The problem provides a cumulative frequency polygon for a statistical series grouped into classes with an amplitude of 5. We need to: 1. Read the total frequency of the series from the graph.
Probability and StatisticsCumulative Frequency PolygonFrequency DistributionMedianData AnalysisStatistical Series
2025/4/28
1. Problem Description
The problem provides a cumulative frequency polygon for a statistical series grouped into classes with an amplitude of
5. We need to:
1. Read the total frequency of the series from the graph.
2. Graphically determine the median of the series.
3. Create a table of cumulative frequencies from the polygon.
4. Create a table of frequencies knowing that the frequency of the interval [50; 55[ is
7
0.
2. Solution Steps
1. Total Frequency:
The total frequency is the cumulative frequency corresponding to the last class. From the graph, the last value on the x-axis is 65 and the corresponding cumulative frequency is
2
0
0. Therefore, the total frequency is
2
0
0.
2. Median:
The median is the value that separates the higher half from the lower half of the data. Since the total frequency is 200, the median corresponds to the value at the cumulative frequency of 200/2 =
1
0
0. From the graph, the cumulative frequency of 100 corresponds to the value of
5
2.
3. Cumulative Frequency Table:
We can read the cumulative frequencies directly from the graph:
- Class below 50: 0
- Class below 55: 70
- Class below 60: 140
- Class below 65: 170
- Class below 70: 200
4. Frequency Table:
We know the cumulative frequencies from the previous step:
- Cumulative frequency below 50: 0
- Cumulative frequency below 55: 70
- Cumulative frequency below 60: 140
- Cumulative frequency below 65: 170
- Cumulative frequency below 70: 200
To find the frequency of each class, we subtract the cumulative frequency of the previous class from the current cumulative frequency:
- Class [45; 50[: 0
- Class [50; 55[: 70 - 0 = 70
- Class [55; 60[: 140 - 70 = 70
- Class [60; 65[: 170 - 140 = 30
- Class [65; 70[: 200 - 170 = 30
3. Final Answer
1. The total frequency is
2
0
0.
2. The median is approximately
5
2.
3. Cumulative Frequency Table:
- Class below 50: 0
- Class below 55: 70
- Class below 60: 140
- Class below 65: 170
- Class below 70: 200
4. Frequency Table:
- Class [45; 50[: 0
- Class [50; 55[: 70
- Class [55; 60[: 70
- Class [60; 65[: 30
- Class [65; 70[: 30