Step 1 — Find the sum: $\sum x_i = 5\times4=20$. Known three: $3+4+4=11$. So $x_4+x_5=9$.

Step 2 — Find sum of squares: Variance $=\frac{\sum x_i^2}{n}-\bar{x}^2 \Rightarrow \frac{\sum x_i^2}{5}-16=5.2 \Rightarrow \sum x_i^2=106$.

Known: $3^2+4^2+4^2=9+16+16=41$. So $x_4^2+x_5^2=65$.

Step 3 — Solve: $x_4+x_5=9$ and $x_4^2+x_5^2=65$.

$(x_4+x_5)^2=81 \Rightarrow 2x_4x_5=81-65=16 \Rightarrow x_4x_5=8$.

$(x_4-x_5)^2=(x_4+x_5)^2-4x_4x_5=81-32=49$

$|x_4-x_5|=\mathbf{7}$

The average number of pages in 1940 was 30. Twice this amount is $2 \times 30 = 60$ pages.

Check each year:

• 1940: 30 pages (not $\geq 60$) ✗
• 1950: 55 pages (not $\geq 60$) ✗
• 1960: 82 pages ($\geq 60$) ✓
• 1970: 70 pages ($\geq 60$) ✓
• 1980: 74 pages ($\geq 60$) ✓

Three years (1960, 1970, and 1980) had at least twice the 1940 average.

This two-blank sentence requires logical consistency between both answers.

Blank (i): The second clause tells us that “high” artists ceded (gave up) the depiction of everyday objects to commercial artists. This implies that depicting ordinary things was not part of serious American art. So Blank (i) = missing from.

• “Valued in” or “crucial to” would directly contradict the idea that high artists abandoned this type of depiction.

Blank (ii): The artists surrendered the depiction of objects from everyday life — these are ordinary and unremarkable objects, i.e., commonplace.

• “Beautiful” or “complex” do not match the subject of “everyday objects.”

Correct Answers: Blank (i) = A (missing from), Blank (ii) = E (commonplace).