What is the difference between mean, median, and mode?

Mean = sum of all values ÷ number of values (average); affected by outliers. Median = middle value when data sorted; not affected by outliers; better for skewed data. Mode = most frequent value; can have multiple modes; useful for categorical data. Example: for {1, 2, 2, 3, 100}: mean = 21.6, median = 2, mode = 2. Median and mode better represent this skewed data.

How do you find the median for even and odd number of values?

Odd n: sort data, median = value at position (n+1)/2. Example: {3,5,7,9,11}, n=5, median at position 3 = 7. Even n: sort data, median = average of values at positions n/2 and n/2+1. Example: {2,4,6,8}, n=4, median = (4+6)/2 = 5.

What is the difference between a bar graph and a histogram?

Bar graph: used for categorical/discrete data; bars have gaps between them; bars are of equal width. Histogram: used for continuous data (class intervals); NO gaps between bars (bars touch); width may vary (but usually equal). Bar graphs compare different categories; histograms show frequency distribution of continuous data.

Mean, Median and Mode

Statistics • Class 9 Mathematics • NCERT • CBSE

Mean is the arithmetic average of all data values. Median is the middle value when data is arranged in order. Mode is the value that appears most frequently. Together these are called measures of central tendency.

Key Formulas

Mean: x̄ = Σxᵢ / n
Mean (frequency): x̄ = Σfᵢxᵢ / Σfᵢ
Median (odd n): position (n+1)/2
Median (even n): average of n/2 th and (n/2+1) th values
Range = Maximum − Minimum

Frequently Asked Questions

What is the difference between mean, median, and mode?: Mean = sum of all values ÷ number of values (average); affected by outliers. Median = middle value when data sorted; not affected by outliers; better for skewed data. Mode = most frequent value; can have multiple modes; useful for categorical data. Example: for {1, 2, 2, 3, 100}: mean = 21.6, median = 2, mode = 2. Median and mode better represent this skewed data.
How do you find the median for even and odd number of values?: Odd n: sort data, median = value at position (n+1)/2. Example: {3,5,7,9,11}, n=5, median at position 3 = 7. Even n: sort data, median = average of values at positions n/2 and n/2+1. Example: {2,4,6,8}, n=4, median = (4+6)/2 = 5.
What is the difference between a bar graph and a histogram?: Bar graph: used for categorical/discrete data; bars have gaps between them; bars are of equal width. Histogram: used for continuous data (class intervals); NO gaps between bars (bars touch); width may vary (but usually equal). Bar graphs compare different categories; histograms show frequency distribution of continuous data.

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