Question

I need to find the mean, mode, median, variance and standard deviation of this data:
101,102,100,110,109,109,108,109

Answer 1

Alright...so lets handle the mode and the median first..

mode = number that appears most often..
median = number in the middle when all numbers are aligned least to greatest...

what are those 2?

Answer 2

mode=109?

Answer 3

correct :)

Answer 4

median= 108? or 109?

Answer 5

Well lets see...
From least to greatest we have

\[\large 100, 101, 102, 108, 109, 109, 109, 110\]

So the middle would be

\[\large \cancel{100}, \cancel{101}, \cancel{102}, \color \red{108, 109}, \cancel{109}, \cancel{109},\cancel{ 110}\]

When we end up with 2 numbers...what we do ..is average them...add them together and divide by 2...what do we get?

Answer 6

108.5? :)

Answer 7

Perfect...

Alright...now...we want the mean...do you know how to find that?

Answer 8

THANKS, no :(

Answer 9

That's okay hun, that's what we're going to figure out :)

So the mean...you know how we just averaged those 2 numbers to find the median?

Well the mean...is the average of all your numbers...

So what you do...is add up every number you have....and then divide the answer you get by the number of numbers you added...

So here...add up all of them...and then divide by 8 since there are 8 numbers...what do we get?

Answer 10

118.5?

Answer 11

Hmm...I get something different but lets check I may have made a mistake...

\[\large \frac{100 + 101 + 102 + 108 + 109 + 109 + 109 + 110}{8} = \frac{848}{8} = 106\]

Look good? :)

Answer 12

you are so nice :) thankyou for your patience!

Answer 13

what about the variance :)?

Answer 14

mmhmm that's the next one...alright...so we have the mean right?

For the variance...we need to see how far away EACH number is from that mean...

So mean = 106

how far is 100 from 106? well it is -6 right?

continue on from there finding all the other numbers

so how far is:

100 from 106
101 from 106?
102 from 106?
108 from 106?
109 from 106?
109 from 106?
109 from 106?
110 from 106?

Answer 15

-5,-4,2,3,3,3,4? :):)

Answer 16

Great....so now...we take all those differences ...and square them...(raise the to the 2nd power) and then add all the results

so we have

\[\large (-6^2) + (-5^2) + (-4^2) + (2^2) + (3^2) + (3^2) +(3^2) + (4^2) \]

what do we get when we add all those?

Answer 17

92 right?

Answer 18

Im sorry 124!!

Answer 19

sorry hun I was away...umm lets see

\[\large (-6^2) + (-5^2) + (-4^2) + (2^2) + (3^2) + (3^2) +(3^2) + (4^2)\]
\[\large 36 + 25 + 16 + 4 + 9 + 9 + 9 + 16 = 241\]

Is what I get...hmm where did you go off?

Answer 20

I dont know, I think i am kind of tired, ive been doing math whole day. Sorry haha

Answer 21

but thank you so much for your patience! how can I find the standard deviation?

Answer 22

We aren't done with the variance :P

Alright...what we do now...with the 214 we have...is divide it by 8 ...(like we did with the mean)....so the variance will be

\[\large \frac{241}{8} = ?\]

Answer 23

30.12 :)?

Answer 24

ehh we'll keep the 5 at the end for now :P
\[\large Variance = 30.125\]

so ready for the standard deviation? its soooo difficult......(sarcasm) :P

Answer 25

HAHAHAH dont make fun of me hahaha you are the worst

Answer 26

ok please help me do my extra hard algebra so I can finally take a break

Answer 27

I would never hun :P

haha but alright...the standard deviation is just the square root of the Variance

\[\large \sqrt{30.125} = ?\]

Answer 28

5.48?

Answer 29

we'll round up to 5.49...but yes....And you are all done :)

Answer 30

THANK YOU SO MUCH!! would you please just answer one more thing?

Answer 31

of course :)

Answer 32

If I have to find the mode of decimal numbers, how can I find it if no numbers are repeated?

Answer 33

Then there would be no mode :)

Answer 34

12.5,12.7,14.9,11.3,11.7,10.9, is there no mode here? :)

Answer 35

There is none indeed :)

Answer 36

THANKYOU SO MUCH JOHN :) I really appreciate it!

Answer 37

Anytime hun :)