Table Analysis - Calculating

For each of the following statements, select Yes if the statement can be shown to be true based on the information in the table. Otherwise, select No.

That's right!

First calculate the range for goods. Sort the column titled "Goods" and find the extreme values: notice that the greatest value is 8,903 and the smallest is -9,483. Subtract these numbers to find the range.

$$8{,}903 - (-9{,}483) = 18{,}386$$

Now find the range for services in the same way. If you sort the column titled "Services," you get that the extreme values are 3,501 and -1,384. Subtract these values.

$$3{,}501 - (-1{,}384) = 4{,}885$$

Finally, divide these ranges to see how much greater the range for goods is. You can Ballpark this value as follows:

$$\frac{18{,}368}{4{,}885} \approx \frac{20{,}000}{5{,}000} = 4$$

Therefore, the range of balances of goods is about four times (not five times) the range of balances of services, so the statement is false.

You are correct!

Use the column titled "Services" to find the US trade balance of services in 1971 and 1976.

• 1971: 958

• 1976: 3,401

Then use the formula below to calculate the percent change.

$$\displaystyle\mbox{Percent change} = \frac{\mbox{Difference}}{\mbox{Original}} \cdot 100\%$$ For this formula, the difference is $$3{,}401 - 958 = 2{,}443$$ and the original value is 958. Plug these numbers into the formula and __Ballpark__ its value. $$\frac{2{,}443}{958} \approx \frac{2{,}500}{1{,}000} = 2.5 ~\rightarrow~ 250\%$$ Therefore, the statement is false. The percent change is closer to 250%.

Great!

By the values in the column titled "Total," the total trade balance decreased from $2,939,000,000 in 1966 to $2,604,000,000 in 1967.

In the description, the trade balance is described as being the value of exports minus the value of imports. Thus, it is possible that a decrease in exports caused the decrease in the trade balance. But it is also possible that it was caused by the value of imports increasing, and the value of exports stayed the same or even increased.

For instance, one possibility is the following:

• In 1966, exports were $4,000,000,000 and imports were $1,061,000,000, so the balance was $2,939,000,000.

• In 1967, exports were $4,100,000,000 and imports were $1,496,000,000, so the balance was $2,604,000,000.

In this example, notice that the value of exports increased from 1966 to 1967. Therefore, the statement cannot be shown to be true, so the answer is No.

Incorrect.

First calculate the range for goods. Sort the column titled "Goods" and find the extreme values: notice that the greatest value is 8,903 and the smallest is -9,483. Subtract these numbers to find the range.

$$8{,}903 - (-9{,}483) = 18{,}386$$

Now find the range for services in the same way. If you sort the column titled "Services," you get that the extreme values are 3,501 and -1,384. Subtract these values.

$$3{,}501 - (-1{,}384) = 4{,}885$$

Finally, divide these ranges to see how much greater the range for goods is. You can Ballpark this value as follows:

$$\frac{18{,}368}{4{,}885} \approx \frac{20{,}000}{5{,}000} = 4$$

Therefore, the range of balances of goods is about four times (not five times) the range of balances of services, so the statement is false.

Incorrect.

Use the column titled "Services" to find the US trade balance of services in 1971 and 1976.

• 1971: 958

• 1976: 3,401

Then use the formula below to calculate the percent change. $$\displaystyle\mbox{Percent change} = \frac{\mbox{Difference}}{\mbox{Original}} \cdot 100\%$$ For this formula, the difference is $$3{,}401 - 958 = 2{,}443$$ and the original value is 958. Plug these numbers into the formula and __Ballpark__ its value. $$\frac{2{,}443}{958} \approx \frac{2{,}500}{1{,}000} = 2.5 ~\rightarrow~ 250\%$$ Therefore, the statement is false. The percent change is closer to 250%.

Incorrect.

By the values in the column titled "Total," the total trade balance decreased from $2,939,000,000 in 1966 to $2,604,000,000 in 1967.

In the description, the trade balance is described as being the value of exports minus the value of imports. Thus, it is possible that a decrease in exports caused the decrease in the trade balance. But it is also possible that it was caused by the value of imports increasing, and the value of exports stayed the same or even increased.

For instance, one possibility is the following:

• In 1966, exports were $4,000,000,000 and imports were $1,061,000,000, so the balance was $2,939,000,000.

• In 1967, exports were $4,100,000,000 and imports were $1,496,000,000, so the balance was $2,604,000,000.

In this example, notice that the value of exports increased from 1966 to 1967. Therefore, the statement cannot be shown to be true, so the answer is No.

Yes

No

Yes

No

Yes

No