Questions: The table below gives the number of elementary school children in 16 school districts in a particular region. (a) Construct a cumulative frequency distribution. (b) Construct a cumulative relative frequency distribution. (c) Draw a frequency polygon. (d) Draw a relative frequency ogive. Number of Elementary Students in School Districts 1952 2400 1139 2500 1260 3712 3110 4800 3254 1050 3252 1503 1734 3640 3414 4400 (a) Complete the cumulative frequency distribution. Students in a District Cumulative Frequency 1000-1999 2000-2999 3000-3999 4000-4999

The table below gives the number of elementary school children in 16 school districts in a particular region. (a) Construct a cumulative frequency distribution. (b) Construct a cumulative relative frequency distribution. (c) Draw a frequency polygon. (d) Draw a relative frequency ogive. Number of Elementary Students in School Districts 1952 2400 1139 2500 1260 3712 3110 4800 3254 1050 3252 1503 1734 3640 3414 4400 (a) Complete the cumulative frequency distribution. Students in a District Cumulative Frequency 1000-1999 2000-2999 3000-3999 4000-4999
Transcript text: The table below gives the number of elementary school children in 16 school districts in a particular region. (a) Construct a cumulative frequency distribution. (b) Construct a cumulative relative frequency distribution. (c) Draw a frequency polygon. (d) Draw a relative frequency ogive. \begin{tabular}{|llll|} \hline \multicolumn{3}{|c|}{\begin{tabular}{c} Number of Elementary \\ Students in \\ Stuol \\ Sthol \end{tabular}} & School Districts \\ \hline 1952 & 2400 & 1139 & 2500 \\ 1260 & 3712 & 3110 & 4800 \\ 3254 & 1050 & 3252 & 1503 \\ 1734 & 3640 & 3414 & 4400 \\ \hline \end{tabular} (a) Complete the cumulative frequency distribution. \begin{tabular}{|c|c|c|} \hline \begin{tabular}{c} Students in a \\ District \end{tabular} & \multicolumn{2}{|c|}{\begin{tabular}{c} Cumulative \\ Frequency \end{tabular}} \\ \hline $1000-1999$ & & \\ \hline $2000-2999$ & & \\ \hline $3000-3999$ & & \\ \hline $4000-4999$ & & \\ \hline \end{tabular}
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Solution

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Solution Steps

Step 1: Organize the Data

The given data for the number of elementary school children in 16 school districts is: \[ \{1952, 2400, 1139, 2500, 1260, 3712, 3110, 4800, 3254, 1050, 3252, 1503, 1734, 3640, 3414, 4400\} \]

Step 2: Create Frequency Distribution

We need to create a cumulative frequency distribution for the given intervals: \[ 1000-1999, 2000-2999, 3000-3999, 4000-4999 \]

Step 3: Calculate Cumulative Frequencies
  • For \(1000-1999\): 1139, 1260, 1050, 1503, 1734 (5 values)
  • For \(2000-2999\): 1952, 2400, 2500 (3 values)
  • For \(3000-3999\): 3110, 3254, 3252, 3712, 3640, 3414 (6 values)
  • For \(4000-4999\): 4800, 4400 (2 values)

Cumulative frequencies:

  • \(1000-1999\): 5
  • \(2000-2999\): 5 + 3 = 8
  • \(3000-3999\): 8 + 6 = 14
  • \(4000-4999\): 14 + 2 = 16

Final Answer

\[ \begin{array}{|c|c|} \hline \text{Students in a District} & \text{Cumulative Frequency} \\ \hline 1000-1999 & 5 \\ \hline 2000-2999 & 8 \\ \hline 3000-3999 & 14 \\ \hline 4000-4999 & 16 \\ \hline \end{array} \]

{"axisType": 3, "coordSystem": {"xmin": 1000, "xmax": 5000, "ymin": 0, "ymax": 16}, "commands": ["y = 5 if x <= 1999 else 8 if x <= 2999 else 14 if x <= 3999 else 16"], "latex_expressions": ["$Cumulative Frequency$"]}

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