A pie chart is constructed for the following data :

Month	January	February	March	April	May	June
Number of computers sold	500	700	840	750	890	820

What will be the difference between the central angles of the sectors representing the number of computers sold in March and January ?

Correct Answer: 27.2°

To find the difference between the central angles of the sectors representing the number of computers sold in March and January, we first calculate the total number of computers sold across all months.

Step 1: Calculate the total number of computers sold.

Total computers sold = 500 (January) + 700 (February) + 840 (March) + 750 (April) + 890 (May) + 820 (June)

$\text{Total}=500+700+840+750+890+820=4500$

Step 2: Find the difference in the number of computers sold between March and January.

Number of computers sold in March = 840

Number of computers sold in January = 500

$\text{Difference}=840-500=340$

Step 3: Calculate the difference between the central angles.

The total angle in a pie chart is equal to 360°.

The required difference between the central angles can be calculated using the formula:

$\text{Central Angle Difference}=\left(\frac{\text{Difference in Sales}}{\text{Total Sales}}\right)\times 360°$

Substituting the values into the formula:

$\text{Central Angle Difference}=\left(\frac{340}{4500}\right)\times 360°$

Simplifying the calculation:

$\text{Central Angle Difference}=\frac{340\times 360}{4500}=\frac{340\times 4}{50}=\frac{1360}{50}=27.2°$

Thus, the difference between the central angles of the sectors representing March and January is 27.2°.