Stem and leaf diagrams

Introduction Stem and leaf diagrams are used to: retain raw data values (possibly rounded) provide a diagrammatic representation of the distribution - like bar chart find median, quartiles etc

Stages in drawing a stem and leaf Decide on and provide a key for the stem and leaf. The leaf is always the smallest (least significant) digit - you may need to round in some circumstances Draw a preliminary stem and leaf directly from the raw data - this is likely to mean the leafs are unordered Draw a new stem and leaf diagram with the leaves put into numerical order. If needed add the number of leaves

Example - drawing a stem and leaf Question:- 29 students were set a simple task. Their completion times to the nearest second were: 47 61 53 43 46 46 68 48 72 57 48 54 41 63 49 42 58 65 45 44 43 51 45 38 46 44 52 43 47 (a) set these data into a stem and leaf diagram (b) find the median, quartiles and inter-quartile range Answer (a):- (1) key: 4|7 means 47 (2) put values into preliminary diagram: 3 4 5 6 7 Completion times stem leaf

Example - drawing a stem and leaf Question:- 29 students were set a simple task. Their completion times to the nearest second were: 47 61 53 43 46 46 68 48 72 57 48 54 41 63 49 42 58 65 45 44 43 51 45 38 46 44 52 43 47 (a) set these data into a stem and leaf diagram (b) find the median, quartiles and inter-quartile range Answer (a):- (1) key: 4|7 means 47 (2) put values into preliminary diagram: Completion times 3 4 5 6 7 7

Example - drawing a stem and leaf Question:- 29 students were set a simple task. Their completion times to the nearest second were: 47 61 53 43 46 46 68 48 72 57 48 54 41 63 49 42 58 65 45 44 43 51 45 38 46 44 52 43 47 (a) set these data into a stem and leaf diagram (b) find the median, quartiles and inter-quartile range Answer (a):- (1) key: 4|7 means 47 (2) put values into preliminary diagram: Completion times 3 4 5 6 7 7 1

Example - drawing a stem and leaf Question:- 29 students were set a simple task. Their completion times to the nearest second were: 47 61 53 43 46 46 68 48 72 57 48 54 41 63 49 42 58 65 45 44 43 51 45 38 46 44 52 43 47 (a) set these data into a stem and leaf diagram (b) find the median, quartiles and inter-quartile range Answer (a):- (1) key: 4|7 means 47 (2) put values into preliminary diagram: Completion times 3 4 5 6 7 7 3 1

Example - drawing a stem and leaf Question:- 29 students were set a simple task. Their completion times to the nearest second were: 47 61 53 43 46 46 68 48 72 57 48 54 41 63 49 42 58 65 45 44 43 51 45 38 46 44 52 43 47 (a) set these data into a stem and leaf diagram (b) find the median, quartiles and inter-quartile range Answer (a):- (1) key: 4|7 means 47 (2) put values into preliminary diagram: Completion times 3 4 5 6 7 7 3 3 1

Example - drawing a stem and leaf Question:- 29 students were set a simple task. Their completion times to the nearest second were: 47 61 53 43 46 46 68 48 72 57 48 54 41 63 49 42 58 65 45 44 43 51 45 38 46 44 52 43 47 (a) set these data into a stem and leaf diagram (b) find the median, quartiles and inter-quartile range Answer (a):- (1) key: 4|7 means 47 (2) put values into preliminary diagram: Completion times 3 4 5 6 7 7 3 6 3 1

Example - drawing a stem and leaf Question:- 29 students were set a simple task. Their completion times to the nearest second were: 47 61 53 43 46 46 68 48 72 57 48 54 41 63 49 42 58 65 45 44 43 51 45 38 46 44 52 43 47 (a) set these data into a stem and leaf diagram (b) find the median, quartiles and inter-quartile range Answer (a):- (1) key: 4|7 means 47 (2) put values into preliminary diagram: Completion times 3 4 5 6 7 7 3 6 6 3 1

Example - drawing a stem and leaf Question:- 29 students were set a simple task. Their completion times to the nearest second were: 47 61 53 43 46 46 68 48 72 57 48 54 41 63 49 42 58 65 45 44 43 51 45 38 46 44 52 43 47 (a) set these data into a stem and leaf diagram (b) find the median, quartiles and inter-quartile range Answer (a):- (1) key: 4|7 means 47 (2) put values into preliminary diagram: Completion times 3 4 5 6 7 7 3 6 6 3 1 8

