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

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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

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1 Attachment
  • phi
Can you count how many numbers are in your "leaf plot" ?
16

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Other answers:

  • phi
now count, starting from the top, until you get to number 8 can you do that ?
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 ?
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) ?
a 6
  • phi
so what is the 9th number ?
6
  • phi
not just 6. remember to "tag on" the key number
oh... 62?
  • phi
almost. the 2 goes first
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 ?
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.
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
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)
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
ok
  • phi
which of the choices *might* be the answer ?
D?
  • phi
what does choice D say about the median (I can't read it)
The mean is decreased by about 1.2 and the median is decreased by 3.
  • phi
and what about choice B ?
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
i know the simple way lol. add up all the numbers and divide by the amount of numbers. (total divided by 16)
d
  • phi
that is how you do it. but first we need to write the numbers 06+08+12+15+18+ etc
i think the total is 61
  • phi
it is more than that. what are the 16 numbers you are using ?
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 ?
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 ?
10, 10, 10, 16 , 18 and 19
  • phi
almost. but you put a 1 in front. You should be the "key number" in front
so... 20, 20, 20, 26, 28, 29?
  • phi
yes, and finally the last row
20, 21, 22, 22, 24
  • phi
the last row starts with 3 | use the "3" (not a 2)
361/16?
361/16?
  • phi
06+08+12+15+18+20+20+20+26+28+29+30+31+32+32+34 then divide by 16
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=
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
i was wrong, the answer is B
  • phi
Yes, choice B is closest. it says the mean goes down by about 0.7
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.
thanks again :D
  • phi
yw

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