Math

QuestionFind the grouped frequency distribution for these test scores: 83, 85, 97, 91, 92, 82, 90, 89, 91, 83, 93, 88, 86, 84, 98. Class width is 5. Then, draw a frequency polygon with midpoints labeled.

Studdy Solution

STEP 1

Assumptions1. The test scores are given as83,85,97,91,92,82,90,89,91,83,93,88,86,84,98. The class width for the grouped frequency distribution is53. The classes are defined as follows78.5 to83.5,83.5 to88.5,88.5 to93.5,93.5 to98.54. The frequency of each class is the number of test scores that fall within that class

STEP 2

First, we need to count the number of test scores that fall within each class. This is done by comparing each test score to the boundaries of each class.

STEP 3

Count the number of test scores that fall within the class78.5 to83.5.
Frequency78.583.5=2Frequency_{78.5-83.5} =2

STEP 4

Count the number of test scores that fall within the class83. to88..
Frequency83.88.=4Frequency_{83.-88.} =4

STEP 5

Count the number of test scores that fall within the class88.5 to93.5.
Frequency88.593.5=7Frequency_{88.5-93.5} =7

STEP 6

Count the number of test scores that fall within the class93.5 to98.5.
Frequency93.598.5=2Frequency_{93.5-98.5} =2

STEP 7

Now that we have the frequencies for each class, we can complete the grouped frequency distribution.\begin{tabular}{|lc|} \hline Test scores & Frequency \\ \hline78.5 to83.5 &2 \\ 83.5 to88.5 &4 \\ 88.5 to93.5 &7 \\ 93.5 to98.5 &2 \\ \hline\end{tabular}

STEP 8

To draw the frequency polygon, we first need to find the midpoint of each class. The midpoint of a class is the average of the lower and upper boundaries of the class.
Midpoint=Lowerboundary+Upperboundary2Midpoint = \frac{{Lower\, boundary + Upper\, boundary}}{2}

STEP 9

Calculate the midpoint for the class78.5 to83.5.
Midpoint78.583.5=78.5+83.52Midpoint_{78.5-83.5} = \frac{{78.5 +83.5}}{2}

STEP 10

Calculate the midpoint for the class83.5 to88.5.
Midpoint83.588.5=83.5+88.52Midpoint_{83.5-88.5} = \frac{{83.5 +88.5}}{2}

STEP 11

Calculate the midpoint for the class88.5 to93.5.
Midpoint88.593.5=88.5+93.5Midpoint_{88.5-93.5} = \frac{{88.5 +93.5}}{}

STEP 12

Calculate the midpoint for the class93.5 to98.5.
Midpoint93.598.5=93.5+98.52Midpoint_{93.5-98.5} = \frac{{93.5 +98.5}}{2}

STEP 13

Now that we have the midpoints for each class, we can plot the frequency polygon. On the x-axis, we plot the midpoints of the classes. On the y-axis, we plot the frequencies of the classes. Connect the points with straight lines to form the frequency polygon.

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