Example - drawing a stem and leaf Question:- 29 students were set a simple task. Their completion times to the nearest second were: 47 61 53 43 46 46 68 48 72 57 48 54 41 63 49 42 58 65 45 44 43 51 45 38 46 44 52 43 47 (a) set these data into a stem and leaf diagram (b) find the median, quartiles and inter-quartile range Answer (a):- (1) key: 4|7 means 47 (2) put values into preliminary diagram: Completion times 3 4 5 6 7 7 3 6 6 8 3 1 8

Example - drawing a stem and leaf Question:- 29 students were set a simple task. Their completion times to the nearest second were: 47 61 53 43 46 46 68 48 72 57 48 54 41 63 49 42 58 65 45 44 43 51 45 38 46 44 52 43 47 (a) set these data into a stem and leaf diagram (b) find the median, quartiles and inter-quartile range Answer (a):- (1) key: 4|7 means 47 (2) put values into preliminary diagram: Completion times 3 4 5 6 7 7 3 6 6 8 3 1 8 2

Example - drawing a stem and leaf Question:- 29 students were set a simple task. Their completion times to the nearest second were: 47 61 53 43 46 46 68 48 72 57 48 54 41 63 49 42 58 65 45 44 43 51 45 38 46 44 52 43 47 (a) set these data into a stem and leaf diagram (b) find the median, quartiles and inter-quartile range Answer (a):- (1) key: 4|7 means 47 (2) put values into preliminary diagram: Completion times 3 4 5 6 7 7 3 6 6 8 3 7 1 8 2

Example - drawing a stem and leaf Question:- 29 students were set a simple task. Their completion times to the nearest second were: 47 61 53 43 46 46 68 48 72 57 48 54 41 63 49 42 58 65 45 44 43 51 45 38 46 44 52 43 47 (a) set these data into a stem and leaf diagram (b) find the median, quartiles and inter-quartile range Answer (a):- (1) key: 4|7 means 47 (2) put values into preliminary diagram: Completion times 3 4 5 6 7 7 3 6 6 8 8 3 7 1 8 2

Example - drawing a stem and leaf Question:- 29 students were set a simple task. Their completion times to the nearest second were: 47 61 53 43 46 46 68 48 72 57 48 54 41 63 49 42 58 65 45 44 43 51 45 38 46 44 52 43 47 (a) set these data into a stem and leaf diagram (b) find the median, quartiles and inter-quartile range Answer (a):- (1) key: 4|7 means 47 (2) put values into preliminary diagram: Completion times 3 4 5 6 7 7 3 6 6 8 8 3 7 4 1 8 2

Example - drawing a stem and leaf Question:- 29 students were set a simple task. Their completion times to the nearest second were: 47 61 53 43 46 46 68 48 72 57 48 54 41 63 49 42 58 65 45 44 43 51 45 38 46 44 52 43 47 (a) set these data into a stem and leaf diagram (b) find the median, quartiles and inter-quartile range Answer (a):- (1) key: 4|7 means 47 (2) put values into preliminary diagram: Completion times 3 4 5 6 7 7 3 6 6 8 8 1 3 7 4 1 8 2

Example - drawing a stem and leaf Question:- 29 students were set a simple task. Their completion times to the nearest second were: 47 61 53 43 46 46 68 48 72 57 48 54 41 63 49 42 58 65 45 44 43 51 45 38 46 44 52 43 47 (a) set these data into a stem and leaf diagram (b) find the median, quartiles and inter-quartile range Answer (a):- (1) key: 4|7 means 47 (2) put values into preliminary diagram: Completion times 3 4 5 6 7 7 3 6 6 8 8 1 3 7 4 1 8 3 2

Example - drawing a stem and leaf Question:- 29 students were set a simple task. Their completion times to the nearest second were: 47 61 53 43 46 46 68 48 72 57 48 54 41 63 49 42 58 65 45 44 43 51 45 38 46 44 52 43 47 (a) set these data into a stem and leaf diagram (b) find the median, quartiles and inter-quartile range Answer (a):- (1) key: 4|7 means 47 (2) put values into preliminary diagram: Completion times 3 4 5 6 7 7 3 6 6 8 8 1 9 3 7 4 1 8 3 2

