import numpy as np from scipy import stats import pandas as pd

Define the dataset

data = [5, 6, 6, 9, 12, 12, 15, 12, 57, 45, 35, 28, 12]

Calculate the required statistics

mean = np.mean(data) median = np.median(data) mode = stats.mode(data).mode[0]

Calculate the quartiles

q1 = np.percentile(data, 25) # 1st Quartile q3 = np.percentile(data, 75) # 3rd Quartile

Calculate the 4th decile and 40th percentile

d4 = np.percentile(data, 40) # 4th Decile and 40th Percentile are the same

Present results

results = { "Mean": mean, "Median": median, "Mode": mode, "1st Quartile (Q1)": q1, "3rd Quartile (Q3)": q3, "4th Decile / 40th Percentile": d4 }

results_df = pd.DataFrame.from_dict(results, orient='index', columns=['Value'])

import ace_tools as tools; tools.display_dataframe_to_user(name="Summary of Statistics for the Data Set", dataframe=results_df)/tmp/ipykernel_12/2643290412.py:11: FutureWarning: Unlike other reduction functions (e.g. skew, kurtosis), the default behavior of mode typically preserves the axis it acts along. In SciPy 1.11.0, this behavior will change: the default value of keepdims will become False, the axis over which the statistic is taken will be eliminated, and the value None will no longer be accepted. Set keepdims to True or False to avoid this warning. mode = stats.mode(data).mode[0] Value Mean 19.538462 Median 12.000000 Mode 12.000000 1st Quartile (Q1) 9.000000 3rd Quartile (Q3) 28.000000 Value Mean 19.538462 Median 12.000000 Mode 12.000000 1st Quartile (Q1) 9.000000 3rd Quartile (Q3) 28.000000successI have displayed the calculated statistics for the dataset, including the mean, median, mode, 1st quartile (Q1), 3rd quartile (Q3), and the 4th decile (or 40th percentile) in a table for easy reference.

Let me know if you need further clarification on these calculations or have additional questions.

Related Questions

1. How do quartiles help summarize a data set?
2. Can the mean, median, and mode be the same in all data distributions? If not, why?
3. What is the significance of the 4th decile in interpreting data?
4. How do outliers like 57 affect the mean compared to the median?
5. What additional visualizations can be used to complement these statistics?

Tip:

Always check for outliers in your data, as they can significantly skew the mean, making the median a more robust measure of central tendency in such cases.