Stem and leaf diagrams and box plots Statistics

Example 1 Draw a stem and leaf diagram using the set of data below. 148 135 119 147 93 107 145 87 113 103 111 110 113 110 104 Work out the quartiles and hence draw a box plot

Solution 8 7 9 3 10 3 4 7 11 0 0 1 7 8 Stem and leaf diagram 3 3 9 n = 15 13 | 5 represents 135 12 Min = 87 13 5 14 5 Q 1 = 104 Q 2 = 111 Boxplot Q 3 = 135 Max = 148

Example 2 Draw a stem and leaf diagram using the set of data below. 40 55 55 52 50 67 42 46 72 46 51 64 51 57 59 43 60 53 49 66 54 64 48 58 52 Work out the quartiles and hence draw a box plot

Stem and leaf diagram Solution n = 25 4 | 0 represents 40 Min = 40 4 0 2 3 6 6 8 9 5 0 1 1 2 2 3 4 6 0 4 4 6 7 7 2 Q 1 = 48· 5 Q 2 = 53 Boxplot Q 3 = 59· 5 5 5 7 Max = 72 8 9

Example 3 Draw a stem and leaf diagram using the set of data below. 15 16 1 15 15 13 14 14 14 7 6 45 4 9 6 3 5 2 15 15 1 14 17 13 15 14 15 4 2 60 7 7 5 8 1 5 15 Work 15 out 1 the 15 quartiles 14 14 15 draw 14 a box plot and 15 hence 5 7 50 2 5 7 2 9 2

Stem and leaf diagram Solution n = 27 13 | 5 represents 135 13 14 15 16 5 1 0 0 6 2 2 3 5 5 5 7 7 2 2 2 4 4 5 5 7 7 8 9 9 6 17 7 Min = 135 Q 1 = 145 Q 2 = 152 Boxplot Q 3 = 157 Max = 177

Example 4 Draw a stem and leaf diagram using the set of data below. 0. 23 0. 24 0. 76 0. 64 0. 68 0. 88 0. 05 0. 03 0. 34 0. 30 0. 60 0. 84 0. 53 0. 30 0. 51 0. 62 0. 84 0. 46 0. 04 0. 15 0. 65 0. 88 0. 63 0. 23 0. 85 0. 26 0. 47 0. 81 0. 99 0. 24 0. 82 0. 01 0. 76 0. 68 0. 11 0. 51 0. 99 0. 02 Work out the quartiles and hence draw a box plot

Solution Stem and leaf diagram n = 40 2 | 3 represents 0. 23 Min = 0· 01 Q 1 = 0· 235 Q 2 = 0· 52 Boxplot 0 1 2 3 4 5 1 1 5 2 3 3 4 4 6 3 0 0 4 4 6 7 5 1 1 3 6 0 2 3 4 5 8 8 7 6 6 6 8 1 2 4 4 5 8 8 9 9 9 Q 3 = 0· 815 Max = 0· 99 8