ST104a Live Session Exercise 1 In this exercise you will practise aspects of data visualisation and descriptive statistics. In statistical analysis, there are usually simply too many numbers to make sense of just by staring at them. Data visualisation and descriptive statistics attempt to summarise key features of the data to make them understandable and easy to communicate. The main function of diagrams is to bring out interesting features of a dataset visually by displaying its distribution, i.e. summarising the whole sample distribution of a variable. Descriptive statistics allow us to summarise one feature of the sample distribution in a single number. Here you will work with measures of central tendency, measures of dispersion and skewness. 1. A police officer recorded the speed of 30 cars on a road with a 30 miles per hour (mph) speed limit. The recorded data are shown below: 25.6 25.7 25.7 25.8 25.8 26.2 26.9 27.5 27.7 27.8 27.9 27.9 28.3 28.4 28.5 28.8 28.9 28.9 29.0 29.1 29.2 29.3 29.5 29.7 29.8 30.1 30.1 30.2 33.2 34.9 (a) Construct a stem-and-leaf diagram for these data. (b) Draw a suitable histogram for these data. (c) Comment on the shape of the sample distribution. (d) Determine the median of the data using the stem-and-leaf diagram in (a). (e) Produce a boxplot for these data. (f) Using the following summary statistics, calculate the sample mean and sample standard deviation of the recorded speeds: Sum of data = x = 856.4 and Sum of squares of data = r = 24,574.06. i (g) Comment on the relative values of the mean and median. (h) What percentage of the data fall within one sample standard deviation of the sample mean? And what percentage fall within two sample standard deviations of the sample mean?