Analyzing Stem-and-Leaf Plots in Statistical Data
Body weight expressed as a percentage of ideal. Body weights of 18 diabetics expressed as a
percentage of ideal (defined as body weight ÷ ideal body weight × 100) are shown here. Construct a stemand-leaf plot of these data and interpret your findings.
107 119 99 114 120 104 88 114 124 116
101 121 152 100 125 114 95 117
8 : 8
9 : 59
10 : 0147
11 : 444679
12 : 0145
13 :
14:
15: 2
Spread: Information ranges
from 88 to 152.
Shape: Shewed negatively
with the addition of a high
outlier.
Location: Median is 114
Air samples. An environmental study looked at suspended particulate matter in air samples (µg/m3) at
two different sites. Data are listed here. Construct side-by-side stemplots to compare the two sites.
Site 1: 68 22 36 32 42 24 28 38
Site 2: 36 38 39 40 36 34 33 32
842 : 2 :
862 : 3 : 2346689
2 : 4 : 0
: 5 :
8 : 6 :
High outlier within site 1
There is a greater spread of variability
displayed in site 1 over site 2
There are overlapping of similar
locations sampled.
What would you report? A small data set (n = 9) has the following values {3.5, 8.1, 7.4, 4.0, 0.7, 4.9,
8.4, 7.0, 5.5}. Plot the data as a stemplot and then report an appropriate measure of central location and
spread for the data.
Variable: site 1
Decimal point is at the colon.
Leaf unit = 0.1
0 : 7
1 :
2 :
3 : 5
4 : 09
5 : 5
6 :
7 : 04
8 : 14
Central location: 5.5 (median)
Spread: Data ranges from 0.7 to 8.4
Analyzing Stem-and-Leaf Plots in Statistical Data
Stem-and-leaf plots are an effective way to visually represent data, providing insights into the distribution, spread, and central tendency of a dataset. In this essay, we will examine stem-and-leaf plots for three different sets of data and interpret the findings to gain a deeper understanding of the information they convey.
Body Weight Expressed as a Percentage of Ideal for Diabetics
The first dataset we explore is the body weights of 18 diabetics expressed as a percentage of their ideal weight. The stem-and-leaf plot for this data indicates a spread ranging from 88 to 152. The shape of the distribution is skewed negatively due to the presence of a high outlier at 152. The median body weight percentage is calculated to be 114. This suggests that most individuals in the sample are close to their ideal weight percentage, with a few outliers affecting the overall distribution.
Suspended Particulate Matter in Air Samples at Two Sites
Moving on to the analysis of suspended particulate matter in air samples at two different sites, we observe side-by-side stem plots for Site 1 and Site 2. Site 1 shows a high outlier, indicating variability in the data. Site 1 also exhibits a wider spread compared to Site 2. However, there are overlapping values between the two sites, suggesting similarities in the levels of suspended particulate matter at certain instances.
Small Data Set Analysis
Lastly, we examine a small dataset with values {3.5, 8.1, 7.4, 4.0, 0.7, 4.9, 8.4, 7.0, 5.5}. The stem-and-leaf plot for this dataset reveals a spread from 0.7 to 8.4. The central location is represented by the median value of 5.5. This indicates that the middle value in the dataset is 5.5. The spread of the data suggests that the values vary between the lowest and highest values observed in the dataset.
In conclusion, stem-and-leaf plots provide valuable insights into the distribution and characteristics of datasets. By analyzing these plots, we can identify trends, outliers, and central tendencies within the data, allowing for a more comprehensive understanding of the information being presented.
By delving into these examples and interpretations, we can appreciate the significance of stem-and-leaf plots as a tool for statistical analysis and visualization of data.