This revision note will guide you on how to create a stem and leaf plot while comparing the pros and cons of different statistical plots. These diagrams display data distribution by identifying patterns for Quantitative Data Analysis.
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Stem and leaf diagrams help to organise large amounts of numerical data by splitting each value into two parts:
This visualization tool preserves individual data points while showing their distribution. To create an effective stem and leaf diagram:
Stem and leaf plots can be used with whole numbers and decimal values. Always include appropriate units in your key when necessary.
The masses of 10 marbles are given as shown:
56 g, 63 g, 74 g, 50 g, 61 g, 72 g, 58 g, 65 g, 76 g, 67 g.
Represent the data using a stem-and-leaf diagram.
Step 1: The stem will be the digits in the tens place. The stem is arranged in numerical order.
Step 2: Work from left to right in the data set. The leaves are placed in the corresponding rows.
Step 3: The leaves are put in ascending order (smallest to largest).
Step 4: Create a key and the title
The stem-and-leaf diagram shows the number of candies in a gift box.
(i) What is the most common number of candies?
(ii) Find the percentage of gift boxes with more than 55 candies.
(i) The most common number of candies is 59. (ans)
(ii) Total number of gift boxes = 22
Number of gift boxes with more than 55 candies = 13 (ans)
Percentage = 13/22 × 100% = 59.1% (to 3 s.f.) (ans)
When two sets of data are given, we can use a stem-and-leaf diagram with a common stem to represent the data. This is known as a back-to-back Stem-and-leaf diagram
The results of a Mathematics Quiz for two Secondary 2 classes are given as shown.
Class 2A 70 45 63 68 98 85 70 50 66 47
Class 2B 55 79 92 78 42 80 82 88 90 94
(i) Construct a back-to-back stem-and-leaf diagram
(ii) Calculate the percentage of students who scored 80 and above in each class
(iii) Which class performed better in the quiz ? Use the back-to-back stem-and-leaf diagram in (i) to explain your answer.
(i)
(ii) Class 2A students scored 80 and above = 2, percentage =2/10 × 100% = 20% (ans)
Class 2B students scored 80 and above = 6, percentage = 6/10 × 100% = 60%(ans)
(iii) Class 2B performed better than class 2A as there are more students in class 2B scored 80 and above than class 2A.
The choice of statistical representation depends on the data set and the purpose of collection. Let’s explore the key advantages and disadvantages of each statistical plot type.
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