The digits of data values are used to organize data sets in a stem-and-leaf plot method. Each data value is divided into a stem (left most digit or digits) and a leaf (right most digit or digits). A stem-and-leaf plot depicts the distribution of data from the lowest to the highest value.
The arrangement of coins in ascending order is shown in the image below:
Examples
Example 1: Make a stem and leaf plot of the lengths of 10 mobile calls.
Solution:
Step 1: Sort the information into ascending order that is 3, 5, 7, 14, 19, 21, 26, 32, 33, and 44.
Step 2: Pick your stems and leaves. Use the tens digits for the stems and the ones digits for the leaves because the data values range from 2 to 55. Make sure the key is included.
Step 3: To the left of the vertical line, mention the stems.
Step 4: To the right of the vertical line, write the leaves for each stem.
Phone Call Length
Key: 2|6 = 26 Minutes
Example 2: The heights of several houseplants are depicted in the stem-and-leaf plot. Use the information to answer the question, “What is a typical house plant height?”
Key: 1|1 = 11 Inches
Solution: We can find the height of the houseplant by finding its mean, median and mode.
Mean = \(\frac{1 + 2 + 4 + 5 + 6 + 8 + 9 + 11 + 11 + 11 + 12 + 13 + 15 + 22 + 32}{15}\)
Mean = 10.8
Median = 11
Mode = 11
Hence, the height of the house plant will be 11 inches.
Example 3: The stem-and-leaf graph depicts student quiz results.
(a) How many students received a score of less than 8?
(b) How many students received a score of at least 9?
(c) How is the data disseminated?
Quiz Scores
Key 9|9 = 9.9 Points
Solution :
(a) Scores 6.6,7.0,7.5,7.7, and 7.8 are the five scores that are less than 8. So, five students received a grade of less than eight.
(b) There are four nine-point scores: 9.0, 9.2, 9.9, and 10.0. At least 9 points were earned by four students.
(c) Only a few people have low quiz scores, and only a few people have high quiz scores. As a result, the majority of the results are in the middle, ranging from 8.1 to 8.9 points.
Bringing data together in a systematic way that makes it easier to read is what data organization is all about. Tallies and frequency tables can be used to organize data. Tallies are a method of counting in which you record each item as you count it by drawing a short vertical line.
The following five steps make up this procedure.
Step 1: Decide what kind of data you’d like to collect.
The first step is to decide what information you want to collect.
Step 2: Set a time limit for collecting data.
Step 3: Decide on a data collection strategy.
Step 4: Collect the information.
Step 5: Analyze the data and put your findings into practise.
We can use a variety of tools to collect data, whether qualitative or quantitative, such as surveys, focus groups, interviews, and questionnaires. We can use charts and graphs to help organize data, such as bar graphs, frequency charts, picture graphs, and line graphs, to help visualize what’s going on.