Example - drawing a stem and leaf Question:- 29 students were set a simple task. Their completion times to the nearest second were: 47 61 53 43 46 46 68 48 72 57 48 54 41 63 49 42 58 65 45 44 43 51 45 38 46 44 52 43 47 (a) set these data into a stem and leaf diagram (b) find the median, quartiles and inter-quartile range Answer (a):- (1) key: 4|7 means 47 (2) put values into preliminary diagram: Completion times 3 4 5 6 7 7 3 6 6 8 8 1 9 2 3 7 4 1 8 3 2

Example - drawing a stem and leaf Question:- 29 students were set a simple task. Their completion times to the nearest second were: 47 61 53 43 46 46 68 48 72 57 48 54 41 63 49 42 58 65 45 44 43 51 45 38 46 44 52 43 47 (a) set these data into a stem and leaf diagram (b) find the median, quartiles and inter-quartile range Answer (a):- (1) key: 4|7 means 47 (2) put values into preliminary diagram: Completion times 3 4 5 6 7 7 3 6 6 8 8 1 9 2 3 7 4 8 1 8 3 2

Example - drawing a stem and leaf Question:- 29 students were set a simple task. Their completion times to the nearest second were: 47 61 53 43 46 46 68 48 72 57 48 54 41 63 49 42 58 65 45 44 43 51 45 38 46 44 52 43 47 (a) set these data into a stem and leaf diagram (b) find the median, quartiles and inter-quartile range Answer (a):- (1) key: 4|7 means 47 (2) put values into preliminary diagram: Completion times 3 4 5 6 7 7 3 6 6 8 8 1 9 2 3 7 4 8 1 8 3 5 2

Example - drawing a stem and leaf Question:- 29 students were set a simple task. Their completion times to the nearest second were: 47 61 53 43 46 46 68 48 72 57 48 54 41 63 49 42 58 65 45 44 43 51 45 38 46 44 52 43 47 (a) set these data into a stem and leaf diagram (b) find the median, quartiles and inter-quartile range Answer (a):- (1) key: 4|7 means 47 (2) put values into preliminary diagram: Completion times 3 4 5 6 7 7 3 6 6 8 8 1 9 2 5 3 7 4 8 1 8 3 5 2

Example - drawing a stem and leaf Question:- 29 students were set a simple task. Their completion times to the nearest second were: 47 61 53 43 46 46 68 48 72 57 48 54 41 63 49 42 58 65 45 44 43 51 45 38 46 44 52 43 47 (a) set these data into a stem and leaf diagram (b) find the median, quartiles and inter-quartile range Answer (a):- (1) key: 4|7 means 47 (2) put values into preliminary diagram: Completion times 3 4 5 6 7 7 3 6 6 8 8 1 9 2 5 4 3 7 4 8 1 8 3 5 2

Example - drawing a stem and leaf Question:- 29 students were set a simple task. Their completion times to the nearest second were: 47 61 53 43 46 46 68 48 72 57 48 54 41 63 49 42 58 65 45 44 43 51 45 38 46 44 52 43 47 (a) set these data into a stem and leaf diagram (b) find the median, quartiles and inter-quartile range Answer (a):- (1) key: 4|7 means 47 (2) put values into preliminary diagram: Completion times 3 4 5 6 7 7 3 6 6 8 8 1 9 2 5 4 3 3 7 4 8 1 8 3 5 2

Example - drawing a stem and leaf Question:- 29 students were set a simple task. Their completion times to the nearest second were: 47 61 53 43 46 46 68 48 72 57 48 54 41 63 49 42 58 65 45 44 43 51 45 38 46 44 52 43 47 (a) set these data into a stem and leaf diagram (b) find the median, quartiles and inter-quartile range Answer (a):- (1) key: 4|7 means 47 (2) put values into preliminary diagram: Completion times 3 4 5 6 7 7 3 6 6 8 8 1 9 2 5 4 3 3 7 4 8 1 1 8 3 5 2

