For the data shown in the stem-and-leaf plot, what is the effect on the mean and median of adding the value 10 to the data set?
A.
The mean is decreased by about 0.7 and the median is decreased by 2.
B.
The mean is decreased by about 0.7 and the median is decreased by 3.
C.
The mean is decreased by about 1.2 and the median is decreased by 2.
D.
The mean is decreased by about 1.2 and the median is decreased by

- anonymous

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- anonymous

##### 1 Attachment

- phi

Can you count how many numbers are in your "leaf plot" ?

- anonymous

16

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## More answers

- phi

now count, starting from the top, until you get to number 8
can you do that ?

- anonymous

0?

- phi

yes, but that "0" by itself is short for a number. the key tells you how to figure out the number. can you do that ?

- anonymous

the key is 2

- phi

yes, 2, and the "0" means your number
is 20

- phi

next, what is the 9th number? (one past the 8th number)
?

- anonymous

a 6

- phi

so what is the 9th number ?

- anonymous

6

- phi

not just 6. remember to "tag on" the key number

- anonymous

oh... 62?

- phi

almost. the 2 goes first

- anonymous

so 26

- phi

yes. the "median" is the middle number.
when we have 16 numbers, 8 numbers are below the median and 8 are above it.
to find the median we find the average of the 8th number 20 and the 9th number 26
in other words, the median is
(20+26)/2 = what ?

- anonymous

23?

- phi

yes. 23 is the median of that data.
now to answer the question
median of adding the value 10 to the data set?
we have to add "10" to the data , and then find the median of those numbers.

- anonymous

honestly... i'm a little confused.

- phi

to "put 10" into your data
you put a 0 in the row with 1 as the "key" number.
the 0 goes in front of the other numbers. The 0 goes before 2 5 8

- phi

Here is an example, with the 0 in red

##### 1 Attachment

- anonymous

ok

- phi

now we find the median. Because we added an extra number, we now have 17 numbers
the median is the middle number: 8 below the median, 9th number is the median, 8 numbers above.
in other words, start at the top and count until you get the 9th number. (don't leave out the 0 we added)

- anonymous

is the 9th number 20? 0
2^

- phi

yes. and that is the median of the new data set
so we first got 23 as the median
now we get 20 as the median
the median went down by 3

- anonymous

ok

- phi

which of the choices *might* be the answer ?

- anonymous

D?

- phi

what does choice D say about the median (I can't read it)

- anonymous

The mean is decreased by about 1.2 and the median is decreased by 3.

- phi

and what about choice B ?

- anonymous

i'm trying to figure out the mean, but i don't know.

- phi

so the answer might be B or D (but not A or C)
to decide, we need to find the mean (the average) of the 16 numbers
that is a bit painful. Do you know how to do that ?

- phi

you make a list of the numbers by "tagging on" to the front, the key number

- anonymous

i know the simple way lol. add up all the numbers and divide by the amount of numbers. (total divided by 16)

- David27

d

- phi

that is how you do it.
but first we need to write the numbers
06+08+12+15+18+ etc

- anonymous

i think the total is 61

- phi

it is more than that. what are the 16 numbers you are using ?

- anonymous

the key.

- phi

remember the "chart" they show you is using a short cut to write the numbers
the first 5 numbers are
06+08+12+15+18
do you see how I got those ?

- anonymous

added 10 to them

- phi

the first two I got from
0 | 6 8
which is "short" for 06 08

- phi

then the next 3 I got from
1 | 2 5 8
which is short for the numbers 12 15 18
and we want to add them up, so the first 5 numbers added together are
06+08+12+15+18
but we need the rest of the numbers.

- phi

what are the numbers you get from the 3rd row ?

- anonymous

10, 10, 10, 16 , 18 and 19

- phi

almost. but you put a 1 in front. You should be the "key number" in front

- anonymous

so... 20, 20, 20, 26, 28, 29?

- phi

yes,
and finally the last row

- anonymous

20, 21, 22, 22, 24

- phi

the last row starts with
3 |
use the "3" (not a 2)

- anonymous

361/16?

- anonymous

361/16?

- phi

06+08+12+15+18+20+20+20+26+28+29+30+31+32+32+34
then divide by 16

- anonymous

i got 22.5625

- phi

when we add 10 the sum goes from 361 to 371
and the average of the 17 numbers is
371/17=

- anonymous

ok, so would the answer be D?

- phi

the old mean is 22.5625
the new mean (after adding in 10) is 21.8235
the new mean went down by 22.56 - 21.82 = 0.74

- anonymous

i was wrong, the answer is B

- phi

Yes, choice B is closest. it says the mean goes down by about 0.7

- anonymous

ok, thank you sooooo much. i would have figured it out on my own! :D :D :D :D :D :D :D :D

- phi

This problem was a lot of work. Good job.

- anonymous

thanks again :D

- phi

yw

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