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# LECTURE NO. 3

الكلية كلية الصيدلة     القسم  فرع العلوم الاساسية     المرحلة 1
أستاذ المادة نور هادي عيسى عباس الشمري       15/02/2020 12:12:46
Measure of Central Tendency
Lecture 3

There are several types of descriptive measures that can be computed from a set of data (ungrouped or grouped). The three most commonly used are the mean, the median, and the mode.

1. Ungrouped Data
Mean:
Mean is the first and the most commonly measure of central tendency, and it’s determined by adding all the values in population or sample and dividing by the total number of values that are adding.
The population mean is defined by (µ)

µ = ………………… i=1, 2,……, n

The sample mean is defined by ( )
………………………………………… i =1, 2,……, n
The properties of mean are:
1- For a given set of data there is only one mean.
2- Simplicity: is easily understood and easy to compute.
3- Mean is affected by extreme value.

Example: A set data (5, 7, 9, 5, 4).
= = 6
Other set of data with extreme value (5, 7, 9, 5, 24).
= = 10
Median:
The median is that value which located in middle of observations, if these observations are ordered from smallest to largest.
# If the number of observations is even, the median is the average of two middle values.

Example: A set data (10, 54, 10, 33, 21, 53)
Ordered set (10, 10, 21, 33, 53, 54)………….(order the values smallest to largest)
Rank order ( 1, 2, 3, 4, 5, 6)………….(then n=6)

= = = = 27

# If the number of observations is odd, the median is:

Example: A set data (10, 10, 33, 21, 53)
Ordered set (10, 10, 21, 33, 53)…………….(order the values smallest to largest)
Rank order (1, 2, 3, 4, 5)…………….(then n=5)

= = = 21

Mode:
The mode is the value, which occurs most frequency.
Example: (2, 6, 3, 7, 0, 10, 4) ………………………..…………….…………. (No Mode)
(5, 6, 10, 12, 6, 7, 6) ……………………….………………….. (One Mode, 6)
(0, 2, 5, 4, 2, 1, 2, 4, 4) ……………..………………….… (Two Mode, 2, 4)

Comparison of the mean, median and mode:
Data set (2, 2, 4, 5, 7, 9)
Mean= 4.833 Median= 4.5 Mode= 2
If we change the last data point from 9 to 28, the mean equal 8, but the median and the mode remain the same.
1. The mean is sensitive to extremes value but the median is not.
2. For some data set, the mean can give a misleading picture of the observation.
Example: (2, 2, 2, 2, 17) is not very representative roe the data set.
3. The median sometimes ignores potentially useful information because only the middle value (or two middle values) affects the median. The median is the best measure of central tendency when the distributions are small or extremely skewed.
4. The mode can sometimes be useful, but it tends to characterize individuals more than groups.

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