SOLUTION
Given the question in the image, the following are the solution steps to answer the question.
STEP 1: Define the formula for range
[tex]\begin{gathered} \text{Range}=\text{Maximum-Minimum} \\ \text{Range}=Highest\text{ Value-Lowest Value} \end{gathered}[/tex]
STEP 2: Explain how to calculate the values from a pie chart
[tex]Value=percentage\times Total[/tex]
STEP 3: Calculate the housings for each of the THREE families
[tex]\begin{gathered} \text{Housing for }Family\text{ A} \\ \frac{19}{100}\times5400=19\times54=\text{\$}1026\text{ } \\ \\ \text{Housing for Family B} \\ \frac{16}{100}\times4675=\frac{16\times4675}{100}=\text{\$}748\text{ } \\ \\ \text{Housing for Family C} \\ \frac{14}{100}\times6675=\frac{14\times6675}{100}=\text{\$}934.50\text{ } \\ \\ \text{Range}=\text{\$}1026-\text{\$}748=\text{\$}278 \end{gathered}[/tex]
STEP 4: Calculate theRANGE for food for each of the THREE families
[tex]\begin{gathered} \text{Food for Family A} \\ \frac{14}{100}\times5400=14\times54=\text{\$}756\text{ } \\ \\ \text{Food for Family B} \\ \frac{16}{100}\times4675=\frac{16\times4675}{100}=\text{\$}654.50\text{ } \\ \\ \text{Food for Family C} \\ \frac{11}{100}\times6675=\frac{11\times6675}{100}=\text{\$}734.25\text{ } \\ \\ \text{Range}=\text{\$}756-\text{\$}654.50=\text{\$}101.50 \end{gathered}[/tex]
STEP 5: Calculate the RANGE for Childcare for each of the THREE families
[tex]\begin{gathered} \text{Childcare for Family A} \\ \frac{18}{100}\times5400=972 \\ \text{Childcare for Family B} \\ \frac{18}{100}\times4675=841.5 \\ \text{Childcare for Family C} \\ \frac{30}{100}\times6675=\frac{30\times6675}{100}=2002.5 \\ \\ \text{Range}=2002.5-841.5=\text{\$}1161\text{ } \end{gathered}[/tex]
STEP 6: Calculate the RANGE for Transportation for each of the THREE families
[tex]\begin{gathered} \text{Transportation for Family A} \\ \frac{11}{100}\times5400=11\times54=\text{\$}594 \\ \text{Transportation for Family B} \\ \frac{13}{100}\times4675=\frac{13\times4675}{100}=\text{\$}607.75\text{ } \\ \text{Transportation for Family C} \\ \frac{9}{100}\times6675=\frac{9\times6675}{100}=\text{\$}600.75 \\ \\ \text{Range}=\text{\$}607.75-\text{\$}594=\text{\$}13.75 \end{gathered}[/tex]
STEP 7: Calculate the RANGE for Insurance for each of the THREE families
[tex]\begin{gathered} \text{Insurance for Family A} \\ \frac{23}{100}\times5400=23\times54=\text{\$}1242 \\ \text{Insurance for Family B} \\ \frac{28}{100}\times4675=\frac{28\times4675}{100}=\text{\$}1309 \\ \text{Insurance for Family C} \\ \frac{20}{100}\times6675=\frac{20\times6675}{100}=\text{\$}1335 \\ \\ \text{Range}=\text{\$}1335-\text{\$}1242=\text{\$}93 \end{gathered}[/tex]
STEP 8: Calculate the RANGE for other needs for each of the THREE families
[tex]\begin{gathered} \text{Other n}eeds\text{ for Family A} \\ \frac{9}{100}\times5400=9\times54=\text{\$}486 \\ \text{Other n}eeds\text{ for Family B} \\ \frac{7}{100}\times4675=\frac{7\times4675}{100}=\text{\$}327.25 \\ \text{Other n}eeds\text{ for Family C} \\ \frac{6}{100}\times6675=\frac{6\times6675}{100}=\text{\$}400.5 \\ \\ \text{Range}=\text{\$}486-\text{\$}327.25=\text{\$}158.75 \end{gathered}[/tex]
STEP 9: Calculate the RANGE for Taxes for each of the THREE families
[tex]\begin{gathered} \text{Taxes for Family A} \\ \frac{5}{100}\times5400=5\times54=\text{\$}270 \\ \text{Taxes for Family B} \\ \frac{2}{100}\times4675=\frac{2\times4675}{100}=\text{\$}93.50 \\ \text{Taxes for Family C} \\ \frac{10}{100}\times6675=\frac{10\times6675}{100}=\text{\$}667.50\text{ } \\ \\ \text{Range}=\text{\$}667.50-\text{\$}93.50=\text{\$}574 \end{gathered}[/tex]
It can be seen from the steps above that Childcare category has a range of $1161.00 hence this is the category with the highest range of amounts.
ANSWER: Childcare category
