 LESSON
Statistics
8 hours ago by
16 slides # Types of Data​

​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.

# ​Quantitative Data

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.

# ​Data Collection

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.

# ​Data Collection

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.

# ​Data Representation

Frequency Distribution Tables

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

​The first column lists the categories or numerical scores. 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 $\left(\Sigma f\right)$

# ​Pictogram

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.​

# ​Bar Chart

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.

# ​Data Handling

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.

​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.

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

# ​Representative Values

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

# ​Arithmetic Mean or Mean

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

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

# ​Mode

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.​

# ​Median

​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. 