4. The stem-and-leaf diagram below shows the most recent data for the median age, in years, of the population in each of the 35 countries in Europe. For example, there is one country in which the median age of the population is 47.4 years. low: 33.4 37 0 1 2 38 2 39 3 8 40 3 5 8 41 0 1 15 42 5 5 5 6 43 0 0 577 77 data. 44 0 2 2 45 8 46 47 4 Key: 31 means 3.1 (a) Find the values of the median, the lower quartile and the upper quartile for these [2] (b) Any value that is more than 1.5 multiplied by the interquartile range from the nearest quartile can be classed as an outlier. Use this definition of an outlier to show that the only outlier is 33.4. [3] Table 4a shows summary statistics for the most recent data for the median age of the population in the 35 countries in Asia. The two countries in Asia with the highest median age are Japan (47.7 years) and Hong Kong (44.8 years). Two of the statistics are missing. n Mean 35 1048.3 32942.71 Min 19 QI 24.5 Median 29.9 Q3 33.1 Max 47.7 Table 4a (c) Use the definition of an outlier as given in part (b) to show that Japan is the only outlier. 3 of 4 integralmaths.org 12/11/20 MEI [3] Edexcel Collecting & interpreting data Assessment Fig. 4b shows a box plot illustrating the median ages of the European countries x 16 18 20 22 24 26 28 30 32 34 36 38 Fig. 4b 40 42 46 48 50 (d) On a copy of Fig. 4b, using the information given in Table 4a, draw a box plot for the median age in the Asian countries. [3] (e) Referring to the two box plots, make two comparisons between the data in the two regions. [2] (f) Calculate the values of the mean and the standard deviation for the Asian countries. [3] (g) An alternative definition of an outlier is a value that is more than 2 standard deviations from the mean. Show that this definition also makes Hong Kong an outlier. [2]