NumPy arrays offer a mean method, but not median or mode. Write functions `median` and `mode` that use existing NumPy capabilities to determine the median (middle) and mode (most frequent) of the values in an array. Your functions should determine the median and mode regardless of the array’s shape. Test your function on three arrays of different shapes.

Perform the following tasks with pandas Series:

A. Create a Series from the list `[7, 11, 13, 17]`.

B. Create a Series with five elements that are all `100.0`.

C. Create a Series with 20 elements that are all random numbers in the range `0` to `100`. Use method `describe` to produce the Series’ basic descriptive statistics.

D. Create a Series called `temperatures` of the floating-point values `98.6, 98.9, 100.2, and 97.9`. Using the `index` keyword argument, specify the custom indices 'Julie', 'Charlie', 'Sam', and 'Andrea'.

E. Form a dictionary from the names and values in Part (D), then use it to initialize a Series.

Use Python language.

Central tendency measures including mean, median, and mode provide insights into a data set's characteristics. Median is less affected by outliers than mean, which can be skewed. The mode indicates the most common value within the data.

Explanation:

Measures of central tendency like the mean, median, and mode play a critical role in statistical analysis, as they summarize key aspects of a data set. The mean is the arithmetic average of all data points and can be skewed by outliers, meaning it is sensitive to extreme values.

The median is the middle value when data points are arranged in order of magnitude and provides a better measure of center when outliers are present. The mode is the most frequently occurring data point and can reveal the most common value in a data set.

In the case of a bimodal or multimodal data set, there can be more than one mode. When it comes to skewed data, as shown in the example data set where the mean is 7.7, the median is 7.5, and the mode is seven, understanding the relationship between these three measures of central tendency can help decide which is the most appropriate to use in a given context.