Sure! Let's visualize the histogram based on the given frequency table.
The frequency table provides the weight ranges (bins) and the corresponding frequencies:
- Weight range [tex]\( 30-35 \)[/tex] kg has a frequency of 12.
- Weight range [tex]\( 35-40 \)[/tex] kg has a frequency of 8.
- Weight range [tex]\( 40-45 \)[/tex] kg has a frequency of 10.
- Weight range [tex]\( 45-50 \)[/tex] kg has a frequency of 5.
To determine which histogram correctly represents this data, let's break down the characteristics of the correct histogram:
1. X-axis (Weight): This axis should represent the weight ranges. The bins should be labeled as [tex]\( 30-35 \)[/tex], [tex]\( 35-40 \)[/tex], [tex]\( 40-45 \)[/tex], and [tex]\( 45-50 \)[/tex].
2. Y-axis (Frequency): This axis should represent the frequency of students falling within each weight range. The heights of the bars should correspond to the frequencies as follows:
- The bar for [tex]\( 30-35 \)[/tex] should have a height of 12.
- The bar for [tex]\( 35-40 \)[/tex] should have a height of 8.
- The bar for [tex]\( 40-45 \)[/tex] should have a height of 10.
- The bar for [tex]\( 45-50 \)[/tex] should have a height of 5.
Using these criteria, you should look for a histogram with the following characteristics:
- The first bar (representing the [tex]\( 30-35 \)[/tex] kg range) is the tallest, reaching up to 12 on the Y-axis.
- The second bar (representing the [tex]\( 35-40 \)[/tex] kg range) is shorter, reaching up to 8 on the Y-axis.
- The third bar (representing the [tex]\( 40-45 \)[/tex] kg range) is slightly shorter than the first but taller than the second, reaching up to 10 on the Y-axis.
- The fourth bar (representing the [tex]\( 45-50 \)[/tex] kg range) is the shortest, reaching up to 5 on the Y-axis.
Make sure to select the histogram that matches these details. If you have specific histograms provided as options, compare them against these criteria to determine the correct one.