Example - drawing a stem and leaf Question:- 29 students were set a simple task. Their completion times to the nearest second were: 47 61 53 43 46 46 68 48 72 57 48 54 41 63 49 42 58 65 45 44 43 51 45 38 46 44 52 43 47 (a) set these data into a stem and leaf diagram (b) find the median, quartiles and inter-quartile range Answer (a):- (1) key: 4|7 means 47 (2) put values into preliminary diagram: Completion times 3 4 5 6 7 7 3 6 6 8 8 1 9 2 5 4 3 5 3 7 4 8 1 1 8 3 5 2

Example - drawing a stem and leaf Question:- 29 students were set a simple task. Their completion times to the nearest second were: 47 61 53 43 46 46 68 48 72 57 48 54 41 63 49 42 58 65 45 44 43 51 45 38 46 44 52 43 47 (a) set these data into a stem and leaf diagram (b) find the median, quartiles and inter-quartile range Answer (a):- (1) key: 4|7 means 47 (2) put values into preliminary diagram: Completion times 3 4 5 6 7 8 7 3 6 6 8 8 1 9 2 5 4 3 5 3 7 4 8 1 1 8 3 5 2

Example - drawing a stem and leaf Question:- 29 students were set a simple task. Their completion times to the nearest second were: 47 61 53 43 46 46 68 48 72 57 48 54 41 63 49 42 58 65 45 44 43 51 45 38 46 44 52 43 47 (a) set these data into a stem and leaf diagram (b) find the median, quartiles and inter-quartile range Answer (a):- (1) key: 4|7 means 47 (2) put values into preliminary diagram: Completion times 3 4 5 6 7 8 7 3 6 6 8 8 1 9 2 5 4 3 5 6 3 7 4 8 1 1 8 3 5 2

Example - drawing a stem and leaf Question:- 29 students were set a simple task. Their completion times to the nearest second were: 47 61 53 43 46 46 68 48 72 57 48 54 41 63 49 42 58 65 45 44 43 51 45 38 46 44 52 43 47 (a) set these data into a stem and leaf diagram (b) find the median, quartiles and inter-quartile range Answer (a):- (1) key: 4|7 means 47 (2) put values into preliminary diagram: Completion times 3 4 5 6 7 8 7 3 6 6 8 8 1 9 2 5 4 3 5 6 4 3 7 4 8 1 1 8 3 5 2

Example - drawing a stem and leaf Question:- 29 students were set a simple task. Their completion times to the nearest second were: 47 61 53 43 46 46 68 48 72 57 48 54 41 63 49 42 58 65 45 44 43 51 45 38 46 44 52 43 47 (a) set these data into a stem and leaf diagram (b) find the median, quartiles and inter-quartile range Answer (a):- (1) key: 4|7 means 47 (2) put values into preliminary diagram: Completion times 3 4 5 6 7 8 7 3 6 6 8 8 1 9 2 5 4 3 5 6 4 3 7 4 8 1 2 1 8 3 5 2

Example - drawing a stem and leaf Question:- 29 students were set a simple task. Their completion times to the nearest second were: 47 61 53 43 46 46 68 48 72 57 48 54 41 63 49 42 58 65 45 44 43 51 45 38 46 44 52 43 47 (a) set these data into a stem and leaf diagram (b) find the median, quartiles and inter-quartile range Answer (a):- (1) key: 4|7 means 47 (2) put values into preliminary diagram: Completion times 3 4 5 6 7 8 7 3 6 6 8 8 1 9 2 5 4 3 5 6 4 3 3 7 4 8 1 2 1 8 3 5 2

Example - drawing a stem and leaf Question:- 29 students were set a simple task. Their completion times to the nearest second were: 47 61 53 43 46 46 68 48 72 57 48 54 41 63 49 42 58 65 45 44 43 51 45 38 46 44 52 43 47 (a) set these data into a stem and leaf diagram (b) find the median, quartiles and inter-quartile range Answer (a):- (1) key: 4|7 means 47 (2) put values into preliminary diagram: Completion times 3 4 5 6 7 8 7 3 6 6 8 8 1 9 2 5 4 3 5 6 4 3 7 3 7 4 8 1 2 1 8 3 5 2

