MTH302 Business Mathematics & Statistics Solution & Discussion

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(In descriptive statistics) an indication of the middle point of distribution for a particular group. Measures include the mean average score, the median or middle score of distribution, and the mode, the most frequently occurring measure.

 

 

Measures of Central Tendency
Definition of Measures of Central Tendency

• A measure of central tendency is a measure that tells us where the middle of a bunch of data lies.
• The three most common measures of central tendency are the mean, the median, and the mode.

More about Measures of Central Tendency

• Mean: Mean is the most common measure of central tendency. It is simply the sum of the numbers divided by the number of numbers in a set of data. This is also known as average.
• Median: Median is the number present in the middle when the numbers in a set of data are arranged in ascending or descending order. If the number of numbers in a data set is even, then the median is the mean of the two middle numbers.
• Mode: Mode is the value that occurs most frequently in a set of data.

Examples of Measures of Central Tendency

• For the data 1, 2, 3, 4, 5, 5, 6, 7, 8 the measures of central tendency are
  Mean =
  Median = 5
  Mode = 5

Solved Example on Measures of Central Tendency

Find the measures of central tendency for the data set 3, 7, 9, 4, 5, 4, 6, 7, and 9.
Choices:
A. Mean = 6, median = 6 and modes are 4, 7 and 9
B. Mean = 6, median = 6 and mode is 4
C. Mean = 6, median = 6 and modes are 4 and 9
D. Mean = 6, median = 9 and modes are 4, 7 and 9
Correct Answer: A
Solution:
Step 1: Mean, median and mode of a data set are the measures of central tendency.
Step 2: Mean of the data set =                 [Formula.]
Step 3:                                 [Substitute the values.]
Step 4:                      [Add the data values in the numerator and divide.]
Step 5: The data set in the ascending order is 3, 4, 4, 5, 6, 7, 7, 9, and 9. So, Median of the set is 6.      [Median is the middle data value of the ordered set.]
Step 6: Mode is/are the data value(s) that appear most often in the data set. So, the modes of the data set are 4, 7 and 9.
Step 7: So, the measures of central tendency of the given set of data are mean = 6, median = 6 and modes are 4, 7, and 9.

Related Terms for Measures of Central Tendency

• Mean
• Average
• Median
• Mode
• Data

 

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