Frequency Distribution, Histogram, Measure of Central Tendency

Frequency Distribution

Frequency distribution is a way to organize and display data so that we can see how often different values occur.

Let's Understand this concept using our pizza dine-in restaurant example if we want to understand what sizes of pizzas our customers prefer. We can keep track of the size of every pizza ordered during the week.

Here's how we might create a frequency distribution:

1.?????? List the sizes: List all the pizza sizes we offer. We offer small, medium, large, and extra-large pizzas.

2.?????? Count the occurrences: For each size, count how many times customers ordered that size during the week. For example, maybe customers ordered 20 small pizzas, 30 medium pizzas, 25 large pizzas, and 15 extra-large pizzas.

3.?????? Create the distribution table: Make a table where one column lists the pizza sizes, and another column shows how many times each size was ordered. It might look something like this:

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4.?????? Analyse the distribution: Now we can see which pizza sizes are the most popular. In this example, medium pizzas are ordered the most, followed by large, small, and then extra-large. This information can help us make decisions about the menu, pricing, and inventory management.

So, a frequency distribution in this pizza dine-in example would show us how many times each pizza size was ordered, helping us understand our customer’s preferences.

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Histogram

A histogram is a graphical representation of the frequency distribution. A histogram is a?graph?that focuses on numerical data and shows how often each value occurs within specific ranges.

So, if we want to create a histogram of the pizza sizes and Number of orders we can represent it in the following manner

Since the data consists of pizza sizes and their corresponding orders, a histogram might not be the best choice as histograms are typically used for continuous numerical data. The above image is of a bar graph to understand the concept.

Measures of Central Tendency

A measure of central tendency is a way to summarize or describe a set of data by identifying a typical or central value around which the data tends to cluster.

Let's understand measures of central tendency in the context of a pizza dine-in example:

Mean: To find the mean size of pizzas ordered, we first need to calculate the total number of pizzas ordered and then divide it by the total number of different pizza sizes.

Total number of orders = 20 (Small) + 30 (Medium) + 25 (Large) + 15 (Extra-Large) = 90

Mean = Total number of orders / Total number of sizes = 90 / 4 = 22.5

So, the mean size of pizzas ordered is 22.5.

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Median: To find the median size of pizzas ordered, we'll arrange the sizes in ascending or descending order and find the middle value.

First, arrange the sizes by order frequency: Extra-Large (15), Small (20), Large (25), Medium (30).

Since there's an even number of data points (4), we take the average of the two middle values:

Median = (20 + 25) / 2 = 45 / 2 = 22.5

So, the median size of pizzas ordered is 22.5.

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Mode: To find the mode, we'll identify the size that appears most frequently.

In this case, Medium (30 orders) is the size that appears most frequently.

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So, the mode size of pizzas ordered is Medium.

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These measures help us understand the central tendencies in the sizes of pizzas ordered, which can guide decisions such as ingredient purchasing and menu planning.

When to Use Them:

Mean for balancing data (but need to watch out for extreme values).

Median when data has outliers (like a super high or low score).

Mode when we want to know the most common value.

Thank you

Saurabh Vanikar

Connect with me on my Medium Account

Please find the links to my previous posts.

Post 1?— Statistics is Everywhere

Post 2?— Types of Statistics

Post 3?— Central Tendency of the Distribution

Post 4?— What is Data?

Post 5?— Types of data

Post 6?— Sampling Techniques Part 1

Post 7?— Sampling Techniques Part 2

Post 8?— Sampling Techniques Part 3

Post 9?— Hypothesis Testing

Post 10 — Variables

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