Question

airplane speeds the airborne speeds in miles per hour of 21 planes are shown.

class frequency
366-386 3
387-407 2
408-428 2
429-449 2
450-470 1
471-491 2
492-512 3
513-533 6
21

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part: 0 / 2

part 1 of 2

draw the percentile graph using class boundaries for the x-axis and the percentages for the y-axis. round the answer to nearest percent.

Answer:

To create a percentile (ogive) graph, we first need to find the cumulative frequency and then the cumulative percentage for each class boundary. Here are the steps:

Step 1: Determine Class Boundaries

For a class like \( 366 - 386 \), the lower boundary is \( 365.5 \) (subtract 0.5 from the lower class limit) and the upper boundary is \( 386.5 \) (add 0.5 to the upper class limit). We do this for all classes:

Class	Lower Boundary	Upper Boundary	Frequency (\( f \))
\( 387 - 407 \)	\( 386.5 \)	\( 407.5 \)	2
\( 408 - 428 \)	\( 407.5 \)	\( 428.5 \)	2
\( 429 - 449 \)	\( 428.5 \)	\( 449.5 \)	2
\( 450 - 470 \)	\( 449.5 \)	\( 470.5 \)	1
\( 471 - 491 \)	\( 470.5 \)	\( 491.5 \)	2
\( 492 - 512 \)	\( 491.5 \)	\( 512.5 \)	3
\( 513 - 533 \)	\( 512.5 \)	\( 533.5 \)	6

Step 2: Calculate Cumulative Frequency (\( CF \))

Cumulative frequency is the sum of frequencies up to each class boundary.

Class	Upper Boundary	Frequency (\( f \))	Cumulative Frequency (\( CF \))
\( 387 - 407 \)	\( 407.5 \)	2	\( 3 + 2 = 5 \)
\( 408 - 428 \)	\( 428.5 \)	2	\( 5 + 2 = 7 \)
\( 429 - 449 \)	\( 449.5 \)	2	\( 7 + 2 = 9 \)
\( 450 - 470 \)	\( 470.5 \)	1	\( 9 + 1 = 10 \)
\( 471 - 491 \)	\( 491.5 \)	2	\( 10 + 2 = 12 \)
\( 492 - 512 \)	\( 512.5 \)	3	\( 12 + 3 = 15 \)
\( 513 - 533 \)	\( 533.5 \)	6	\( 15 + 6 = 21 \)

Step 3: Calculate Cumulative Percentage

Cumulative percentage is \( \frac{CF}{N} \times 100 \), where \( N = 21 \) (total frequency).

Class	Upper Boundary	Cumulative Frequency (\( CF \))	Cumulative Percentage (\( \% \))
\( 387 - 407 \)	\( 407.5 \)	\( 5 \)	\( \frac{5}{21} \times 100 \approx 24\% \)
\( 408 - 428 \)	\( 428.5 \)	\( 7 \)	\( \frac{7}{21} \times 100 \approx 33\% \)
\( 429 - 449 \)	\( 449.5 \)	\( 9 \)	\( \frac{9}{21} \times 100 \approx 43\% \)
\( 450 - 470 \)	\( 470.5 \)	\( 10 \)	\( \frac{10}{21} \times 100 \approx 48\% \)
\( 471 - 491 \)	\( 491.5 \)	\( 12 \)	\( \frac{12}{21} \times 100 \approx 57\% \)
\( 492 - 512 \)	\( 512.5 \)	\( 15 \)	\( \frac{15}{21} \times 100 \approx 71\% \)
\( 513 - 533 \)	\( 533.5 \)	\( 21 \)	\( \frac{21}{21} \times 100 = 100\% \)

Step 4: Plot the Percentile Graph

• X-axis: Use the upper class boundaries (\( 386.5, 407.5, 428.5, 449.5, 470.5, 491.5, 512.5, 533.5 \)).
• Y-axis: Use the cumulative percentages (\( 14\%, 24\%, 33\%, 43\%, 48\%, 57\%, 71\%, 100\% \)).

Plot points at \( (386.5, 14) \), \( (407.5, 24) \), \( (428.5, 33) \), \( (449.5, 43) \), \( (470.5, 48) \), \( (491.5, 57) \), \( (512.5, 71) \), and \( (533.5, 100) \). Then connect the points with a smooth line to form the ogive (percentile graph).

Final Answer (for the Graph)

The percentile graph is constructed by plotting the upper class boundaries on the x-axis and their corresponding cumulative percentages on the y-axis, then connecting the points. The key coordinates are:

Upper Boundary	Cumulative Percentage
\( 407.5 \)	\( 24\% \)
\( 428.5 \)	\( 33\% \)
\( 449.5 \)	\( 43\% \)
\( 470.5 \)	\( 48\% \)
\( 491.5 \)	\( 57\% \)
\( 512.5 \)	\( 71\% \)
\( 533.5 \)	\( 100\% \)

Plot these points and connect them to create the ogive.