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Data Handling - Categorical and Numerical Data

Grade 6IB

Review the key concepts, formulae, and examples before starting your quiz.

🔑Concepts

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Categorical Data (Qualitative Data) describes characteristics or labels that can be divided into groups (e.g., eye color, favorite subjects, or types of vehicles).

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Numerical Data (Quantitative Data) consists of numbers that represent counts or measurements. This is further divided into Discrete and Continuous data.

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Discrete Numerical Data involves values that are countable and usually whole numbers (e.g., the number of students in a class: 2525, 2626, 2727).

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Continuous Numerical Data involves measurements that can take any value within a range, often including decimals (e.g., the height of a plant: 12.512.5 cmcm or the temperature: 36.6∘C36.6^{\circ}C).

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A Frequency Table is a method of organizing data using tally marks to show how often each value or category occurs.

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The Mean is the mathematical average of a set of numbers.

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The Mode is the value that appears most frequently in a data set.

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The Range is the difference between the highest and lowest values in a data set, showing the spread of the data.

📐Formulae

Mean=Sum of all valuesTotal number of values\text{Mean} = \frac{\text{Sum of all values}}{\text{Total number of values}}

Range=Maximum Value−Minimum Value\text{Range} = \text{Maximum Value} - \text{Minimum Value}

💡Examples

Problem 1:

Calculate the mean of the following heights (in cmcm): 140,150,145,155,160140, 150, 145, 155, 160.

Solution:

140150145155+160750\begin{array}{r} 140 \\ 150 \\ 145 \\ 155 \\ + 160 \\ \hline 750 \end{array} Sum of values =750= 750. Number of values =5= 5. Mean =7505=150= \frac{750}{5} = 150 cmcm.

Explanation:

First, sum all the heights using vertical addition. Then, divide the total sum (750750) by the count of the data points (55).

Problem 2:

A survey asked students for their favorite fruit: Apple, Banana, Apple, Orange, Banana, Apple. Identify the type of data and find the mode.

Solution:

Data Type: Categorical. Counts: Apple =3= 3, Banana =2= 2, Orange =1= 1. Mode: Apple.

Explanation:

The data consists of names/categories, so it is Categorical. Since 'Apple' appears most frequently (33 times), it is the mode.

Problem 3:

Find the Range of the following data set: 22,45,12,67,34,5022, 45, 12, 67, 34, 50.

Solution:

Maximum value =67= 67. Minimum value =12= 12. Range =67−12=55= 67 - 12 = 55.

Explanation:

The range is found by subtracting the smallest number (1212) from the largest number (6767) in the set.