bus-stat-book1

Therefore where the purpose is to know the point of

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Unformatted text preview: series of individual observations, mode is often found by mere inspection. Example 29: 2 , 7, 10, 15, 10, 17, 8, 10, 2 ∴ Mode = M0 =10 In some cases the mode may be absent while in some cases there may be more than one mode. 128 Example 30: 1. 12, 10, 15, 24, 30 (no mode) 2. 7, 10, 15, 12, 7, 14, 24, 10, 7, 20, 10 ∴ the modes are 7 and 10 Grouped Data: For Discrete distribution, see the highest frequency and corresponding value of X is mode. Continuous distribution : See the highest frequency then the corresponding value of class interval is called the modal class. Then apply the formula. 1 ×C Mode = M 0 = l + 1 + 2 l = Lower limit of the model class 1 = f1-f0 2 =f1-f2 f1 = frequency of the modal class f0 = frequency of the class preceding the modal class f2 = frequency of the class succeeding the modal class The above formula can also be written as f1 -f 0 Mode = l + ×c 2f1 - f 0 - f 2 Remarks : 1. If (2f1-f0-f2) comes out to be zero, then mode is obtained by the following formula taking absolute differences within vertical lines. ( f1 − f 0 ) 2. M0= l + ×c | f1 − f 0 | + | f1 − f 2 | 3. If mode lies in the first class interval, then f0 is taken as zero. 129 4. The computation of mode poses no problem in distributions with open-end classes, unless the modal value lies in the open-end class. Example 31: Calculate mode for the following : C- I 0-50 50-100 100-150 150-200 200-250 250-300 300-350 350-400 400 and above f 5 14 40 91 150 87 60 38 15 Solution: The highest frequency is 150 and corresponding class interval is 200 – 250, which is the modal class. Here l=200,f1=150,f0=91, f2=87, C=50 Mode = M0 = l + = 200 + f1 -f 0 ×c 2f1 - f 0 - f 2 150-91 × 50 2 × 150 − 91 − 87 2950 122 = 200 + 24.18 = 224.18 = 200 + Determination of Modal class : For a frequency distribution modal class corresponds to the maximum frequency. But in any one (or more) of the following cases 130 i.If the maximum frequency is repeated ii.If the maximum frequency occurs in the beginning or at the end of the distribution iii.If there are irregularities in t...
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