The lengths (mm) of twenty leaves of a certain variety of plant in a botanical garden are given as145, 162, 175, 129, 165, 118, 126, 154, 125, 174, 116, 138, 147, 142, 179, 129, 164, 132, 160, 175, 146, 133, 121, 132, and 142.If the width of the class interval is taken as 10, which of the following frequency tables represents the given data?aLength (mm) Number of leaves116โ125 4126โ135 6136โ145 4146โ155 3156โ165 4166โ175 3176โ185 1bLength (mm) Number of leaves116โ125 6126โ135 4136โ145 1146โ155 3156โ165 4166โ175 3176โ185 4cLength (mm) Number of leaves116โ125 4126โ135 3136โ145 4146โ155 6156โ165 4166โ175 3176โ185 1dLength (mm) Number of leaves116โ125 1126โ135 4136โ145 4146โ155 3156โ165 4166โ175 6176โ185 3
Question
The lengths (mm) of twenty leaves of a certain variety of plant in a botanical garden are given as145, 162, 175, 129, 165, 118, 126, 154, 125, 174, 116, 138, 147, 142, 179, 129, 164, 132, 160, 175, 146, 133, 121, 132, and 142.If the width of the class interval is taken as 10, which of the following frequency tables represents the given data?aLength (mm) Number of leaves116โ125 4126โ135 6136โ145 4146โ155 3156โ165 4166โ175 3176โ185 1bLength (mm) Number of leaves116โ125 6126โ135 4136โ145 1146โ155 3156โ165 4166โ175 3176โ185 4cLength (mm) Number of leaves116โ125 4126โ135 3136โ145 4146โ155 6156โ165 4166โ175 3176โ185 1dLength (mm) Number of leaves116โ125 1126โ135 4136โ145 4146โ155 3156โ165 4166โ175 6176โ185 3
Solution
To answer this question, we need to count the number of leaves that fall into each class interval.
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Class interval 116-125: The leaves with lengths in this interval are 118, 125, 121, 116. So, there are 4 leaves in this interval.
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Class interval 126-135: The leaves with lengths in this interval are 129, 126, 129, 132, 133, 132. So, there are 6 leaves in this interval.
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Class interval 136-145: The leaves with lengths in this interval are 145, 138, 142, 142. So, there are 4 leaves in this interval.
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Class interval 146-155: The leaves with lengths in this interval are 154, 147, 146. So, there are 3 leaves in this interval.
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Class interval 156-165: The leaves with lengths in this interval are 162, 165, 164, 160. So, there are 4 leaves in this interval.
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Class interval 166-175: The leaves with lengths in this interval are 175, 174, 175. So, there are 3 leaves in this interval.
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Class interval 176-185: The leaves with lengths in this interval are 179. So, there is 1 leaf in this interval.
So, the correct frequency table is:
Length (mm) Number of leaves 116โ125 4 126โ135 6 136โ145 4 146โ155 3 156โ165 4 166โ175 3 176โ185 1
Therefore, the answer is option a.
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