During which month was the percentage increase in sales from the previous month’s sales the highest?

We need to find which month had the highest percentage increase compared to the previous month.

Percentage increase formula:

$\dfrac{\text{New Value} - \text{Old Value}}{\text{Old Value}} \times 100$

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From the chart, we have most monthly sales figures. We need to find the missing values for 2016.

For Q2 2016 (Apr, May, Jun): Forms arithmetic progression with Jun $= 500$ and quarter total $= 1440$

Let Apr $= a$, May $= a + d$, Jun $= a + 2d = 500$

Sum: $3a + 3d = 1440$, so $a + d = 480$

Since $a + 2d = 500$, we get $d = 20$

Therefore: Apr $= 460$, May $= 480$, Jun $= 500$

For Q4 2016 (Oct, Nov, Dec): Forms arithmetic progression with Dec $= 840$ and quarter total $= 2280$

Let Oct $= b$, Nov $= b + e$, Dec $= b + 2e = 840$

Sum: $3b + 3e = 2280$, so $b + e = 760$

Since $b + 2e = 840$, we get $e = 80$

Therefore: Oct $= 680$, Nov $= 760$, Dec $= 840$

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Calculating percentage increases for each month:

2016:

• Feb: $\dfrac{320 - 240}{240} \times 100 = 33.33\%$

• Mar: $\dfrac{360 - 320}{320} \times 100 = 12.50\%$

• Apr: $\dfrac{460 - 360}{360} \times 100 = 27.78\%$

• May: $\dfrac{480 - 460}{460} \times 100 = 4.35\%$

• Jun: $\dfrac{500 - 480}{480} \times 100 = 4.17\%$

• Jul: $\dfrac{600 - 500}{500} \times 100 = 20.00\%$

• Aug: $\dfrac{680 - 600}{600} \times 100 = 13.33\%$

• Sep: $\dfrac{720 - 680}{680} \times 100 = 5.88\%$

• Oct: $\dfrac{680 - 720}{720} \times 100 = -5.56\%$ (decrease)

• Nov: $\dfrac{760 - 680}{680} \times 100 = 11.76\%$

• Dec: $\dfrac{840 - 760}{760} \times 100 = 10.53\%$

2017:

• Jan: $\dfrac{900 - 840}{840} \times 100 = 7.14\%$

• Feb: $\dfrac{960 - 900}{900} \times 100 = 6.67\%$

• Mar: $\dfrac{1020 - 960}{960} \times 100 = 6.25\%$

• Apr: $\dfrac{1080 - 1020}{1020} \times 100 = 5.88\%$

• May: $\dfrac{1140 - 1080}{1080} \times 100 = 5.56\%$

• Jun: $\dfrac{1200 - 1140}{1140} \times 100 = 5.26\%$

• Jul: $\dfrac{1320 - 1200}{1200} \times 100 = 10.00\%$

• Aug: $\dfrac{1400 - 1320}{1320} \times 100 = 6.06\%$

• Sep: $\dfrac{1480 - 1400}{1400} \times 100 = 5.71\%$

• Oct: $\dfrac{1560 - 1480}{1480} \times 100 = 5.41\%$

• Nov: $\dfrac{1620 - 1560}{1560} \times 100 = 3.85\%$

• Dec: $\dfrac{1680 - 1620}{1620} \times 100 = 3.70\%$

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The highest percentage increase is $33.33\%$ in February 2016.

Therefore, February 2016 had the highest percentage increase in sales from the previous month.