Example - drawing a stem and leaf Question:- 29 students were set a simple task. Their completion times to the nearest second were: 47 61 53 43 46 46 68 48 72 57 48 54 41 63 49 42 58 65 45 44 43 51 45 38 46 44 52 43 47 (a) set these data into a stem and leaf diagram (b) find the median, quartiles and inter-quartile range Answer (a):- (1) key: 4|7 means 47 (2) put values into preliminary diagram: Completion times 3 4 5 6 7 8 7 3 6 6 8 8 1 9 2 5 4 3 5 6 4 3 7 3 7 4 8 1 2 1 8 3 5 2 (3) re draw diagram with leafs in numerical order:

Example - drawing a stem and leaf Answer (a):- (3) re draw diagram with leafs in numerical order: Completion times 3 4 5 6 7 8 7 3 6 6 8 8 1 9 2 5 4 3 5 6 4 3 7 3 7 4 8 1 2 1 8 3 5 2 Completion times 3 4 5 6 7

Example - drawing a stem and leaf Answer (a):- (3) re draw diagram with leafs in numerical order: Completion times 3 4 5 6 7 8 7 3 6 6 8 8 1 9 2 5 4 3 5 6 4 3 7 3 7 4 8 1 2 1 8 3 5 2 Completion times 3 4 5 6 7 8

Example - drawing a stem and leaf Answer (a):- (3) re draw diagram with leafs in numerical order: Completion times 3 4 5 6 7 8 7 3 6 6 8 8 1 9 2 5 4 3 5 6 4 3 7 3 7 4 8 1 2 1 8 3 5 2 Completion times 3 4 5 6 7 8 1

Example - drawing a stem and leaf Answer (a):- (3) re draw diagram with leafs in numerical order: Completion times 3 4 5 6 7 8 7 3 6 6 8 8 1 9 2 5 4 3 5 6 4 3 7 3 7 4 8 1 2 1 8 3 5 2 Completion times 3 4 5 6 7 8 1 2

Example - drawing a stem and leaf Answer (a):- (3) re draw diagram with leafs in numerical order: Completion times 3 4 5 6 7 8 7 3 6 6 8 8 1 9 2 5 4 3 5 6 4 3 7 3 7 4 8 1 2 1 8 3 5 2 Completion times 3 4 5 6 7 8 1 2 3

Example - drawing a stem and leaf Answer (a):- (3) re draw diagram with leafs in numerical order: Completion times 3 4 5 6 7 8 7 3 6 6 8 8 1 9 2 5 4 3 5 6 4 3 7 3 7 4 8 1 2 1 8 3 5 2 Completion times 3 4 5 6 7 8 1 2 3 3

Example - drawing a stem and leaf Answer (a):- (3) re draw diagram with leafs in numerical order: Completion times 3 4 5 6 7 8 7 3 6 6 8 8 1 9 2 5 4 3 5 6 4 3 7 3 7 4 8 1 2 1 8 3 5 2 Completion times 3 4 5 6 7 8 1 2 3 3 3

Example - drawing a stem and leaf Answer (a):- (3) re draw diagram with leafs in numerical order: Completion times 3 4 5 6 7 8 7 3 6 6 8 8 1 9 2 5 4 3 5 6 4 3 7 3 7 4 8 1 2 1 8 3 5 2 Completion times 3 4 5 6 7 8 1 2 3 3 3 4

Example - drawing a stem and leaf Answer (a):- (3) re draw diagram with leafs in numerical order: Completion times 3 4 5 6 7 8 7 3 6 6 8 8 1 9 2 5 4 3 5 6 4 3 7 3 7 4 8 1 2 1 8 3 5 2 Completion times 3 4 5 6 7 8 1 2 3 3 3 4 4

Example - drawing a stem and leaf Answer (a):- (3) re draw diagram with leafs in numerical order: Completion times 3 4 5 6 7 8 7 3 6 6 8 8 1 9 2 5 4 3 5 6 4 3 7 3 7 4 8 1 2 1 8 3 5 2 Completion times 3 4 5 6 7 8 1 2 3 3 3 4 4 5

Example - drawing a stem and leaf Answer (a):- (3) re draw diagram with leafs in numerical order: Completion times 3 4 5 6 7 8 7 3 6 6 8 8 1 9 2 5 4 3 5 6 4 3 7 3 7 4 8 1 2 1 8 3 5 2 Completion times 3 4 5 6 7 8 1 2 3 3 3 4 4 5 5

