what is Arithmetic Mean in Individual, discrete and continuous series in class 11

Arithmetic Mean, often known as the average, is a measure of central tendency that is calculated by adding up all the values in a data set and then dividing the sum by the number of values in the set.

1. Individual Series: In an individual series, the arithmetic mean is calculated by adding all the individual data points and dividing by the number of data points. For example, if you have the numbers 1, 2, 3, 4, and 5, the arithmetic mean would be (1+2+3+4+5)/5 = 3.

2. Discrete Series: In a discrete series, each data point has a frequency associated with it. The arithmetic mean is calculated by multiplying each data point by its frequency, adding these products, and then dividing by the total frequency. For example, if you have the numbers 1, 2, and 3 with frequencies of 2, 3, and 1 respectively, the arithmetic mean would be [(12)+(23)+(3*1)]/(2+3+1) = 1.83.

3. Continuous Series: In a continuous series, the data is grouped into intervals or classes. The arithmetic mean is calculated by finding the midpoint of each interval, multiplying this by the frequency of the interval, adding these products, and then dividing by the total frequency. For example, if you have intervals of 1-10, 11-20, and 21-30 with frequencies of 2, 3, and 1 respectively, the midpoints would be 5.5, 15.5, and 25.5. The arithmetic mean would be [(5.52)+(15.53)+(25.5*1)]/(2+3+1) = 14.5.