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Q. 1 In 1798 the scientist Henry Cavendish used a torsion balance to estimate the density of the earth as a multiple of the density of water. He ran his experiment 29 times and obtained the following results: 5.50 5.575.42 5.6 5.53 5.47 4.88 5.62 5.63 4.07 .29 5.34 5.26 5.44 5.46 5.55 5.34 5.30 5.36 5.79 5.75 5.295.10 5.86 5.58 5.27 5.85 5.65 5.39 a) Construct an appropriate stem-and-leaf plot of this data b) Describe the distribution of the dataset based on the stem-and-leaf plot. c) Calculate the mean and median of the dataset. Which do you think is the better measure of location for this dataset? Why? d) Calculate the 5% 10% and 20% trimmed means for this dataset. e) Calculate the inter-quartile range of the data.
math   Statistics-And-Probability   
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a) The stem and leaf plot is as follows: Descriptive statistics Density 29 count Stem and Leaf plot for Density stem unit1 leaf unit0.1 Frequency Stem Leaf 14. 1:3 29 5 1222 2333334444 5 5555566667788 b) From the stem and leaf plot, observe that the distribution of the data set is skewed to the right because the number of observations are fall from right.Calculate mean. (5.5+5.57+.5.39) 29 157.17 29 5.42 Calculate median The median is middle number of the ascending order of the data for the data set has odd number of observations The given data series is odd series so the middle number of ascending order of the data is the median 4.07 4.88 5.10 5.26 5.27 5.29 5.30 5.34 5.34 5.36 5.39 5.42 5.44 5.46 5.47 5.50 5.53 5.55 5.57 5.58 5.61 5.62 5.63 5.63 5.75 5.795.85 5.86 From the above ascending order of the data, observe that the median is 5.46 because it is middle number in the data set Therefore, the median is 5.46 The mean is the better measure of location because its involves each and every observation in the data setd) Calculate 5% trimmed mean. The trimmed value is, Trimmed value = n × p 29 × 0.05 = 1.45 The trimmed value is 2 so discard first and last 2 observation in the ascending order of the data and calculate the mean (5.10+5.26+ 25 +5.75 +5.79) 136.51 25 - 5.46 Calculate 10% trimmed mean. The trimmed value is,Trimmed value-nxp 29 × 0.1 2.9 The trimmed value is 3 so discard first and last 3 observations in the ascending ord the data and calculate the mean. (5.26 +5.27 23 +5.75) 125.62 23 - 5.462 Calculate 20% trimmed mean The trimmed value i s, Trimmed value-nx p 29x0.2 The trimmed value is 6 so discard first and last 6 observations in the ascending order of the data and calculates the mean(20%)ATX, 17 92.77 17 = 5.457 e) Use Excel to find the inter-quartile range Descriptive statisticS Density 29 count 1st quart

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