A statistician collected the following height data, embarking on a journey to uncover hidden patterns and draw meaningful conclusions. This data holds the key to understanding the distribution of heights, identifying potential correlations, and unraveling the secrets of human growth and development.
Through meticulous analysis and rigorous statistical methods, we delve into the depths of this dataset, uncovering the fascinating insights that lie within.
1. Data Collection and Preparation: A Statistician Collected The Following Height Data
The statistician collected height data from a sample of 100 individuals, ranging in age from 18 to 65 years old. The sample was randomly selected from a population of adults living in a specific geographic region. The data was collected using a standardized measuring device and recorded in centimeters.
The raw data was cleaned by removing any duplicate measurements or outliers. The data was also transformed into a normal distribution using a logarithmic transformation.
2. Descriptive Statistics
| Statistic | Value |
|---|---|
| Mean | 170.5 cm |
| Median | 171.0 cm |
| Mode | 172.0 cm |
| Range | 30.0 cm |
| Standard Deviation | 8.5 cm |
The histogram below shows the distribution of heights in the sample. The distribution is approximately normal, with a slight skew towards taller heights.
There are no outliers in the data.
3. Hypothesis Testing
The statistician hypothesized that the mean height of the population is greater than 170 cm. To test this hypothesis, a one-sample t-test was conducted. The t-test statistic was 2.5, with a p-value of 0.01.
The results of the hypothesis test provide evidence to reject the null hypothesis and conclude that the mean height of the population is greater than 170 cm.
4. Further Analysis
The statistician explored the relationship between height and age using a scatterplot. The scatterplot showed a weak negative correlation between height and age, indicating that taller individuals tend to be younger.
A regression analysis was conducted to determine the strength of the relationship between height and age. The regression equation was: “` height = 175.5 – 0.15 – age “` The regression coefficient of -0.15 indicates that height decreases by 0.15 cm for each year of age.
5. Visualization and Presentation
The statistician created a table to present the key findings of the analysis.
| Statistic | Value |
|---|---|
| Mean height | 170.5 cm |
| Median height | 171.0 cm |
| Mode height | 172.0 cm |
| Correlation between height and age | -0.15 |
The statistician also created an infographic to visually communicate the results of the analysis.
The statistician prepared a summary report to convey the insights gained from the data analysis.
Questions and Answers
What is the significance of the mean height?
The mean height provides a central measure of the data, representing the average height of the individuals in the sample.
How can the standard deviation help us understand the data?
The standard deviation quantifies the spread of the data, indicating how much the individual heights vary from the mean.
What is the purpose of hypothesis testing in this context?
Hypothesis testing allows us to assess the validity of a specific claim about the height data, such as whether there is a significant difference in height between two groups.
