**Answer:**

The mean will increase more than the median, but both will increase.

[third option listed]

**Step-by-step explanation:**

the <em>median </em>of a data set is the number in the middle [when listed from lowest to highest in value]

1 2 3 4 5 6 **7** 8 9 10 11 12 13

is the current median

let's consider what adding 12 would mean--it would mean that we move the median slightly higher [further along in the data set] because there are more numbers (but let's try this out to confirm:)

1 2 3 4 5 6 **7 8** 9 10 11 12 12 13

[if a median placement is shared between two numbers, the mean/average of those two numbers is taken, and that is considered to be the median]

so, **7.5 **is the current median

**(this is an increase of 0.5)**

--

the <em>mean</em> of a data set is what we commonly refer to as the "average"

[you find this value by adding all of the numbers in the data set together and dividing by the number of terms in the data set]

1 2 3 4 5 6 7 8 9 10 11 12 13

mean of original data set:

1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 + 11 + 12 + 13 [= 91]

_______________________________________

13

[91 ÷ 13 = 7]

because our number is <em>greater </em>than our original mean [12 > 7], we know that the mean must increase:

[91 + 12 = 103]

[103 ÷ 14 ≈ 9.36]

**[we had an increase of 2.36]**

so, median increased by 0.5, mean increased by 2.36

**so, both values increased, whilst the mean increased by **<em>**more **</em>**than the median **[as to be expected]

you could also express this as **"The mean will increase more than the median, but both will increase." **[third option listed]

hope this helps!! :)