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Thought-Process to Discover Knowledge

Welcome to nubtrek.

Books and other education websites provide "matter-of-fact" knowledge. Instead, nubtrek provides a thought-process to discover knowledge.

In each of the topic, the outline of the thought-process, for that topic, is provided for learners and educators.

Read in the blogs more about the unique learning experience at nubtrek.
mathsStatistics and ProbabilityStatistics : Analysis of Data

### Cumulative Frequency

In this page, the following are introduced with examples

•  range of data

•  frequency of a data-point

•  cumulative frequency

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We studied about the following in the earlier class.

Data : Collection of information is data.
eg: Height of students in cm -- 90, 97, 91, 92, 90

Statistics is study of recording, representing, and analysis of data.

This topic goes into details of collecting and organizing data.

Consider the data: Number of glasses of water students drink during the school time is given below.

2, 3, 1, 4, 1,
1, 2, 2, 1, 2,
3, 2, 2, 3, 5,
2, 5, 1, 1, 2,
2, 1, 3, 2, 2,
1, 2, 1, 2, 2,
3, 2, 2, 5, 4,
2, 1, 3, 1, 2

What is this form of data referred as?

• raw data
• raw data
• plain data
• small data

The answer is "raw data".

Which of the following is a meaning for the word "raw"?

• tasting bad; smelling bad
• in the original form; not modified for any purpose
• in the original form; not modified for any purpose

Then answer is "in the original form; not modified for any purpose".

Consider the data: Number of glasses of water students drink during the school time. Which of the following is a suitable representation when recording the data?

• pictograph
• bar-graph
• tally marks
• tally marks

The answer is "tally marks". The figure illustrates the tally marks for the given data.

Consider the data: Number of glasses of water students drink during the school time. Which of the following is a suitable representation to present the recorded data?

• table form
• table form
• hidden form

The answer is "table form". The recorded data is converted into table form and this is illustrated in the figure.

Consider the data: Number of glasses of water students drink during the school time. What is the minimum number of glass-of-water a student drinks?

• 1
• 1
• 5

The answer is "1". From the table, the minimum number of glass of water is chosen as 1.

Consider the data: Number of glasses of water students drink during the school time. What is the maximum number of glass-of-water a student drinks?

• 1
• 5
• 5

The answer is "5". From the table, the maximum number of glasses-of-water is chosen as 5.

In a given data, the values have a minimum and maximum. All the data values are within the minimum and maximum. This is called "range" of the data. In the given example, the range of data is 1 to 5.

Which of the following is a meaning for the word "range"?

• the possible values within a lower limit and an upper limit
• the possible values within a lower limit and an upper limit
• the competition to win

The answer is "the possible values within a lower limit and an upper limit".

What is the term used to refer "the possible values within a lower limit and an upper limit"?

• Pronunciation : Say the answer once
Spelling: Write the answer once

The answer is "range".

Consider the data: Number of glasses of water students drink during the school time. How many students had 4 glasses-of-water?

• 2
• 2
• no one

The answer is "2". From the table, the row where the number of glasses of 4 is chosen and the column "count" provides the answer 2.

In a data, the data-values are counted and the number of times a data-value repeats is called "frequency" of the data-value. In the given example,

•  the frequency of 1 is 11

•  the frequency of 2 is 18

•  the frequency of 3 is 6

•  the frequency of 4 is 2

•  the frequency of 5 is 3

Which of the following is a meaning for the word "frequency"?

• satisfying thirst with water
• the count or rate at which something happens
• the count or rate at which something happens

The answer is "the count or rate at which something happens".

What is the term used to refer "the count or rate at which something happens"?

• Pronunciation : Say the answer once
Spelling: Write the answer once

The answer is "frequency".

Consider the data: Number of glasses of water students drink during the school time. How many students had 3 glasses-of-water or less ?

• 6
• 35
• 35

The answer is "35".

In a data set, the data-values are ordered in ascending order. The count of data-values that are less than or equal to a specific data value is called the "cumulative frequency" at the specific data-value. In the given example,

•  the cumulative frequency at 1 is 11

•  the cumulative frequency at 2 is 29

•  the cumulative frequency at 3 is 35

•  the cumulative frequency at 4 is 37

•  the cumulative frequency at 5 is 40

Which of the following is a meaning for the word "cumulative"?

• describing in detail with illustrations
• increasing by successive addition
• increasing by successive addition

The answer is "increasing by successive addition".

What is the term used to refer "increasing by successive addition"?

• Pronunciation : Say the answer once
Spelling: Write the answer once

The answer is "cumulative".

Range of data : The possible values within a lower limit and an upper limit is called the range of data.

Frequency of a data point : The number of times a data value is repeated is the frequency of the data.

Cumulative Frequency : The number of times a data value or the data-values lower than that value is repeated, is the cumulative frequency at the data value.

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