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MEAN

MEAN IN STATISTICS: GRAPHICAL REPRESENTATION

The mean is a statistical measure of central tendency that is calculated by adding up all of the values in a dataset and dividing by the total number of values. It represents the average value of the data.

Advantages of using the mean:

• It is widely used and easily understood by most people.
• It can be used to compare datasets with different numbers of values.
• It is a useful measure of central tendency when the dataset is normally distributed.

Disadvantages of using the mean:

• It can be sensitive to extreme values (outliers), which can skew the results.
• It may not be a useful measure of central tendency if the dataset is not normally distributed.
• It can be misleading when used with discrete data or when there are gaps in the data.

MEAN FOR UNGROUP DATA

Formula: 

        Mean =  \(\overline{X}=\frac{\sum X}{n}\)

    Where X= data values

Example:

Let's say we have the following dataset: 2, 5, 8, 10, 12

The mean would be calculated as follows:

Mean = (2 + 5 + 8 + 10 + 12) / 5

Mean = 37 / 5

Mean = 7.4

Advantages of using ungrouped data:

• It can provide a more detailed view of the dataset.
• It can be useful when there are only a few values.
• It is easy to calculate and interpret.

Disadvantages of using ungrouped data:

• It can be affected by extreme values or outliers.
• It can be difficult to compare datasets with different numbers of

MEAN FOR GROUP DATA

Grouped data is a way of organizing data into groups or classes based on a range of values. This is useful when the dataset is large or when there are many different values.

Formula:

Mean for grouped data = \(\overline{X}=\frac{\sum fX}{\sum f}\)

f = frequency of each class

x = mid point of the the each class

Example:

Let's say we have the following grouped dataset:

Class	Frequency
0-10	4
10-20	8
20-30	12
30-40	6
40-50	2

The mean would be calculated as follows:

Mean = ((5 x 4) + (15 x 8) + (25 x 12) + (35 x 6) + (45 x 2)) / (4 + 8 + 12 + 6 + 2)

Mean = (20 + 120 + 300 + 210 + 90) / 32

Mean = 21.25

Advantages of using grouped data:

• It can be a useful way to handle large datasets.
• It can reduce the impact of outliers or extreme values.
• It can make it easier to identify patterns or trends in the data.

Disadvantages of using grouped data:

• It can result in a loss of precision and detail.
• It may not accurately represent the distribution of the data.
• It can be more difficult to calculate and interpret than ungrouped data.

Q1: A company wants to determine the average salary of its employees. The following table shows the frequency distribution of salaries in thousands of dollars. What is the mean salary?

Salary (in thousands of dollars) Number of Employees 20 - 30 5 30 - 40 10 40 - 50 15 50 - 60 20 60 - 70 10
represent Salary (in thousands of dollars)

Q2: The following table shows the scores of 10 students in a math test. What is the mean score?

Student Score 1 85 2 92 3 78 4 88 5 90 6 95 7 82 8 90 9 87 10 91

SAMPLE MCQs quiz

MEAN IN STATISTICS

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