Stem and Leaf question, stats

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In summary, the article "Bolted Connection Design values based on Eurpoean yeidl Model" includes specific gravity values for various wood types used in construction. A stem-and-leaf display was constructed to show the distribution of these values, with the stems representing tenths and the leaves representing hundredths. The display reveals two modes at 0.42 and 0.67, potentially indicating the presence of typical soft and hard woods.
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mr_coffee
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Hi everyone, I just started stats and had a question.

Question:
The accompanying specific gravity values for various wood types used in construction appeared in the article "Bolted Connection Design values based on Eurpoean yeidl Model"
.31 .35 .36 .36 .37 .38 .40 .40 .40
.41 .41 .42 .42 .42 .42 .42 .43 .44
.45 .46 .46 .47 .48 .48 .48 .51 .54
.55 .55 .58 .62 .66 .66 .67 .68 .75

Construct a stem-and-leaf display using repeated stems and comment on any interesting features of the display.An example of repeated stems are like:
For example, if evertyhing is in the 60's, 70's, 80's or 90's, we could use 6L for lower 60's. Like (leaves 0,1,2,3) and 6H for high 60's with leaves (5,6,7,8,9).

So for my problem above would it look somthing like this?
I have:
.30's, .40's, .50's, .60's, and a .75

So would I have for the .30 a High and a Low the low being (0, 1, 2, 3 , 4) and 3H (.30 HIGH) being (5,6,7,8,9).

so would it be something like this?
3L|1
3H|56678
4L|000112222234
4H|5667888
5L|144
5H|58
6L|2
6H|6678
7H|5

Then It wants me to label the Stem and Leaf.

For example if it was whole numbers like 60,70,80,88,etc
Stem would be the tens
Leaf would be the ones.

So because these are all like .30, .40,.50
Would the stem unit be tenths, and leaf: hundredths?

Also would the trend I'm seeing is that there a lot of low 40's but few high 70's?

Thanks!
 
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  • #2
I would label the stems as follows:

0.3L | 1
0.3H | 56678
0.4L | 000112222234
0.4H | 5667888
0.5L | 14
0.5H | 558
0.6L | 2
0.6H | 6678
0.7L |
0.7H | 5

And, yes, the stems are tenths and the leave are hundredths.
If we treat 0.55 and 0.75 as outliers, then two "modes" are apparent: 0.42 and 0.67.
Without looking at the original data, I might suspect that 0.42 was a typical soft wood and 0.67 was a typical hard wood.
 

1. What is a stem and leaf plot?

A stem and leaf plot is a way to display numerical data in a visual format. It involves splitting each data point into a "stem" and a "leaf" which represents the last digit of the data. The stems are listed on the left side of the plot and the leaves are listed on the right side, forming a list of ordered data points.

2. How do you create a stem and leaf plot?

To create a stem and leaf plot, follow these steps:

  • Step 1: Write out all the data points in a vertical column.
  • Step 2: Identify the largest and smallest values in the data set.
  • Step 3: Decide on the stem value, which will be the first one or two digits of the data points.
  • Step 4: Write the stems in a vertical column on the left side of the plot.
  • Step 5: Write the leaves (last digit) next to their corresponding stem.
  • Step 6: Order the leaves in ascending order.
  • Step 7: Add a key to the plot, indicating the scale used.

3. What is the purpose of using a stem and leaf plot?

A stem and leaf plot allows for a quick visual representation of data, making it easier to identify patterns and trends within the data set. It also preserves the original data points, unlike other types of graphs that may round or group data.

4. When should a stem and leaf plot be used?

A stem and leaf plot is most useful when dealing with small to medium sized data sets, typically less than 50 data points. It is also helpful when comparing two or more data sets, as they can be displayed side by side for easy comparison.

5. What are the advantages and disadvantages of using a stem and leaf plot?

Advantages:

  • Provides a quick visual representation of data.
  • Preserves the original data points.
  • Allows for easy comparison of multiple data sets.
Disadvantages:
  • Not as useful for large data sets, as it can become cluttered and difficult to read.
  • Can be time consuming to create by hand.
  • Not as commonly used as other types of graphs, so may be less familiar to some individuals.

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