Question

marcy and her friends experimented with different types and amounts of laundry detergents. they ran some loads of laundry, hoping to find the perfect combination of fresh smell and cleanliness! amount of laundry detergent (tablespoons) $1\frac{1}{4}$ $1$ $2$ $1\frac{1}{4}$ $2$ $1\frac{3}{4}$ $1\frac{1}{2}$ $2$ $1\frac{3}{4}$ $1\frac{1}{2}$ $1\frac{3}{4}$ $1\frac{1}{4}$ $1$ use the data in the list to complete the line plot below. click to select the x’s. to clear a column, click on the number line below it. amount of laundry detergent line plot with xs and number line: $1$, $1\frac{1}{4}$, $1\frac{1}{2}$, $1\frac{3}{4}$, $2$ tablespoons

Explanation:

To solve this, we first count the frequency of each amount of laundry detergent:

Step 1: Count occurrences of \( 1 \)

Looking at the data: \( 1, 1 \) (wait, let's list all data points: \( 1\frac{1}{4}, 1, 2, 1\frac{1}{4}, 2, 1\frac{3}{4}, 1\frac{1}{2}, 2, 1\frac{3}{4}, 1\frac{1}{2}, 1\frac{3}{4}, 1\frac{1}{4}, 1 \))
Wait, let's list each:

• \( 1 \): Let's check the list. The values are: \( 1\frac{1}{4} \), \( 1 \), \( 2 \), \( 1\frac{1}{4} \), \( 2 \), \( 1\frac{3}{4} \), \( 1\frac{1}{2} \), \( 2 \), \( 1\frac{3}{4} \), \( 1\frac{1}{2} \), \( 1\frac{3}{4} \), \( 1\frac{1}{4} \), \( 1 \). Wait, maybe I missed, let's count again:

Wait the data list (from the table):

1. \( 1\frac{1}{4} \)
2. \( 1 \)
3. \( 2 \)
4. \( 1\frac{1}{4} \)
5. \( 2 \)
6. \( 1\frac{3}{4} \)
7. \( 1\frac{1}{2} \)
8. \( 2 \)
9. \( 1\frac{3}{4} \)
10. \( 1\frac{1}{2} \)
11. \( 1\frac{3}{4} \)
12. \( 1\frac{1}{4} \)
13. \( 1 \)

Now count each:

• \( 1 \): positions 2, 13 → 2 times
• \( 1\frac{1}{4} \): positions 1, 4, 12 → 3 times
• \( 1\frac{1}{2} \): positions 7, 10 → 2 times
• \( 1\frac{3}{4} \): positions 6, 9, 11 → 3 times
• \( 2 \): positions 3, 5, 8 → 3 times

Step 2: Mark X's on the line plot

• For \( 1 \): place 2 X's above \( 1 \)
• For \( 1\frac{1}{4} \): place 3 X's above \( 1\frac{1}{4} \)
• For \( 1\frac{1}{2} \): place 2 X's above \( 1\frac{1}{2} \)
• For \( 1\frac{3}{4} \): place 3 X's above \( 1\frac{3}{4} \)
• For \( 2 \): place 3 X's above \( 2 \)

Final Line Plot (description)

• Above \( 1 \): 2 X's
• Above \( 1\frac{1}{4} \): 3 X's
• Above \( 1\frac{1}{2} \): 2 X's
• Above \( 1\frac{3}{4} \): 3 X's
• Above \( 2 \): 3 X's

(Note: Since this is a line plot interaction, the actual action is to click the appropriate number of times for each column. The counts above guide how many X's to place.)

Answer:

To solve this, we first count the frequency of each amount of laundry detergent:

Step 1: Count occurrences of \( 1 \)

Looking at the data: \( 1, 1 \) (wait, let's list all data points: \( 1\frac{1}{4}, 1, 2, 1\frac{1}{4}, 2, 1\frac{3}{4}, 1\frac{1}{2}, 2, 1\frac{3}{4}, 1\frac{1}{2}, 1\frac{3}{4}, 1\frac{1}{4}, 1 \))
Wait, let's list each:

• \( 1 \): Let's check the list. The values are: \( 1\frac{1}{4} \), \( 1 \), \( 2 \), \( 1\frac{1}{4} \), \( 2 \), \( 1\frac{3}{4} \), \( 1\frac{1}{2} \), \( 2 \), \( 1\frac{3}{4} \), \( 1\frac{1}{2} \), \( 1\frac{3}{4} \), \( 1\frac{1}{4} \), \( 1 \). Wait, maybe I missed, let's count again:

Wait the data list (from the table):

1. \( 1\frac{1}{4} \)
2. \( 1 \)
3. \( 2 \)
4. \( 1\frac{1}{4} \)
5. \( 2 \)
6. \( 1\frac{3}{4} \)
7. \( 1\frac{1}{2} \)
8. \( 2 \)
9. \( 1\frac{3}{4} \)
10. \( 1\frac{1}{2} \)
11. \( 1\frac{3}{4} \)
12. \( 1\frac{1}{4} \)
13. \( 1 \)

Now count each:

• \( 1 \): positions 2, 13 → 2 times
• \( 1\frac{1}{4} \): positions 1, 4, 12 → 3 times
• \( 1\frac{1}{2} \): positions 7, 10 → 2 times
• \( 1\frac{3}{4} \): positions 6, 9, 11 → 3 times
• \( 2 \): positions 3, 5, 8 → 3 times

Step 2: Mark X's on the line plot

• For \( 1 \): place 2 X's above \( 1 \)
• For \( 1\frac{1}{4} \): place 3 X's above \( 1\frac{1}{4} \)
• For \( 1\frac{1}{2} \): place 2 X's above \( 1\frac{1}{2} \)
• For \( 1\frac{3}{4} \): place 3 X's above \( 1\frac{3}{4} \)
• For \( 2 \): place 3 X's above \( 2 \)

Final Line Plot (description)

• Above \( 1 \): 2 X's
• Above \( 1\frac{1}{4} \): 3 X's
• Above \( 1\frac{1}{2} \): 2 X's
• Above \( 1\frac{3}{4} \): 3 X's
• Above \( 2 \): 3 X's

(Note: Since this is a line plot interaction, the actual action is to click the appropriate number of times for each column. The counts above guide how many X's to place.)