We saw what happens to the mean when values are included or removed from the collection. What happens to the mean if every value in the collection increases by some fixed number?
Answer
The mean increases by that same fixed number.
Data 2, 4, 6 → mean 4
Add 5 to each → 7, 9, 11 → mean = 27 ÷ 3 = 9 = 4 + 5 ✓
Why it happens: the whole dot plot slides bodily along the number line. The gaps between the dots are untouched, so the point that balanced them before still balances them — it has just moved along with everything else. Nothing about the shape of the data changed, only its position.
Q2.
Consider the data: 8, 3, 10, 13, 4, 6, 7, 7, 8, 8, 5. Calculate its mean.
Tip: 79 ÷ 11 = 7.1818…, a repeating decimal. The book rounds it to 7.18, which is what the dot plot on page 106 shows.
Q3.
Now, consider this data with every value increased by 10: 18, 13, 20, 23, 14, 16, 17, 17, 18, 18, 15. What is its mean? Is there a quicker way to find out?
Answer
The mean is 17.18, and yes — there is a much quicker way.
Quick way: every value went up by 10, so the mean goes up by 10.
New mean = 7.18 + 10 = 17.18
Long way (as a check): new sum = 79 + (11 × 10) = 79 + 110 = 189
New mean = 189 ÷ 11 = 17.18 ✓
Why it happens: adding 10 to each of 11 values adds 11 × 10 = 110 to the total. Dividing that extra 110 among the same 11 values gives each an extra 10. On the dot plot the whole pattern has shifted 10 places to the right, and so has the balance point — the mean sits in exactly the same relative position among the dots.