When Maximum Meets Square Root

Thu, 05 Dec 2024 00:00:00 +0000

I recently came across a YouTube Short by Grant Sanderson, and I have to say, it blew my mind! The idea that the distributions describing the result of the maximum of two random numbers and the square root of one of those numbers are the same is simply too good to be true. His explanation in the video is pure brilliance!

Inspired by this, I decided to write a quick R script to simulate both of these processes and compare their distributions.

n_samples <- 100000

# Generate 100,000 pairs of random numbers between 0 and 1
rand_pairs <- replicate(n_samples, runif(2, min = 0, max = 1))

# Calculate the maximum of each pair
max_rand <- apply(rand_pairs, 2, max)

# Calculate the square root of a randomly selected number from each pair
sqrt_rand <- apply(rand_pairs, 2, function(x) sqrt(sample(x, 1)))

Why This is So Cool

What I love about this is that it’s not just a random coincidence. There’s a beautiful symmetry in how the square root transformation and the maximum function work in tandem to produce the same kind of distribution. It’s a reminder of how interconnected different concepts in probability and statistics can be, and it really made me appreciate the elegance of randomness!

Diwali Sales Data

Tue, 29 Oct 2024 00:00:00 +0000

The Diwali Sales dataset, featured in the TidyTuesday project for the week of November 14, 2023, provides a comprehensive look at retail sales during the Diwali festival in India. It offers a detailed snapshot of consumer behavior during one of the most significant festive periods in India.

Key Business Questions

Insights and Trends

Age Group Spending:
- The age group 26-35 spends the most during Diwali. This demographic is likely to have higher disposable income and a greater inclination towards festive shopping.
Gender-Based Expenditure:
- Within each age group, spending patterns vary significantly between genders. In general, females tend to spend more than males across all age groups.
Occupational Insights:
- For individuals aged 26-35, the predominant occupations are in IT, healthcare, aviation, and banking. This suggests that marketing strategies aimed at these professional groups could be advantageous.
State-Wise Spending:
- States such as Uttar Pradesh, Maharashtra, Karnataka, and Delhi rank among the highest in spending.
Marital Status Influence:
- Married individuals tend to spend more than unmarried ones. This trend is consistent across both genders.

Recommendations

Targeted Marketing Campaigns:
- Focus marketing efforts on the 26-35 age group, especially targeting professionals and business owners. Tailor campaigns to highlight products and offers that appeal to this demographic.
Gender-Specific Strategies:
- Develop gender-specific marketing strategies. For example, create campaigns that resonate with female consumers in high-spending states.
State-Specific Promotions:
- Implement state-specific promotions, particularly in states with high spending. Customize offers and discounts to cater to the preferences of consumers in these regions.
Enhanced Customer Engagement:
- Use insights from occupational data to engage with customers through personalized communication. Offer exclusive deals and loyalty programs for professionals.

diwali <- read.csv("Diwali Sales Data.csv")
glimpse(diwali)

## Rows: 11,251
## Columns: 15
## $ User_ID          <int> 1002903, 1000732, 1001990, 1001425, 1000588, 1000588,…
## $ Cust_name        <chr> "Sanskriti", "Kartik", "Bindu", "Sudevi", "Joni", "Jo…
## $ Product_ID       <chr> "P00125942", "P00110942", "P00118542", "P00237842", "…
## $ Gender           <chr> "F", "F", "F", "M", "M", "M", "F", "F", "M", "F", "M"…
## $ Age.Group        <chr> "26-35", "26-35", "26-35", "0-17", "26-35", "26-35", …
## $ Age              <int> 28, 35, 35, 16, 28, 28, 25, 61, 35, 26, 34, 20, 20, 2…
## $ Marital_Status   <int> 0, 1, 1, 0, 1, 1, 1, 0, 0, 1, 0, 0, 1, 1, 1, 0, 1, 0,…
## $ State            <chr> "Maharashtra", "Andhra\xa0Pradesh", "Uttar Pradesh", …
## $ Zone             <chr> "Western", "Southern", "Central", "Southern", "Wester…
## $ Occupation       <chr> "Healthcare", "Govt", "Automobile", "Construction", "…
## $ Product_Category <chr> "Auto", "Auto", "Auto", "Auto", "Auto", "Auto", "Auto…
## $ Orders           <int> 1, 3, 3, 2, 2, 1, 4, 1, 2, 4, 1, 2, 2, 4, 3, 2, 3, 1,…
## $ Amount           <dbl> 23952.00, 23934.00, 23924.00, 23912.00, 23877.00, 238…
## $ Status           <lgl> NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, N…
## $ unnamed1         <lgl> NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, N…

Data Cleaning

Renaming Andhra\xa0Pradesh to Andhra Pradesh.
Converting Marital_Status column values to a factor.
- This would help with clear color differentiation for 1 (as red) and 2 (as blue), instead of a color range of values between 0 and 1.
Removing columns that contain only NA values.
Getting rid of rows where there aren’t any values recorded for the Amount column.

diwali <- diwali |> 
    mutate(State = recode(State, "Andhra\xa0Pradesh" = "Andhra Pradesh"), .keep = "all" ) |> 
    mutate(Marital_Status = as.factor(Marital_Status)) |> 
    select(-Status, -unnamed1) |> 
    filter(!is.na(Amount))

glimpse(diwali)

