This question aims to find the **frequency distribution** of the qualitative data by using knowledge of the frequency distribution.

**Frequency distribution** is a representation of several observations in a tabular form. It displays information within the **given intervals**. A frequency distribution shows the number of **repeated items** in a tabular or descriptive form. It can be represented as tally marks or simple digits.

**Qualitative analysis** is the numerical analysis and interpretation of observations for analyzing the underlying meanings of **relationship patterns.**

## Expert Answer

When an event occurs more than one time, the number at which it occurs, again and again, is called **frequency.** The list of frequencies for all events in data is known as frequency distribution.

**Qualitative data:**

Qualitative data describes the **quality** and category in which the data falls. It classifies data based on its use.

This table shows the types of different smartphones and how these **smartphones** are being used frequently nowadays. The use of smartphones is described by the **frequency distribution** in the given table.

We can infer from the given data that **iPhones** are the most used smartphones. **Android** is a competitor of iPhones as its frequency is $ 12 $. Next, we have the **Windows phone** whose frequency is $ 8 $. **Amazon’s Fire Phone** has a frequency of $ 5 $. The relative frequencies of this are calculated by:

\[ R.f = \frac { f } { n } \]

Here, $ f $ is the frequency of usage of each smartphone and $ n $ is the **total frequency**.

Here, $ n $ is $ 40 $ and relative frequencies can be calculated accordingly.

## Numerical Solution

The relative frequency for an android is:

\[ R.f = \frac { 12 } { 40 } \]

\[ R.f = 0 . 3 \]

The relative frequency for the Window phone:

\[ R.f = \frac { 8 } { 40 } \]

\[ R.f = 0 . 2 \]

The relative frequency for an iPhone is:

\[ R.f = \frac { 15 } { 40 } \]

\[ R.f = 0 . 375 \]

The relative frequency of an Amazon’s fire phone is:

\[ R.f = \frac { 5 } { 40 } \]

\[ R.f = 0 . 125 \]

These relative frequencies are tabulated in the table above.

## Example

Alia has a packet of $ 20 $ bubblegums. Her favorite bubblegums have $ 6 $ red and $ 6 $ yellow color. How frequently does she eat all the candies? Find the relative frequency of her favorite candies.

\[ R.f = \frac {6 + 6 } { 20 } \]

\[ R.f = \frac { 12 } { 20 } \]

\[ R.f = 0 . 6 \]

\[ R.f = 60 \% \]

*Image/Mathematical drawings are created in Geogebra.*