Example - drawing a stem and leaf Answer (a):- (3) re draw diagram with leafs in numerical order: Completion times 3 4 5 6 7 8 7 3 6 6 8 8 1 9 2 5 4 3 5 6 4 3 7 3 7 4 8 1 2 1 8 3 5 2 Completion times 3 4 5 6 7 8 1 2 3 3 3 4 4 5 5 6

Example - drawing a stem and leaf Answer (a):- (3) re draw diagram with leafs in numerical order: Completion times 3 4 5 6 7 8 7 3 6 6 8 8 1 9 2 5 4 3 5 6 4 3 7 3 7 4 8 1 2 1 8 3 5 2 Completion times 3 4 5 6 7 8 1 2 3 3 3 4 4 5 5 6 6

Example - drawing a stem and leaf Answer (a):- (3) re draw diagram with leafs in numerical order: Completion times 3 4 5 6 7 8 7 3 6 6 8 8 1 9 2 5 4 3 5 6 4 3 7 3 7 4 8 1 2 1 8 3 5 2 Completion times 3 4 5 6 7 8 1 2 3 3 3 4 4 5 5 6 6 6

Example - drawing a stem and leaf Answer (a):- (3) re draw diagram with leafs in numerical order: Completion times 3 4 5 6 7 8 7 3 6 6 8 8 1 9 2 5 4 3 5 6 4 3 7 3 7 4 8 1 2 1 8 3 5 2 Completion times 3 4 5 6 7 8 1 2 3 3 3 4 4 5 5 6 6 6 7

Example - drawing a stem and leaf Answer (a):- (3) re draw diagram with leafs in numerical order: Completion times 3 4 5 6 7 8 7 3 6 6 8 8 1 9 2 5 4 3 5 6 4 3 7 3 7 4 8 1 2 1 8 3 5 2 Completion times 3 4 5 6 7 8 1 2 3 3 3 4 4 5 5 6 6 6 7 7

Example - drawing a stem and leaf Answer (a):- (3) re draw diagram with leafs in numerical order: Completion times 3 4 5 6 7 8 7 3 6 6 8 8 1 9 2 5 4 3 5 6 4 3 7 3 7 4 8 1 2 1 8 3 5 2 Completion times 3 4 5 6 7 8 1 2 3 3 3 4 4 5 5 6 6 6 7 7 8

Example - drawing a stem and leaf Answer (a):- (3) re draw diagram with leafs in numerical order: Completion times 3 4 5 6 7 8 7 3 6 6 8 8 1 9 2 5 4 3 5 6 4 3 7 3 7 4 8 1 2 1 8 3 5 2 Completion times 3 4 5 6 7 8 1 2 3 3 3 4 4 5 5 6 6 6 7 7 8 8

Example - drawing a stem and leaf Answer (a):- (3) re draw diagram with leafs in numerical order: Completion times 3 4 5 6 7 8 7 3 6 6 8 8 1 9 2 5 4 3 5 6 4 3 7 3 7 4 8 1 2 1 8 3 5 2 Completion times 3 4 5 6 7 8 1 2 3 3 3 4 4 5 5 6 6 6 7 7 8 8 9

Example - drawing a stem and leaf Answer (a):- (3) re draw diagram with leafs in numerical order: Completion times 3 4 5 6 7 8 7 3 6 6 8 8 1 9 2 5 4 3 5 6 4 3 7 3 7 4 8 1 2 1 8 3 5 2 Completion times 3 4 5 6 7 8 1 2 3 3 3 4 4 5 5 6 6 6 7 7 8 8 9 1

Example - drawing a stem and leaf Answer (a):- (3) re draw diagram with leafs in numerical order: Completion times 3 4 5 6 7 8 7 3 6 6 8 8 1 9 2 5 4 3 5 6 4 3 7 3 7 4 8 1 2 1 8 3 5 2 Completion times 3 4 5 6 7 8 1 2 3 3 3 4 4 5 5 6 6 6 7 7 8 8 9 1 2

Example - drawing a stem and leaf Answer (a):- (3) re draw diagram with leafs in numerical order: Completion times 3 4 5 6 7 8 7 3 6 6 8 8 1 9 2 5 4 3 5 6 4 3 7 3 7 4 8 1 2 1 8 3 5 2 Completion times 3 4 5 6 7 8 1 2 3 3 3 4 4 5 5 6 6 6 7 7 8 8 9 1 2 3

