Math Problem Statement

Draw a histogram, a frequency polygon, and a cumulative frequency curve using the given data.

Solution

The image contains a problem asking to "Draw a histogram, a frequency polygon, and a cumulative frequency curve" using the given dataThe image contains a problem asking to "Draw a histogram, a frequency polygon, and a cumulative frequency curve" using the given

Here is the data extracted:

Mass (F)Frequency (f)
0.55
5-107
10-158
15-2013
20-257
25-306
30-354
35-401

Steps to draw the three types of graphs:

  1. Histogram: Plot the mass intervals on the x-axis and the corresponding frequency on the y-axis. Each interval will have a rectangular bar with a height representing the frequency.

  2. Frequency Polygon: This is drawn by connecting the midpoints of the tops of the histogram bars with straight lines. The midpoint of each class is calculated and plotted against the frequency.

  3. Cumulative Frequency Curve (Ogive): For this, we create a cumulative frequency table and plot the cumulative frequency against the upper class boundaries. The curve is a smooth line that rises progressively.

Let me know if you'd like me to generate these graphs or help with further calculations! Also, here are 5 questions based on this dataThe image contains a problem asking to "Draw a histogram, a frequency polygon, and a cumulative frequency curve" using the given

Here is the data extracted:

Mass (F)Frequency (f)
0.55
5-107
10-158
15-2013
20-257
25-306
30-354
35-401

Steps to draw the three types of graphs:

  1. Histogram: Plot the mass intervals on the x-axis and the corresponding frequency on the y-axis. Each interval will have a rectangular bar with a height representing the frequency.

  2. Frequency Polygon: This is drawn by connecting the midpoints of the tops of the histogram bars with straight lines. The midpoint of each class is calculated and plotted against the frequency.

  3. Cumulative Frequency Curve (Ogive): For this, we create a cumulative frequency table and plot the cumulative frequency against the upper class boundaries. The curve is a smooth line that rises progressively.

Let me know if you'd like me to generate these graphs or help with further calculations! Also, here are 5 questions based on this

  1. How do you calculate the midpoint for each class in a frequency distribution?
  2. What is the total frequency, and how does it relate to the cumulative frequency curve?
  3. Can you explain the difference between a histogram and a frequency polygon?
  4. Why is it important to use cumulative frequency in data analysis?
  5. How would the shape of the histogram change if we changed the class width?

Tip: When constructing a frequency polygon, make sure the starting and ending points touch the x-axis, extending slightly beyond the data range.

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Math Problem Analysis

Mathematical Concepts

Statistics
Data Visualization
Frequency Distribution

Formulas

Midpoint = (Lower class boundary + Upper class boundary) / 2

Theorems

Histogram Construction
Frequency Polygon
Cumulative Frequency Curve

Suitable Grade Level

Grades 9-11