$\left[\begin{array}{lllllllll}43 & 45 & 50 & 47 & 51 & 58 & 52 & 47 & 0 \\ 61 & 50 & 45 & 55 & 57 & 41 & 46 & 49 & 31 \\ 59 & 44 & 53 & 57 & 49 & 40 & 48 & 52 & 51\end{array}\right]\\Using the class intervals of 43-44, 45-49 ...
a) construct the frequency table
b) draw a histogram for the distribution.
c) draw a frequency polygon for it.

Create class intervals: 40-44, 45-49, 50-54, 55-59, 60-64.
Count data points within each interval: 4, 8, 7, 5, 1.
Construct a frequency table with class intervals and their frequencies.
Draw a histogram and frequency polygon based on the frequency table. Frequency Table: See explanation ​

Explanation

Analyze the problem and data We are given a 3x9 data matrix and asked to construct a frequency table, a histogram, and a frequency polygon using class intervals of width 5: 40-44, 45-49, 50-54, 55-59, and 60-64.

Prepare the data First, we need to count the number of data points that fall within each class interval. The data matrix is:


[ 43 ​ 45 ​ 50 ​ 47 ​ 51 ​ 58 ​ 52 ​ 47 ​ 0 61 ​ 50 ​ 45 ​ 55 ​ 57 ​ 41 ​ 46 ​ 49 ​ 31 59 ​ 44 ​ 53 ​ 57 ​ 49 ​ 40 ​ 48 ​ 52 ​ 51 ​ ]
We can flatten this matrix into a 1D array: [43, 45, 50, 47, 51, 58, 52, 47, 0, 61, 50, 45, 55, 57, 41, 46, 49, 31, 59, 44, 53, 57, 49, 40, 48, 52, 51].

Construct the frequency table Now, let's count the frequencies for each class interval:


40-44: The numbers in this interval are 43, 44, 41, 40. So, the frequency is 4.
45-49: The numbers in this interval are 45, 47, 47, 45, 46, 49, 49, 48. So, the frequency is 8.
50-54: The numbers in this interval are 50, 51, 52, 50, 53, 52, 51. So, the frequency is 7.
55-59: The numbers in this interval are 58, 55, 57, 57, 59. So, the frequency is 5.
60-64: The number in this interval is 61. So, the frequency is 1.

Therefore, the frequency table is:



Class Interval
Frequency



40-44
4


45-49
8


50-54
7


55-59
5


60-64
1



Draw the histogram and frequency polygon Next, we draw a histogram. The x-axis represents the class intervals, and the y-axis represents the frequencies. Each bar's height corresponds to the frequency of its respective class interval.

Finally, we draw a frequency polygon. This is done by connecting the midpoints of the tops of the histogram bars with straight lines. The midpoints are (42, 4), (47, 8), (52, 7), (57, 5), and (62, 1).
Examples
Frequency tables, histograms, and frequency polygons are used in various real-life scenarios. For example, a teacher can use these tools to visualize the distribution of student scores on a test. A business can use them to analyze sales data or customer demographics. In epidemiology, these tools can help visualize the distribution of disease cases across different age groups or geographic regions, providing insights into public health trends and potential interventions.

Answered by GinnyAnswer | 2025-07-08