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stat study guide - Sample Mean Formula: x= xi n Compute the...

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Sample Mean Formula: n x x i = Compute the sample mean given the class size data for five college classes: 46 54 42 46 32 1 2 3 4 5 5 46 54 42 46 32 5 44 x x x x x + + + + = + + + + = = The sample mean class size is 44 students. Median: Arrange the data in ascending order (smallest value to largest value). 1. For an odd number of observations, the median is the middle value. 2. For an even number of observations, the median is the average of the two middle values. Mode: The mode is the value that occurs with the greatest frequency. Compute the mode given the class size data of five college classes: 32 42 46 46 54 Because the values 46 occur more often than any other value – 46 is the mode. Compute the median given the class size data of five college classes: 32 42 46 46 54 Because n=5 is odd, the median is the middle value. Median class size: 46 Compute the median given the class size data of five college classes: 32 42 46 50 54 58 Because n=6 is even, the median is the average of the two middle values. 46 50 48 2 Median + = = Median class size: 48 Calculating the p th Percentile: Step 1 : Arrange the data in ascending order (smallest value to largest value). Step 2 : Compute an index i n p i = 100 where p is the percentile of interest and n is the number of observations. Step 3 : (a) If i is not an integer, round up . The next integer greater than I denotes the position of the p th percentile. (b) If i is an integer, the p th percentile is the average of the values in positions i and i + 1. Quartiles: Q 1 = first quartile, or 25 th percentile Q 2 = second quartile, or 50 th percentile (also the median) Q 3 = third quartile, or 75 th percentile The computations of Q 1 and Q 3 require the use of the rule for finding the 25 th and 75 th percentiles. Those calculations follow: For Q 1 , 25 12 3 100 100 p i n = = = Because i is an integer, step 3(b) indicates that the first quartile, or 25 th percentile, is the average of the third and fourth values; thus, Q 1 = (2850+2880)/2 = $2865. Calculate the 85 th percentile given the monthly starting salary of 12 recent graduates: 2850, 2950, 3050, 2880, 2755, 2710, 2890, 3130, 2940, 3325, 2920, 2880. Step 1: Arrange data in ascending order. 2710 2755 2850 2880 2880 2890 2920 2940 2950 3050 3130 3325 Step 2: 85 12 10.2 100 100 p i n = = = Step 3: Because i is not an integer, round up. The position of the 85 th percentile is the next integer greater than 10.2, the 11 th position. The 85 th percentile is the value in the 11 th position, or 3130. For Q 3 , 75 12 9 100 100 p i n = = = Because i is an integer, step 3(b) indicates that the third quartile, or 75 th percentile, is the average of the ninth and tenth values; thus, Q 3 = (2950+3050)/2 = $3000. Range:
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stat study guide - Sample Mean Formula: x= xi n Compute the...

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