

Excel, which is the computer tool I use most now other than Word, goes nuts if you put spaces in numbers.

Learn something new every day.
 
I live in the UK and currently, I am preparing for the Functional Skills Level-2 Maths. I got Masters in Organic Chemistry but the course that I want to do requires this qualification in order to apply. I am really greatful for the help I get from this wonderful forum! Have a nice weekend!
 
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