School has a number of teachers with the following ages:
[table]
21 37 49 27 49 42 26 33 46 40
50 29 23 24 29 31 16 22 27 38
30 26 42 39 44 23 31 32 41 46
46 31 33 29 28 43 47 40 34 44
26 38 34 49 45 27 25 33 39 40
[/table]
a) Put the data in a frequency table.
b) Draw a histogram for the data.
c) Draw the corresponding frequency polygon.
Draw a histogram and a frequency polygon of the frequency distribution in Table 20.11.
Table 20.11
[table]
Class | 0-9 | 10-19 | 20-29 | 30-39 | 40-49 | 50-89
Frequency | 7 | 18 | 20 | 22 | 15 | 17
[/table]
Answer (2)
Create a frequency table for the age data with class intervals: 15-19, 20-24, 25-29, 30-34, 35-39, 40-44, 45-49, 50-54.
Draw a histogram for the age data using the frequency table.
Draw a frequency polygon by connecting the midpoints of the histogram bars.
Draw a histogram and frequency polygon for the frequency distribution in Table 20.11.
Explanation
Problem Analysis We are given a dataset of teacher ages and asked to create a frequency table, histogram, and frequency polygon. We are also given a frequency distribution table and asked to create a histogram and frequency polygon for it.
Frequency Table - Choosing Class Intervals First, let's create a frequency table for the given age data. We need to determine appropriate class intervals. The minimum age is 16 and the maximum age is 50. We can use class intervals of width 5, starting from 15.
Frequency Table - Defining Class Intervals The class intervals will be: 15-19, 20-24, 25-29, 30-34, 35-39, 40-44, 45-49, 50-54. Now, we count the number of data points falling into each class interval.
Frequency Table - Result The frequency table is as follows:
Age Group
Frequency
15-19
1
20-24
5
25-29
11
30-34
10
35-39
5
40-44
9
45-49
8
50-54
1
Histogram - Age Data Next, we draw a histogram for the age data. The x-axis represents the age groups, and the y-axis represents the frequency. The height of each bar corresponds to the frequency of that age group.
Frequency Polygon - Age Data Then, we draw a frequency polygon for the age data. This is done by connecting the midpoints of the tops of the histogram bars with straight lines. The polygon starts and ends at the x-axis.
Histogram and Frequency Polygon - Table 20.11 Now, let's draw a histogram and frequency polygon for the given frequency distribution in Table 20.11.
Table 20.11:
Class
0-9
10-19
20-29
30-39
40-49
50-89
Frequency
7
18
20
22
15
17
Histogram - Table 20.11 For the histogram, the x-axis represents the class intervals (0-9, 10-19, 20-29, 30-39, 40-49, 50-89), and the y-axis represents the frequency. The height of each bar corresponds to the frequency of that class interval.
Frequency Polygon - Table 20.11 For the frequency polygon, we connect the midpoints of the tops of the histogram bars with straight lines. The polygon starts and ends at the x-axis.
Examples
Frequency tables, histograms, and frequency polygons are used in many real-world scenarios to visualize and analyze data. For example, a company might use a histogram to visualize the distribution of customer ages, which can help them target their marketing efforts more effectively. Similarly, a teacher might use a frequency table to summarize student test scores, which can help them identify areas where students are struggling. These tools provide a clear and concise way to understand complex data sets, making them valuable in various fields.
We constructed a frequency table for the ages of teachers, created a histogram to represent these frequencies, and drew a frequency polygon based on the midpoints of the histogram. We also outlined steps for a second frequency distribution given in Table 20.11. These tools help in visualizing and analyzing age data effectively.
;