## Rows: 11,239
## Columns: 13
## $ User_ID          <int> 1002903, 1000732, 1001990, 1001425, 1000588, 1000588,…
## $ Cust_name        <chr> "Sanskriti", "Kartik", "Bindu", "Sudevi", "Joni", "Jo…
## $ Product_ID       <chr> "P00125942", "P00110942", "P00118542", "P00237842", "…
## $ Gender           <chr> "F", "F", "F", "M", "M", "M", "F", "M", "F", "M", "F"…
## $ Age.Group        <chr> "26-35", "26-35", "26-35", "0-17", "26-35", "26-35", …
## $ Age              <int> 28, 35, 35, 16, 28, 28, 25, 35, 26, 34, 20, 20, 26, 2…
## $ Marital_Status   <fct> 0, 1, 1, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1, 0, 0, 1, 1, 1,…
## $ State            <chr> "Maharashtra", "Andhra Pradesh", "Uttar Pradesh", "Ka…
## $ Zone             <chr> "Western", "Southern", "Central", "Southern", "Wester…
## $ Occupation       <chr> "Healthcare", "Govt", "Automobile", "Construction", "…
## $ Product_Category <chr> "Auto", "Auto", "Auto", "Auto", "Auto", "Auto", "Auto…
## $ Orders           <int> 1, 3, 3, 2, 2, 1, 4, 2, 4, 1, 2, 2, 4, 2, 1, 1, 1, 4,…
## $ Amount           <dbl> 23952.00, 23934.00, 23924.00, 23912.00, 23877.00, 238…

What age group spent the most?

diwali |> 
    select(Age.Group, Amount) |> 
    arrange(Age.Group) |> 
    group_by(Age.Group) |> 
    summarise(Total_Amount = sum(Amount)) |> 
    ggplot(aes(Age.Group, Total_Amount, fill = Age.Group)) + 
    geom_col() +
    scale_fill_manual(values = col_theme) +
    labs(
        title = "Top-Spending Age Group",
        subtitle = "Identifying High-Value Demographics",
        x = NULL,
        y = "Expenditure"
            ) +
    theme(plot.title = element_text(size = 18, face = "bold")) +
    scale_y_continuous(labels = comma) +
    guides(fill = guide_legend(reverse = TRUE)) +
    coord_flip()

What is the expenditure across genders for each age group

diwali |> 
    select(Age.Group, Gender, Amount) |> 
    arrange(Age.Group) |> 
    group_by(Age.Group, Gender) |> 
    summarise(Total_Amount = sum(Amount), .groups = "drop") |> 
    ggplot(aes(Age.Group, Total_Amount, fill = Gender)) + 
    geom_col() +
    scale_fill_manual(values = col_theme) +
    labs(
        title = "Spending Patterns by Age Group and Gender",
        subtitle = "A Comparative Analysis",
        x = NULL,
        y = "Expenditure"
            ) +
    theme(plot.title = element_text(size = 18, face = "bold")) +
    scale_y_continuous(labels = comma) +
    guides(fill = guide_legend(reverse = TRUE)) +
    coord_flip()

What are the occupations of people between 26-35

diwali |> 
    select(Age.Group, Occupation) |> 
    filter(Age.Group == "26-35") |> 
    group_by(Occupation) |> 
    summarise(Number_Of_Individuals = n()) |> 
    mutate(Occupation = fct_reorder(Occupation, Number_Of_Individuals)) |> 
    ggplot(aes(Occupation, Number_Of_Individuals, fill = Occupation)) +
    geom_col() +
    scale_fill_manual(values = col_theme) +
    labs(
        title = "Key Occupations Among 26-35 Age Group",
        x = NULL,
        y = "Number of Individuals"
            ) +
    theme(plot.title = element_text(size = 18, face = "bold")) +
    scale_y_continuous(labels = comma) +
    guides(fill = guide_legend(reverse = TRUE)) +
    coord_flip()

Which state spent the most (segregated by gender)?

diwali |> 
select(State, Amount, Gender) |> 
group_by(State, Gender) |> 
summarise(Total_Amount = sum(Amount), .groups = "drop") |> 
mutate(State = fct_reorder(State, Total_Amount)) |> 
ggplot(aes(State, Total_Amount, fill = Gender)) +
geom_col() +
scale_fill_manual(values = col_theme) +
labs(
    title = "Top-Spending States by Gender",
    subtitle = "Regional Breakdown of Consumer Spending",
    x = NULL,
    y = "Expenditure"
        ) +
theme(plot.title = element_text(size = 18, face = "bold")) +
scale_y_continuous(labels = comma) +
guides(fill = guide_legend(reverse = TRUE)) +
coord_flip()

Finding expenditure of females and males along with thier marital status

diwali |> 
    select(State, Marital_Status, Gender, Amount) |>
    arrange(State, Gender) |> 
    group_by(State, Gender, Marital_Status) |> 
    summarise(Total_Amount = sum(Amount), .groups = "drop") |> 
    mutate(State = fct_reorder(State, Total_Amount)) |> 
    ggplot(aes(State, Total_Amount, fill = Marital_Status)) +
    geom_bar(stat = "identity", position = "dodge") +
    labs(title = "Comapring expenditures between married and unmarried individuals", 
         subtitle = "Segregated by gender") +
    facet_wrap(~ Gender) +
    coord_flip() +
    theme(axis.text.x = element_text(angle = 45, hjust = 1, size = 10)) +
    scale_fill_manual(values = col_theme) +
    labs(
        title = "Spending Trends by Gender and Marital Status",
        subtitle = "Understanding Consumer Profiles",
        x = NULL,
        y = "Expenditure"
            ) +
    theme(plot.title = element_text(size = 18, face = "bold")) +
    guides(fill = guide_legend(reverse = TRUE)) +
    scale_y_continuous(labels = comma)

Shishir Ashok – Portfolio