## Stem and Leaf Graphs and Tree Diagrams Exercise

 1. The table shows the areas of 20 highest mountains in Australia and New Zealand. Show this information on a stem and leaf diagram, using the first two digits as the stem. The digits on the leaves should be arranged in order from smallest to biggest.

 Name of mountain Location Height (in metres) Malte Brun NZ 3160 Kosciuszko NSW 2230 Silberhorn NZ 3300 Bogong VIC 1990 Tasman NZ 3500 Torres NZ 3160 Jaggungal NSW 2040 Sefton NZ 3160 Townsend NSW 2210 Lendenfeldt NZ 3190 Tate NSW 2040 Cook NZ 3750 Paddy Rushs Bogong NSW 1920 Teichelmann NZ 3160 Perisher NSW 2040 Dampier NZ 3440 Twynham NSW 2180 Gungartan NSW 2060 Hicks NZ 3200 Feathertop VIC 1920

2. The final examination results of a class are given below. The results are shown below:

 Year 11 Examination 43 46 68 85 66 46 71 49 81 93 42 63 72 55 68 76 50 43 53 38

(a) Draw a stem and leaf diagram for this class.
(b) What is the difference between the highest and the lowest score.
(c) What is the median (middle) score in the test.

3. The unordered stem and leaf graph below shows the number of tries scored in a rugby championship by teams in the top two divisions in a season.

The numbers in the stem represent tens.

a. Arrange the numbers on the leaves into order from smallest to largest.
b. What was the highest number of tries scored in the season?
c. What was the lowest number of tries scored in the season?
d. How many teams were there altogether?
e. What was the median (middle) number of tries scored?

4. The unordered back to back stem and leaf graph below shows the weights of the forwards and backs in a rugby squad that toured South Africa.

a. Arrange the numbers on the leaves into order from smallest to largest (remember to start at the stem!).
b. How many players were in the squad?
c. Was the heaviest player, a forward or a back?
d. Find the median (weight) for a back.
e. What weight was the lightest player in the squad?

5. Three fair coins are tossed. One side is called "heads" and the other side is called "tails". Draw a tree diagram to show all of the possible combinations and use the diagram to find the probability that:

a. All three coins are tails
b. There are two heads and a tail (in any order)
c. There are no tails.
d. The first coin is a tail.

 6. The table shows the areas of 20 major natural lakes in New Zealand with areas less than 100 square kilometres. Show this information on a stem and leaf diagram, using the first digit as the stem. The digits on the leaves should be arranged in order from smallest to biggest.

 Name of lake Length (in square kilometres) Rotorua 80 Rotoiti 34 Tarawera 36 Waikaremoana 54 Wairarapa 80 Rototoa 23 Brunner 39 Coleridge 36 Tekapo 88 Ohau 61 Monowai 31 Hauroko 71 Poteriteri 47