Example - drawing a stem and leaf Answer (a):- (3) re draw diagram with leafs in numerical order: Completion times 3 4 5 6 7 8 7 3 6 6 8 8 1 9 2 5 4 3 5 6 4 3 7 3 7 4 8 1 2 1 8 3 5 2 Completion times 3 4 5 6 7 8 1 2 3 3 3 4 4 5 5 6 6 6 7 7 8 8 9 1 2 3 4

Example - drawing a stem and leaf Answer (a):- (3) re draw diagram with leafs in numerical order: Completion times 3 4 5 6 7 8 7 3 6 6 8 8 1 9 2 5 4 3 5 6 4 3 7 3 7 4 8 1 2 1 8 3 5 2 Completion times 3 4 5 6 7 8 1 2 3 3 3 4 4 5 5 6 6 6 7 7 8 8 9 1 2 3 4 7

Example - drawing a stem and leaf Answer (a):- (3) re draw diagram with leafs in numerical order: Completion times 3 4 5 6 7 8 7 3 6 6 8 8 1 9 2 5 4 3 5 6 4 3 7 3 7 4 8 1 2 1 8 3 5 2 Completion times 3 4 5 6 7 8 1 2 3 3 3 4 4 5 5 6 6 6 7 7 8 8 9 1 2 3 4 7 8

Example - drawing a stem and leaf Answer (a):- (3) re draw diagram with leafs in numerical order: Completion times 3 4 5 6 7 8 7 3 6 6 8 8 1 9 2 5 4 3 5 6 4 3 7 3 7 4 8 1 2 1 8 3 5 2 Completion times 3 4 5 6 7 8 1 2 3 3 3 4 4 5 5 6 6 6 7 7 8 8 9 1 2 3 4 7 8 1

Example - drawing a stem and leaf Answer (a):- (3) re draw diagram with leafs in numerical order: Completion times 3 4 5 6 7 8 7 3 6 6 8 8 1 9 2 5 4 3 5 6 4 3 7 3 7 4 8 1 2 1 8 3 5 2 Completion times 3 4 5 6 7 8 1 2 3 3 3 4 4 5 5 6 6 6 7 7 8 8 9 1 2 3 4 7 8 1 3

Example - drawing a stem and leaf Answer (a):- (3) re draw diagram with leafs in numerical order: Completion times 3 4 5 6 7 8 7 3 6 6 8 8 1 9 2 5 4 3 5 6 4 3 7 3 7 4 8 1 2 1 8 3 5 2 Completion times 3 4 5 6 7 8 1 2 3 3 3 4 4 5 5 6 6 6 7 7 8 8 9 1 2 3 4 7 8 1 3 5

Example - drawing a stem and leaf Answer (a):- (3) re draw diagram with leafs in numerical order: Completion times 3 4 5 6 7 8 7 3 6 6 8 8 1 9 2 5 4 3 5 6 4 3 7 3 7 4 8 1 2 1 8 3 5 2 Completion times 3 4 5 6 7 8 1 2 3 3 3 4 4 5 5 6 6 6 7 7 8 8 9 1 2 3 4 7 8 1 3 5 8

Example - drawing a stem and leaf Answer (a):- (3) re draw diagram with leafs in numerical order: Completion times 3 4 5 6 7 8 7 3 6 6 8 8 1 9 2 5 4 3 5 6 4 3 7 3 7 4 8 1 2 1 8 3 5 2 Don’t forget the key Completion times 4|7 means 47 3 4 5 6 7 8 1 2 3 3 3 4 4 5 5 6 6 6 7 7 8 8 9 1 2 3 4 7 8 1 3 5 8 2

Example - drawing a stem and leaf Question:- 29 students were set a simple task. Their completion times to the nearest second were: 47 61 53 43 46 46 68 48 72 57 48 54 41 63 49 42 58 65 45 44 43 51 45 38 46 44 52 43 47 (a) set these data into a stem and leaf diagram (b) find the median, quartiles and inter-quartile range Answer (b):- adding the number of leaves can be helpful when interpreting a diagram Completion times 3 4 5 6 7 8 1 2 3 3 3 4 4 5 5 6 6 6 7 7 8 8 9 1 2 3 4 7 8 1 3 5 8 2 (1) (17) (6) (4)

