Math  /  Data & Statistics

Question\begin{tabular}{|c|c|c|c|c|} \hline \multicolumn{5}{|c|}{ Test scores } \\ \hline 97 & 80 & 94 & 86 & 85 \\ \hline 96 & 80 & 83 & 84 & 95 \\ \hline 98 & 93 & 94 & 81 & 82 \\ \hline \end{tabular}
Send data to calculator (a) Complete the grouped frequency distribution for the data. (Note that the class width is 5.) \begin{tabular}{|cc|} \hline Test scores & Frequency \\ \hline 78.5 to 83.5 & 5 \\ 83.5 to 88.5 & 3 \\ 88.5 to 93.5 & 1 \\ 93.5 to 98.5 & 6 \\ \hline \end{tabular} (b) Using the classes from part (a), draw the frequency polygon for the data. Note that you can add or remove classes from the figure. Label each class with its midpoint.

Studdy Solution

STEP 1

1. The test scores are: 97,80,94,86,85,96,80,83,84,95,98,93,94,81,8297, 80, 94, 86, 85, 96, 80, 83, 84, 95, 98, 93, 94, 81, 82.
2. The class width for the frequency distribution is 5.
3. A frequency polygon is a graphical representation of the frequency distribution.

STEP 2

1. Verify and complete the grouped frequency distribution.
2. Calculate the midpoints of each class.
3. Draw the frequency polygon using the midpoints and frequencies.

STEP 3

List all the test scores:
97,80,94,86,85,96,80,83,84,95,98,93,94,81,82 97, 80, 94, 86, 85, 96, 80, 83, 84, 95, 98, 93, 94, 81, 82

STEP 4

Verify the frequency distribution by counting the number of scores in each class:
- Class 78.578.5 to 83.583.5: Scores 80,80,83,81,8280, 80, 83, 81, 82 (Frequency = 5) - Class 83.583.5 to 88.588.5: Scores 86,85,8486, 85, 84 (Frequency = 3) - Class 88.588.5 to 93.593.5: Scores 9393 (Frequency = 1) - Class 93.593.5 to 98.598.5: Scores 97,94,96,95,98,9497, 94, 96, 95, 98, 94 (Frequency = 6)

STEP 5

Calculate the midpoints for each class:
- Midpoint of 78.578.5 to 83.583.5: 78.5+83.52=81\frac{78.5 + 83.5}{2} = 81 - Midpoint of 83.583.5 to 88.588.5: 83.5+88.52=86\frac{83.5 + 88.5}{2} = 86 - Midpoint of 88.588.5 to 93.593.5: 88.5+93.52=91\frac{88.5 + 93.5}{2} = 91 - Midpoint of 93.593.5 to 98.598.5: 93.5+98.52=96\frac{93.5 + 98.5}{2} = 96

STEP 6

Draw the frequency polygon using the midpoints and frequencies:
- Plot the points: (81,5),(86,3),(91,1),(96,6)(81, 5), (86, 3), (91, 1), (96, 6). - Connect the points with straight lines.
The grouped frequency distribution is verified, and the frequency polygon is drawn using the calculated midpoints and frequencies.

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