The distribution of marks scored by thirty girls in an examination is as follows:
7
45
11
19 64 21 42 27 40 62 56 51
70 68 60 81
43
15 60 50 41 37
61
9
54 35 37 45
49 85 46 76 45
59
Using the class intervals 0-9, 10-19, 20-29 ...
a) Construct the frequency table.
b) Draw a histogram to represent the distribution.
c) Draw a frequency polygon for the distribution.
Answer (2)
The problem involves constructing a frequency table, histogram, and frequency polygon for a given set of marks. The frequency table is created by grouping the marks into class intervals and counting the frequency of each interval. The histogram is a bar graph representing the frequency distribution, and the frequency polygon is a line graph connecting the midpoints of each class interval with their corresponding frequencies.
Construct frequency table with class intervals 0-9, 10-19, 20-29, 30-39, 40-49, 50-59, 60-69, 70-79, 80-89.
Tally frequencies for each class interval: 3, 3, 2, 3, 9, 5, 6, 2, 2.
Visualize the histogram as a bar graph with class intervals on the x-axis and frequencies on the y-axis.
Visualize the frequency polygon as a line graph connecting the midpoints of class intervals with their frequencies.
Explanation
Understand the problem and provided data We are given a set of marks scored by 30 girls and asked to construct a frequency table, a histogram, and a frequency polygon. The class intervals are 0-9, 10-19, 20-29, and so on.
Construct the frequency table First, let's construct the frequency table. The class intervals are: 0-9 10-19 20-29 30-39 40-49 50-59 60-69 70-79 80-89
Now, we count the number of scores falling within each class interval.
Tally the frequencies for each interval The marks are: 5, 7, 45, 11, 19, 64, 21, 42, 27, 40, 62, 56, 51, 70, 68, 60, 81, 43, 15, 60, 50, 41, 37, 61, 9, 54, 35, 37, 45, 49, 85, 46, 76, 45, 59
0-9: 5, 7, 9 (Frequency: 3) 10-19: 11, 19, 15 (Frequency: 3) 20-29: 21, 27 (Frequency: 2) 30-39: 35, 37, 37 (Frequency: 3) 40-49: 45, 42, 40, 43, 41, 45, 49, 46, 45 (Frequency: 9) 50-59: 56, 51, 50, 54, 59 (Frequency: 5) 60-69: 64, 62, 68, 60, 60, 61 (Frequency: 6) 70-79: 70, 76 (Frequency: 2) 80-89: 81, 85 (Frequency: 2)
Present the frequency table The frequency table is:
Class Interval
Frequency
0-9
3
10-19
3
20-29
2
30-39
3
40-49
9
50-59
5
60-69
6
70-79
2
80-89
2
Describe the histogram For the histogram, the x-axis represents the class intervals, and the y-axis represents the frequency. Each bar's height corresponds to the frequency of the respective class interval. Since I cannot draw a histogram here, imagine a bar graph with the above frequencies for each class interval.
Describe the frequency polygon For the frequency polygon, we plot the midpoints of each class interval on the x-axis and the corresponding frequencies on the y-axis. The midpoints are 4.5, 14.5, 24.5, 34.5, 44.5, 54.5, 64.5, 74.5, 84.5. Connect the plotted points with straight lines to form the frequency polygon. The polygon starts and ends at zero frequency by extending the lines to the midpoints of the class intervals before the first and after the last. Since I cannot draw a frequency polygon here, imagine a line graph connecting the points (4.5, 3), (14.5, 3), (24.5, 2), (34.5, 3), (44.5, 9), (54.5, 5), (64.5, 6), (74.5, 2), (84.5, 2).
Examples
Understanding data distribution is crucial in many real-world scenarios. For example, a teacher can use a frequency table, histogram, and frequency polygon to analyze the distribution of test scores in a class. This helps the teacher identify areas where students are struggling and adjust their teaching methods accordingly. Similarly, businesses can use these tools to analyze sales data, customer demographics, or website traffic to make informed decisions about marketing strategies and resource allocation.
We created a frequency table for the marks of thirty girls based on specified class intervals. Using the table, we can draw a histogram and a frequency polygon, both of which visually summarize the distribution of scores. These statistical tools aid in understanding the data more effectively.
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