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7th grade

Mathematics

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LESSON

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SUPERDRAFTStatistics

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7th grade

Mathematics

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Data may be **qualitative **or **quantitative**. Once you know the difference between them, you can know how to use them.

**Qualitative data** - information about **qualities**; information that can not actually be measured. For examples: the color of the sky, the softness of the cat, etc.

**Quantitative data** - information about **quantities**; information that can be measured and written down with numbers. For examples: the amount of money in your wallet, your age, etc.

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Quantitative data can be further divided into two groups: **Discrete data** and **Continuous data**.

**Discrete data** is a numerical data that is collected by counting **exact values**. The data can only be **whole numbers**.

**Continuous data** is a numerical data that is collected by **measuring** and uses approximate values. Examples of continuous data include height and time. Data of this form cannot measured exactly, but it is not limited to whole number quantities.

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Data can be collected in many ways, including observation, measurement, interview and questionnaire.

**Observation** - record what you see. For examples: number of vehicles, color of houses,etc.

**Measurement** - measure using instruments. For examples: weight, height, temperature, etc.

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**Interview** - ask question verbally. For examples: age, favourite food, month of birthday, etc.

**Questionnaire** - ask questions in a written form. For examples: favourite sport, favourite singer, etc.

Collected data need to be **organized** and **represented in graphical** or **tabular form**.

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__Frequency Distribution Tables__

**Frequency distribution tables** are a common way of **organizing and representing data**.

The first column lists the categories or numerical scores.

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The second column is usually used to **tally**, or add-up, the collected data. This helps us to **organize an unsorted dataset**.

The third column contains the **frequency** of the category/score, which is the sum of the tally marks.

At the bottom of the frequency column, we display **the sum of frequencies**

$\left(\Sigma f\right)$

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A pictogram uses **pictures or symbols**. Each picture or symbol stands for a certain number of the same item.

Refer **Textbook SPN21 Mathematics Year 7** on page 190 - 191 for example.

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A **bar chart** is a **statistical representation** which uses bars to represent the number of units (frequencies) of the various items.

Refer **Textbook SPN21 Mathematics Year 7** on page 194 -196 for example.

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Data are the information collected in form of numbers. Data is organized and represented graphically so that it becomes easy to understand and interpret.

The collection, recording and presentation of data help us organize our experiences and draw inferences from them.

Data is organized and represented graphically so that it becomes easy to understand and interpret.

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Consider the data of the ages in years of 10 employee of a office:

40, 44, 26, 29, 33, 30, 24, 52, 28, 35

Data collected above is called raw data. it is difficult to draw inferences from a raw data.

24, 26, 28, 30, 33, 35, 40, 44, 52. Now the data is arranged in ascending order. This arrangement is called an array.

The **difference between the highest and lowest values** in a set of data is called its **range**. Here, range = 52 - 24 = 28 years.

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The same data can further be arranged in a tabular form using **tally marks**.

**Bar graph** is an visual representation of data. It is formed by using bars of uniform widths.

**Mode** of the data is the longest bar, if the bar represents the **frequency**.

A double bar graph can be drawn to compare two sets of observation

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Mean, median, and mode are representative values of a group of observations. They are also called measures of central tendency of the data.

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The average or Arithmetic mean or mean of a given data is defined as

$Mean=\frac{Sum\ of\ all\ observations}{Number\ of\ observations}$

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The observation that occurs maximum number of times in a data.

If each of the values in a data is occuring one time or equal number of times, then all are mode.

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Median refers to the value which lies in the middle of the data when arranged in an increasing or decreasing order with half of the observation above it and other half below it.

If the data has odd number of items, then the median is the middle number.

If the data has an even number of items, then the median is the mean of two middle numbers.

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