Example - drawing a stem and leaf Answer (b):- find the median, quartiles and inter-quartile range Completion times 3 4 5 6 7 8 1 2 3 3 3 4 4 5 5 6 6 6 7 7 8 8 9 1 2 3 4 7 8 1 3 5 8 2 (1) (17) (6) (4) The median is the middle value: n/2 = 29/2 = 14.5  15th value = Not whole - so round up to whole Find the 15th value

Example - drawing a stem and leaf Answer (b):- find the median, quartiles and inter-quartile range Completion times 3 4 5 6 7 8 1 2 3 3 3 4 4 5 5 6 6 6 7 7 8 8 9 1 2 3 4 7 8 1 3 5 8 2 (1) (17) (6) (4) The median is the middle value: n/2 = 29/2 = 14.5  15th value = 47 seconds Not whole - so round up to whole Find the 15th value

Example - drawing a stem and leaf Answer (b):- find the median, quartiles and inter-quartile range Completion times 3 4 5 6 7 8 1 2 3 3 3 4 4 5 5 6 6 6 7 7 8 8 9 1 2 3 4 7 8 1 3 5 8 2 (1) (17) (6) (4) The median is the middle value: n/2 = 29/2 = 14.5  15th value = 47 seconds The lower quartile, Q1, is the 1/4th value: n/4 = 29/4 = 7.25  8th value = not whole - so round up to whole

Example - drawing a stem and leaf Answer (b):- find the median, quartiles and inter-quartile range Completion times 3 4 5 6 7 8 1 2 3 3 3 4 4 5 5 6 6 6 7 7 8 8 9 1 2 3 4 7 8 1 3 5 8 2 (1) (17) (6) (4) The median is the middle value: n/2 = 29/2 = 14.5  15th value = 47 seconds The lower quartile, Q1, is the 1/4th value: n/4 = 29/4 = 7.25  8th value = 44 seconds not whole - so round up to whole

Example - drawing a stem and leaf Answer (b):- find the median, quartiles and inter-quartile range Completion times 3 4 5 6 7 8 1 2 3 3 3 4 4 5 5 6 6 6 7 7 8 8 9 1 2 3 4 7 8 1 3 5 8 2 (1) (17) (6) (4) The median is the middle value: n/2 = 29/2 = 14.5  15th value = 47 seconds The lower quartile, Q1, is the 1/4th value: n/4 = 29/4 = 7.25  8th value = 44 seconds The upper quartile, Q3, is the 3/4th value: 3n/4 = 3x29/4 = 21.75  22nd value = not whole - so round up to whole

Example - drawing a stem and leaf Answer (b):- find the median, quartiles and inter-quartile range Completion times 3 4 5 6 7 8 1 2 3 3 3 4 4 5 5 6 6 6 7 7 8 8 9 1 2 3 4 7 8 1 3 5 8 2 (1) (17) (6) (4) The median is the middle value: n/2 = 29/2 = 14.5  15th value = 47 seconds The lower quartile, Q1, is the 1/4th value: n/4 = 29/4 = 7.25  8th value = 44 seconds The upper quartile, Q3, is the 3/4th value: 3n/4 = 3x29/4 = 21.75  22nd value = 54 seconds not whole -so round up to whole

Example - drawing a stem and leaf Answer (b):- find the median, quartiles and inter-quartile range Completion times 3 4 5 6 7 8 1 2 3 3 3 4 4 5 5 6 6 6 7 7 8 8 9 1 2 3 4 7 8 1 3 5 8 2 (1) (17) (6) (4) The median is the middle value: n/2 = 29/2 = 14.5  15th value = 47 seconds The lower quartile, Q1, is the 1/4th value: n/4 = 29/4 = 7.25  8th value = 44 seconds The upper quartile, Q3, is the 3/4th value: 3n/4 = 3x29/4 = 21.75  22nd value = 54 seconds The inter quartile range = Q3 – Q1 = 54 – 44 = 10 seconds

Note: you are more likely to be required to interpret a stem and leaf diagram than to have to draw one the textbook examples use a stem consisting of one digit. More digits are possible. The range of values should not be too great - otherwise the values may need to be rounded so that the number of stems does not become too large Stem and leaf diagrams can be drawn back to back for comparisons – much like bar charts.