Q.Suppose annual day of your school is to be celebrated. The school has decided to felicitate those parents of the students studying in classes XI and XII, who are the alumni of the same school. In this context, answer the following questions:

Here are the statistical techniques for each scenario:

(a) To find out the number of students whose both parents are alumni of the school, the statistical technique of frequency analysis or conditional counting should be used. This involves counting the occurrences of students who satisfy a specific condition (both parents being alumni).

(b) To determine how varied the age of parents of the students is, measures of dispersion should be used. These statistical measures quantify the spread or variability of data points. Examples include:

• Range: The difference between the maximum and minimum age. …

(a) Which statistical technique should be used to find out the number of students whose both parents are alumni of this school?

To find the number of students whose both parents are alumni, we need a technique that allows us to count occurrences based on specific conditions. This falls under the umbrella of Conditional Counting or Frequency Analysis.

Why Conditional Counting?

The core idea is to filter the entire dataset of students to identify only those records that meet all the specified criteria, and then count how many such records exist. In this scenario, the criteria are:

1. Parent 1 is an alumnus of the school.
2. Parent 2 is an alumnus of the school.

If we imagine a dataset (like a table in a database or a DataFrame in Python Pandas) where each row represents a student and includes information about their parents' alumni status (e.g., Parent1_Alumni_Status, Parent2_Alumni_Status), we would apply a filter.

For example, if Parent1_Alumni_Status and Parent2_Alumni_Status are boolean (True/False) or categorical (Yes/No) fields:

• We would select all student records where Parent1_Alumni_Status is 'Yes' (or True).
• From this filtered set, we would further select records where Parent2_Alumni_Status is also 'Yes' (or True).
• Finally, we would count the number of records remaining after both filters have been applied.

This process is a direct application of conditional counting, which is a fundamental operation in descriptive statistics and data analysis. It helps in understanding the frequency of specific combinations of attributes within a dataset.

SELECT COUNT(*)
FROM Students
WHERE Parent1_Alumni_Status = 'Yes' AND Parent2_Alumni_Status = 'Yes';

import pandas as pd

# Assuming 'students_df' is your DataFrame
# and 'Parent1_Alumni_Status', 'Parent2_Alumni_Status' are boolean columns
num_students = students_df[
    (students_df['Parent1_Alumni_Status'] == True) &
    (students_df['Parent2_Alumni_Status'] == True)
].shape[0]

The statistical technique to be used is Conditional Counting (or Frequency Analysis for a specific combination of attributes).

(b) How varied are the age of parents of the students of that school?

To understand "how varied" a set of data points is, we need to use a measure of dispersion or variability. These measures quantify the spread or scattering of data values around a central tendency (like the mean or median).

Why Standard Deviation?

Among the various measures of dispersion, Standard Deviation is the most commonly used and robust technique to describe how spread out the data points are from the mean.

• Range (maximum age - minimum age) is simple but highly sensitive to outliers. …