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### Lecture Slides (1).pptx

• 1.  Mode: The most repeated or most common or the most frequent Value which occurs in a set of values. The mode is the value in a data set that occur most frequently. A set of data can have more than one mode if two or more values tie for the most frequently occurring value.
• 2.  Collect the sample data. a sample of 20 group was selected at random. 2,4,1,2,3,2,4,2,3,6,8,4,2,1,7,4,2,4,4,3. “most repeated value or values” Mode = 2,4 X Frequency 1 2 2 6 3 3 4 6 5 0 6 1 7 1 8 1
• 3.  For group data Mode = l + (fm – f1) * h (fm- f1) + (fm –f2) here l = lower limit class boundary of the mode group fm= maximum frequency f1 = frequency preceding the fm f2 = frequency following the fm h = class interval
• 4. Marks F Class boundary 30 - 39 2 29.5 – 39.5 40 – 49 3 39.5 – 49.5 50 – 59 11 49.5 – 59.5 60 – 69 20 f1 59.5 – 69.5 70 – 79 32 fm l 69.5 – 79.5 mode group 80- 89 25 f2 79.5 – 89.5 90 - 99 7 90.5 – 99.5
• 5. Mode = l + (fm – f1) * h (fm- f1) + (fm –f2) = 69.5 + ( 32 – 20) * 10 (32 – 20) + (32 – 25) = 69.5 + 120 12+7 mode = 69.5 + 6.32 = 75.82
• 6.  Advantages: 1. It is easy and quick to calculate. 2. It is easy to understand. 3. Extreme values do not effect its values. 4. It can be determined from open end distribution. 5. It can be found by inspection from ungroup data. 6. It can be used for qualitative data.
• 7.  Disadvantage: 1. It is not well defined. 2. It is not based on all the observation of a set of data. 3. It can not be used for further mathematical processing. 4. There may be more then one value of the mode in the set of data. 5. There may be no mode, if there is no common value in the data.
• 8.  Weighted Mean: weighted mean is a special case of arithmetic mean. The mean value of data values that have been weighted according to their relative importance.  when the value are not equal importance, we assign them certain numerical values to express their relative importance. These numerical values are called weights.  Weighted mean =  WX / W
• 9.  The marks obtained by a students in English, Urdu and Statistics were 70, 76 and 82 respectively. Find the suitable average if weights of 5, 4 and 3 are assigned to these subjects.  Weighted mean =  WX / W = 5*70+4*76+3*82 5+4+3 = 900/12 = 75
• 10.  Empirical Relationship among Mean, Median and Mode. 1. If Mean = Median = Mode then distribution is symmetrical. 2. If Mean > Median > Mode then distribution is positively skewed. 3. If Mean < Median < Mode then distribution is negatively Skewed.
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