Questions: 1. This data lists the heights of 24 swimmers in centimeters. Make a histogram with five bins. 155, 155, 156, 157, 158, 159, 159, 160, 162, 162, 163, 163, 164, 165, 166, 167, 167, 168, 168, 170, 172, 174, 175, 177 Height (cm) Frequency

1. This data lists the heights of 24 swimmers in centimeters. Make a histogram with five bins. 155, 155, 156, 157, 158, 159, 159, 160, 162, 162, 163, 163, 164, 165, 166, 167, 167, 168, 168, 170, 172, 174, 175, 177 Height (cm) Frequency
Transcript text: 1. This data lists the heights of 24 swimmers in centimeters. Make a histogram with five bins. \begin{tabular}{lllllllllllll} 155 & 155 & 156 & 157 & 158 & 159 & 159 & 160 & 162 & 162 & 163 & 163 \\ 164 & 165 & 166 & 167 & 167 & 168 & 168 & 170 & 172 & 174 & 175 & 177 \end{tabular} \begin{tabular}{|l|l|} \hline Height (cm) & Frequency \\ \hline & \\ \hline & \\ \hline & \\ \hline & \\ \hline & \\ \hline \end{tabular}
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Solution

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Solution Steps

Step 1: Determine the Range of Heights
  • Identify the minimum and maximum heights from the data.
  • Minimum height: 155 cm
  • Maximum height: 177 cm
  • Range = 177 - 155 = 22 cm
Step 2: Calculate the Bin Width
  • Divide the range by the number of bins to determine the bin width.
  • Number of bins = 5
  • Bin width = Range / Number of bins = 22 / 5 = 4.4 cm
  • Round the bin width to a convenient number, e.g., 5 cm.
Step 3: Define the Bin Intervals
  • Create bin intervals based on the bin width.
  • Bin 1: 155 - 159 cm
  • Bin 2: 160 - 164 cm
  • Bin 3: 165 - 169 cm
  • Bin 4: 170 - 174 cm
  • Bin 5: 175 - 179 cm
Step 4: Tally the Frequencies
  • Count the number of heights that fall into each bin interval.
  • Bin 1 (155 - 159 cm): 7 swimmers
  • Bin 2 (160 - 164 cm): 5 swimmers
  • Bin 3 (165 - 169 cm): 7 swimmers
  • Bin 4 (170 - 174 cm): 3 swimmers
  • Bin 5 (175 - 179 cm): 2 swimmers
Step 5: Fill in the Frequency Table
  • Populate the frequency table with the calculated frequencies.

| Height (cm) | Frequency | |-------------|-----------| | 155 - 159 | 7 | | 160 - 164 | 5 | | 165 - 169 | 7 | | 170 - 174 | 3 | | 175 - 179 | 2 |

Final Answer

  • The histogram should reflect the frequencies in the table, with each bin interval on the x-axis and the corresponding frequency on the y-axis.
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