bus-stat-book1

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Unformatted text preview: ercentiles : The percentile values divide the distribution into 100 parts each containing 1 percent of the cases. The percentile (Pk) is that value of the variable up to which lie exactly k% of the total number of observations. 126 Relationship : P25 = Q1 ; P50 = D5 = Q2 = Median and P75 = Q3 Percentile for Raw Data or Ungrouped Data : Example 27: Calculate P15 for the data given below: 5, 24 , 36 , 12 , 20 , 8 Arranging the given values in the increasing order. 5, 8, 12, 20, 24, 36 th 15(n + 1) P15 = item 100 th 15 × 7 = item 100 = (1.05)th item = 1st item + 0.05 (2nd item – 1st item) = 5 + 0.05 (8-5) = 5 + 0.15 = 5.15 Percentile for grouped data : Example 28: Find P53 for the following frequency distribution. Class interval 0-5 5-10 10-15 15-20 20-25 25-30 30-35 35-40 Frequency 5 8 12 16 20 10 4 3 Solution: Class Interval 0-5 5-10 10-15 15-20 20-25 25-30 30-35 35-40 Total Frequency 5 8 12 16 20 10 4 3 78 127 C.f 5 13 25 41 61 71 75 78 P53 53N −m = l + 100 ×c f = 20 + 41.34 − 41 ×5 20 = 20 + 0.085 = 20.085. Mode : The mode refers to that value in a distribution, which occur most frequently. It is an actual value, which has the highest concentration of items in and around it. According to Croxton and Cowden “ The mode of a distribution is the value at the point around which the items tend to be most heavily concentrated. It may be regarded at the most typical of a series of values”. It shows the centre of concentration of the frequency in around a given value. Therefore, where the purpose is to know the point of the highest concentration it is preferred. It is, thus, a positional measure. Its importance is very great in marketing studies where a manager is interested in knowing about the size, which has the highest concentration of items. For example, in placing an order for shoes or ready-made garments the modal size helps because this sizes and other sizes around in common demand. Computation of the mode: Ungrouped or Raw Data: For ungrouped data or a...
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This note was uploaded on 01/18/2014 for the course BUS 100 taught by Professor Moshiri during the Winter '08 term at UC Riverside.

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