Statistics 1 week 2

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Summary

Measures of Central Tendency: Mode, Median, and Mean

Mode

The mode is the value that appears most frequently in a dataset. It is particularly useful for categorical data where we wish to know which is the most common category.

Example: Consider the dataset: 3, 7, 7, 2, 5, 7, 4. Here, the mode is 7, as it appears more frequently than any other number.

Median

The median is the middle value in an ordered dataset. If the dataset has an odd number of observations, the median is the middle number. If it has an even number of observations, the median is the average of the two middle numbers.

Example: For the dataset: 2, 3, 4, 7, 9, the median is 4. For the dataset: 2, 3, 4, 7, 9, 10, the median is (4+7)/2 = 5.5.

Mean

The mean (or average) is calculated by summing all the values in a dataset and then dividing by the number of values.

Example: For the dataset: 2, 3, 4, 7, 9, the mean is (2+3+4+7+9)/5 = 5.

Frequency, Relative Frequency, and Frequency Distribution Table

Frequency refers to the number of times a particular value appears in a dataset. Relative frequency is the proportion of the total number of observations that a particular value represents. It is calculated by dividing the frequency of a value by the total number of observations.

Example: In a dataset of exam scores: 70, 80, 80, 90, 90, 90, the frequency of 90 is 3,the relative frequency of 90 is 3/6 = 0.5. Similarly for 80 is 2/6=0.33 and the relative frequecy of 70 is 1/6=1/6=0.16. If we add all three relative frequceny that is 0.5+0.33+0.16=1(approx).

Frequency Distribution Table

A frequency distribution table organizes data into categories and shows the frequency of each category. It helps in understanding the distribution of data.

Score	Frequency
70	1
80	2
90	3

Uses of Mode, Median, and Mean

• Mode: Useful in identifying the most common item in categorical data. For example, in a survey of favorite fruits, the mode can tell us the most preferred fruit.
• Median: Effective in skewed distributions as it is not affected by extreme values. For example, in income data, the median gives a better central value than the mean.
• Mean: Provides a measure of central tendency that includes all data points. It is useful in normally distributed data, such as calculating the average score of a class.