bus-stat-book1

Bus-stat-book1

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Unformatted text preview: tive frequencies and get ∑fd 2 7.Substituting the values in the following formula to get the standard deviation Example 13: The daily temperature recorded in a city in Russia in a year is given below. Temperature C 0 No. of days 10 -40 to –30 18 -30 to –20 30 -20 to –10 42 -10 to 0 65 0 to 10 180 10 to 20 20 20 to 30 365 Calculate Standard Deviation. 163 Solution: Temperature -40 to -30 -30 to -20 -20 to -10 -10 to - 0 0 to 10 10 to 20 20 to 30 Mid value (m) -35 -25 -15 -5 5 15 25 No. of days f 10 18 30 42 65 180 20 d= m− (−5n ) 10n -3 -2 -1 0 1 2 3 N=365 fd -30 -36 -30 0 65 360 60 fd 2 90 72 30 0 65 720 180 ∑fd = ∑fd 2 389 =1157 2 1157 389 − × 10 365 365 = 3.1699 - 1.1358 × 10 = 2.0341 × 10 = 1.4262 × 10 = 14.26°c = 7.6.5 Combined Standard Deviation: If a series of N1 items has mean X1 and standard deviation σ1 and another series of N2 items has mean X 2 and standard deviation σ2 , we can find out the combined mean and combined standard deviation by using the formula. 164 Where d1 = X1 − X12 d2 = X2 − X12 Example 14: Particulars regarding income of two villages are given below. Village A B No.of people 600 500 Average income 175 186 Standard deviation of 10 9 income Compute combined mean and combined Standard deviation. Solution: Given N1 = 600, X1 = 175, σ1 = 10 N2 = 500, X2= 186, σ2 = 9 Combined mean = 600 × 175 + 500 × 186 600 + 500 105000 + 93000 1100 198000 = = 180 1100 Combined Standard Deviation: = 165 d1 = X1 − X12 = 175 − 180 = −5 d2 = X2 − X12 =186 – 180 =6 600 × 100 + 500 × 81 + 600 × 25 + 500 × 36 σ12 = 600 + 500 60000 + 40500 + 15000 + 18000 1100 133500 = 1100 = 121.364 = 11.02. 7.6.6 Merits and Demerits of Standard Deviation: Merits: 1. It is rigidly defined and its value is always definite and based on all the observations and the actual signs of deviations are used. 2. As it is based on arithmetic mean, it has all the merits of arithmetic mean. 3. It is the most important and widely used measure of dispersion. 4. It is...
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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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