Ask a New Question
Menu

The table shows the amount of rainfall recorded over the first 10 months of a year. Draw a line plot, if needed.

Amount of Rainfall (inches)
1 3/4, 2 1/2, 3/4, 1 1/4, 2, 1 1/2, 2 3/4, 3 1/4, 1, 2 3/4

Part A
What is the difference between the greatest and least amounts of rainfall in a month?

(1 point)
Responses

1 1/4
inches

1 1 4 inches

1 1/2
inches

1 1 2 inches

2 1/2
inches

2 1 2 inches

2 3/4
inches

2 3 4 inches
Question 2
Part B
If the last 2 months of the year each have the most common amount of rainfall, how much more rain will fall for the year?

(1 point)
Responses

4 1/2
inches

4 1 2 inches

4 3/4
inches

4 3 4 inches

5 1/4
inches

5 1 4 inches

5 1/2
inches

5 1 2 inches
Skip to navigation

1 answer

Let's analyze the data provided and answer the questions step by step.

Given Amounts of Rainfall (in inches):

  1. \(1 \frac{3}{4}\)
  2. \(2 \frac{1}{2}\)
  3. \(\frac{3}{4}\)
  4. \(1 \frac{1}{4}\)
  5. \(2\)
  6. \(1 \frac{1}{2}\)
  7. \(2 \frac{3}{4}\)
  8. \(3 \frac{1}{4}\)
  9. \(1\)
  10. \(2 \frac{3}{4}\)

Part A: Difference Between the Greatest and Least Amounts of Rainfall

  1. Convert the amounts to improper fractions:

    • \(1 \frac{3}{4} = \frac{7}{4}\)
    • \(2 \frac{1}{2} = \frac{5}{2} = \frac{10}{4}\)
    • \(\frac{3}{4} = \frac{3}{4}\)
    • \(1 \frac{1}{4} = \frac{5}{4}\)
    • \(2 = \frac{8}{4}\)
    • \(1 \frac{1}{2} = \frac{3}{2} = \frac{6}{4}\)
    • \(2 \frac{3}{4} = \frac{11}{4}\)
    • \(3 \frac{1}{4} = \frac{13}{4}\)
    • \(1 = \frac{4}{4}\)
    • \(2 \frac{3}{4} = \frac{11}{4}\)

  2. Find the greatest and least amounts:

    • Greatest amount: \(3 \frac{1}{4} = \frac{13}{4} \) inches
    • Least amount: \(\frac{3}{4}\) inches

  3. Calculate the difference: \[ \frac{13}{4} - \frac{3}{4} = \frac{10}{4} = 2 \frac{1}{2} \text{ inches} \]

Part A Answer:

The difference between the greatest and least amounts of rainfall is \(2 \frac{1}{2}\) inches.

Part B: Most Common Amount of Rainfall

List the amounts and how many times each occurs:

  • \(1 \frac{3}{4}\): 1 time
  • \(2 \frac{1}{2}\): 1 time
  • \(\frac{3}{4}\): 1 time
  • \(1 \frac{1}{4}\): 1 time
  • \(2\): 1 time
  • \(1 \frac{1}{2}\): 1 time
  • \(2 \frac{3}{4}\): 2 times
  • \(3 \frac{1}{4}\): 1 time
  • \(1\): 1 time

The most common amount is \(2 \frac{3}{4}\) inches (2 times).

  1. Calculate the total rainfall for the first 10 months:

\[ 1 \frac{3}{4} + 2 \frac{1}{2} + \frac{3}{4} + 1 \frac{1}{4} + 2 + 1 \frac{1}{2} + 2 \frac{3}{4} + 3 \frac{1}{4} + 1 + 2 \frac{3}{4} \]

Converting to improper fractions and calculating:

  • \(1 \frac{3}{4} = \frac{7}{4}\)
  • \(2 \frac{1}{2} = \frac{5}{2} = \frac{10}{4}\)
  • \(\frac{3}{4} = \frac{3}{4}\)
  • \(1 \frac{1}{4} = \frac{5}{4}\)
  • \(2 = \frac{8}{4}\)
  • \(1 \frac{1}{2} = \frac{3}{2} = \frac{6}{4}\)
  • \(2 \frac{3}{4} = \frac{11}{4}\) (occurs twice)
  • \(3 \frac{1}{4} = \frac{13}{4}\)
  • \(1 = \frac{4}{4}\)

Now summing them up:

  1. There are two occurrences of \(2 \frac{3}{4} = \frac{11}{4}\): \[ \text{Total} = \left(\frac{7}{4} + \frac{10}{4} + \frac{3}{4} + \frac{5}{4} + \frac{8}{4} + \frac{6}{4} + 2 \times \frac{11}{4} + \frac{13}{4} + \frac{4}{4}\right) \]

  2. This equals:

\[ \frac{7 + 10 + 3 + 5 + 8 + 6 + 11 + 11 + 4}{4} = \frac{66}{4} = 16.5 \text{ inches} \]

Finally, add the two extra months of \(2 \frac{3}{4} = \frac{11}{4}\):

\[ 2 \times \frac{11}{4} = \frac{22}{4} = 5 \frac{1}{2} \text{ inches.} \]

Adding this to our total rainfall:

\[ 16.5 + 5.5 = 22 \text{ inches} \]

Part B Answer:

The additional amount of rainfall for the year will be \(5 \frac{1}{2}\) inches.