Question

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

Answer 1

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

Answer 2

16

Answer 3

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

Answer 4

0?

Answer 5

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 ?

Answer 6

the key is 2

Answer 7

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

Answer 8

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

Answer 9

a 6

Answer 10

so what is the 9th number ?

Answer 11

6

Answer 12

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

Answer 13

oh... 62?

Answer 14

almost. the 2 goes first

Answer 15

so 26

Answer 16

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 ?

Answer 17

23?

Answer 18

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.

Answer 19

honestly... i'm a little confused.

Answer 20

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

Answer 21

Here is an example, with the 0 in red

Answer 22

ok

Answer 23

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)

Answer 24

is the 9th number 20? 0
2^

Answer 25

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

Answer 26

ok

Answer 27

which of the choices *might* be the answer ?

Answer 28

D?

Answer 29

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

Answer 30

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

Answer 31

and what about choice B ?

Answer 32

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

Answer 33

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 ?

Answer 34

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

Answer 35

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

Answer 36

d

Answer 37

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

Answer 38

i think the total is 61

Answer 39

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

Answer 40

the key.

Answer 41

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 ?

Answer 42

added 10 to them

Answer 43

the first two I got from
0 | 6 8

which is "short" for 06 08

Answer 44

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.

Answer 45

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

Answer 46

10, 10, 10, 16 , 18 and 19

Answer 47

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

Answer 48

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

Answer 49

yes,
and finally the last row

Answer 50

20, 21, 22, 22, 24

Answer 51

the last row starts with
3 |

use the "3" (not a 2)

Answer 52

361/16?

Answer 53

361/16?

Answer 54

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

Answer 55

i got 22.5625

Answer 56

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

Answer 57

ok, so would the answer be D?

Answer 58

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

Answer 59

i was wrong, the answer is B

Answer 60

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

Answer 61

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

Answer 62

This problem was a lot of work. Good job.

Answer 63

thanks again :D

Answer 64

yw