0 added
0 removed
Original
2026-01-01
Modified
2026-02-28
1
<p>To find the modal class from a chart or graph, follow the steps mentioned below: </p>
1
<p>To find the modal class from a chart or graph, follow the steps mentioned below: </p>
2
<p><strong>Step 1:</strong>Identify the highest bar or peak:</p>
2
<p><strong>Step 1:</strong>Identify the highest bar or peak:</p>
3
<p>In a<a>histogram</a>, look for the tallest bar (highest frequency). In a<a>frequency polygon</a>, find the highest peak on the graph. For the<a>bar chart</a>, locate the category with the highest bar.</p>
3
<p>In a<a>histogram</a>, look for the tallest bar (highest frequency). In a<a>frequency polygon</a>, find the highest peak on the graph. For the<a>bar chart</a>, locate the category with the highest bar.</p>
4
<p><strong>Step 2:</strong>Read the class interval:</p>
4
<p><strong>Step 2:</strong>Read the class interval:</p>
5
<p>The modal class is the interval corresponding to the tallest bar or peak. If two bars have the same highest frequency, then the given dataset is bimodal or multimodal.</p>
5
<p>The modal class is the interval corresponding to the tallest bar or peak. If two bars have the same highest frequency, then the given dataset is bimodal or multimodal.</p>
6
<p><strong>Step 3:</strong>Estimate the mode using the formula:</p>
6
<p><strong>Step 3:</strong>Estimate the mode using the formula:</p>
7
<p>If needed, apply the mode formula for grouped data:</p>
7
<p>If needed, apply the mode formula for grouped data:</p>
8
<p> \(\text{Mode} = L + \left( \frac{(f_{1} - f_{0})}{(2f_{1} - f_{0} - f_{2})} \right) \times h\)</p>
8
<p> \(\text{Mode} = L + \left( \frac{(f_{1} - f_{0})}{(2f_{1} - f_{0} - f_{2})} \right) \times h\)</p>
9
<p>Where,</p>
9
<p>Where,</p>
10
<p>L is the lower limit of the modal class</p>
10
<p>L is the lower limit of the modal class</p>
11
<p>fm is the frequency of the modal class</p>
11
<p>fm is the frequency of the modal class</p>
12
<p>f1 is the frequency of the class preceding the modal class</p>
12
<p>f1 is the frequency of the class preceding the modal class</p>
13
<p>f2 is the frequency of the class succeeding the modal class</p>
13
<p>f2 is the frequency of the class succeeding the modal class</p>
14
<p>h is the class width.</p>
14
<p>h is the class width.</p>
15
<p>For example, find the modal class from the graph. </p>
15
<p>For example, find the modal class from the graph. </p>
16
<strong>Marks</strong><strong>Number of Students</strong>0-10 5 10-20 8 20-30 12 30-40 20 40-50 10 50-60 5<p>Here, the tallest bar corresponds to 30-40, so this is the modal class. </p>
16
<strong>Marks</strong><strong>Number of Students</strong>0-10 5 10-20 8 20-30 12 30-40 20 40-50 10 50-60 5<p>Here, the tallest bar corresponds to 30-40, so this is the modal class. </p>
17
<p>Using the Mode formula: \(\text{Mode} = L + \frac{f_1 - f_0}{2f_1 - f_0 - f_2} \times h \)</p>
17
<p>Using the Mode formula: \(\text{Mode} = L + \frac{f_1 - f_0}{2f_1 - f_0 - f_2} \times h \)</p>
18
<p>Where, </p>
18
<p>Where, </p>
19
<p>\(L = 30 \\ \ \\ f_1 = 20 \\ \ \\ f_0 = 12 \\ \ \\ f_2 = 10 \\ \ \\ h = 10 \)</p>
19
<p>\(L = 30 \\ \ \\ f_1 = 20 \\ \ \\ f_0 = 12 \\ \ \\ f_2 = 10 \\ \ \\ h = 10 \)</p>
20
<p> \(\text{Mode} = L + \frac{f_1 - f_0}{2f_1 - f_0 - f_2} \times h \)</p>
20
<p> \(\text{Mode} = L + \frac{f_1 - f_0}{2f_1 - f_0 - f_2} \times h \)</p>
21
<p>\(= 30 + \frac{20 - 10}{2 \times 20 -12- 12} \times 10 \) </p>
21
<p>\(= 30 + \frac{20 - 10}{2 \times 20 -12- 12} \times 10 \) </p>
22
<p>\(= 30 + {8 \over 18} \times 10\) </p>
22
<p>\(= 30 + {8 \over 18} \times 10\) </p>
23
<p>\(= 34.44\)</p>
23
<p>\(= 34.44\)</p>
24
<p>So, modal class is 30-40 and mode is 34.44 marks. </p>
24
<p>So, modal class is 30-40 and mode is 34.44 marks. </p>
25
25