Tut sol - BES Tutorial Sample Solutions, S1/10 WEEK 3...

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1 BES Tutorial Sample Solutions, S1/10 WEEK 3 TUTORIAL EXERCISES (To be discussed in the week starting March 15) 1. Using the car data from Week 2, Question 3: (a) Redo Q3(c) using EXCEL to confirm that the frequency histogram is given by Figure 3.1. (b) Calculate the mean, median and mode for this sample of data and use them to further describe the distribution of ages. Mean 3 . 7 20 11 24 ... 6 5 5 Ordering the data from lowest to highest: 2, 2, 3, 4, 4, 5, 5, 5, 6, 6, 6, 6, 6, 7, 9, 10, 11, 11, 14, 24, 0 1 2 3 4 5 6 7 8 9 10 2 6 10 14 18 22 Frequency Age Figure 3.1: Revised histogram for age of cars
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2 Median = (6+6)/2=6 Mode = 6 The sample mean is to the right of mode and median, suggesting that the sample distribution is skewed towards the right. The cause seems to be the large outlier – one car had an age of 24, which appeared to be very different to the age of other cars. Given the skewness and the outlier, the median is possibly a better measure of central tendency. Hence a typical second-hand car is 6 years old. Alternatively the EXCEL output is: Age Mean 7.3 Standard Error 1.126476 Median 6 Mode 6 Standard Deviation 5.037752 Sample Variance 25.37895 Kurtosis 5.712234 Skewness 2.0983 Range 22 Minimum 2 Maximum 24 Sum 146 Count 20 (c) If the largest observation were removed from this data set, how would the three measures of central tendency you have calculated change? Mean 4 . 6 19 11 6 ... 6 5 5 (Now closer to median) Median = (6+6)/2= 6 (unchanged) Mode = 6 (unchanged)
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3 2. For the following statistical population, compute the mean, range, variance and standard deviation: 3, 3, 5, 12, 13, 14, 17, 20, 21, 21. 9 . 12 10 21 21 20 17 14 13 12 5 3 3 Mean 18 3 21 Range 89 . 45 10 ) 9 . 12 21 ( .... ) 9 . 12 3 ( ) ( 2 2 2 2 N x Variance i 7742 . 6 89 . 45 deviation Standard 3. For the population in Q2 above, what would happen to each of the measures you have calculated if : (a) 4 were added to each data point (observation)?
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Tut sol - BES Tutorial Sample Solutions, S1/10 WEEK 3...

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