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Chapter10. Statistics

10.1 Introduction: A statistic is an algebraic expression that combines scores into a single number. Statistics basically serve two functions: they estimate parameters in population models and they describe the data. It is collection of methods for planning experiments, obtaining data, and then organizing, summarizing, presenting, analyzing, interpreting, and drawing conclusions.

10.2 Measure Of Central Tendency: Central tendency is a representative score. The three measures of central tendency that will be discussed this semester are the mode, median, and mean.

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10.2.1 Mean: The mean or the arithmetic mean is the most commonly used measure of central tendency. It is the sum of the numbers divided by the number of numbers. The symbol m is used for the mean of a population. The symbol M is used for the mean of a sample. The formula for m is ;

m = ΣX/ N

Where, ΣX is sum of all the numbers in the given set and N is the total number of numbers in the set.

Example: Evaluate the mean of 1, 2, 5, 6, 4

Solution: N = 5

ΣX = 1+2+5+6+4 = 18

So, m = 18/5

= 3.6

10.2.2 Median: The median is the middle of a distribution. Half the scores are above the median and half of them are below the median.

When there is an odd number of numbers in a given set, the median is simply the middle number.

For example: in a given set of 2, 8, and 9 the median is 8.

When there is an even number of numbers, the median is the mean of the two middle numbers.

For example: The median of the numbers 2, 4, 7, 12 is;

(4+7)/2 = 5.5

10.2.3 Mode: The mode in a list of numbers refers to the list of numbers that occur most frequently. It is important to note that there can be more than one mode and if no number occurs more than once in the set, then there is no mode for that set of numbers.

Example: find the mode?

14, 52, 12, 14, 15, 14, 21, 14, 17, 27, 14

Solution: in the above given set of numbers, the most frequently occurring number is 14. 14 has occurred 5 times in the set. Hence,

Mode = 14

A distribution may have more than one mode if the two most frequently occurring scores occur the same number of times. Such distributions are called Bimodal.

Example: 12, 11, 14, 12, 54, 10, 11, 21, 24, 12, 11

Solution:12 and 11 both have occurred 3 times, so,

Mode = 12 and 11

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