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From Wikipedia, the free encyclopedia

Grouped data are data formed by aggregating individual observations of a variable into groups, so that a frequency distribution of these groups serves as a convenient means of summarizing or analyzing the data.

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  • ✪ Mean, Median, and Mode of Grouped Data & Frequency Distribution Tables Statistics
  • ✪ CALCULATE MEAN MEDIAN AND MODE FOR GROUPED DATA
  • ✪ Standard Deviation of Grouped Data
  • ✪ Estimated Mean, Median and Quartiles from Continuous Grouped Data
  • ✪ Median of Grouped and Ungrouped Data

Transcription

Contents

Example

The idea of grouped data can be illustrated by considering the following raw dataset:

20 25 24 33 13
26 8 19 31 11
16 21 17 11 34
14 15 21 18 17
Table 1: Time taken (in seconds) by a group of students to
answer a simple math question

The above data can be grouped in order to construct a frequency distribution in any of several ways. One method is to use intervals as a basis.

The smallest value in the above data is 8 and the largest is 34. The interval from 8 to 34 is broken up into smaller subintervals (called class intervals). For each class interval, the amount of data items falling in this interval is counted. This number is called the frequency of that class interval. The results are tabulated as a frequency table as follows:

Time taken (in seconds) Frequency
5 ≤ t < 10 1
10 ≤ t < 15 4
15 ≤ t < 20 6
20 ≤ t < 25 4
25 ≤ t < 30 2
30 ≤ t < 35 3
Table 2: Frequency distribution of the time taken (in seconds) by the group of students to
answer a simple math question


Another method of grouping the data is to use some qualitative characteristics instead of numerical intervals. For example, suppose in the above example, there are three types of students: 1) Below normal, if the response time is 5 to 14 seconds, 2) normal if it is between 15 and 24 seconds, and 3) above normal if it is 25 seconds or more, then the grouped data looks like:

Frequency
Below normal 5
Normal 10
Above normal 5
Table 3: Frequency distribution of the three types of students


Yet another example of grouping the data is the use of some commonly used numerical values, which are in fact "names" we assign to the categories. For example, let us look at the age distribution of the students in a class. The students may be 10 years old, 11 years old or 12 years old. These are the age groups, 10, 11, and 12. Note that the students in age group 10 are from 10 years and 0 days, to 10 years and 364 days old, and their average age is 10.5 years old if we look at age in a continuous scale. The grouped data looks like:

Age Frequency
10 10
11 20
12 10
Table 4: Age distribution of a class of students

Mean of grouped data

An estimate, , of the mean of the population from which the data are drawn can be calculated from the grouped data as:

In this formula, x refers to the midpoint of the class intervals, and f is the class frequency. Note that the result of this will be different from the sample mean of the ungrouped data. The mean for the grouped data in the above example, can be calculated as follows:

Class Intervals Frequency ( f ) Midpoint ( x ) f x
5 and above, below 10 1 7.5 7.5
10 ≤ t < 15 4 12.5 50
15 ≤ t < 20 6 17.5 105
20 ≤ t < 25 4 22.5 90
25 ≤ t < 30 2 27.5 55
30 ≤ t < 35 3 32.5 97.5
TOTAL 20 405


Thus, the mean of the grouped data is


The mean for the grouped data in example 4 above can be calculated as follows:

Age Group Frequency ( f ) Midpoint ( x ) f x
10 10 10.5 105
11 20 11.5 230
12 10 12.5 125
TOTAL 40 460


Thus, the mean of the grouped data is

See also

Notes

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References

  • Newbold, P.; Carlson, W.; Thorne, B. (2009). Statistics for Business and Economics (Seventh ed.). Pearson Education. ISBN 978-0-13-507248-6.
This page was last edited on 16 March 2019, at 07:21
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