Averages:
Average is a number that represents or shows the central tendency of a group of observations of data.
Arithmetic Mean and Range
The average or arithmetic mean or mean of a given data is defined as :
Mean=Sum of all observations / Number of observations
The difference between the highest and the lowest observations in a given data is called its Range.
Example: Ages of all 10 teachers in grade 7 are : 25, 43, 34, 55, 44, 60, 32, 29, 35, 40.
Mean = 43+34+55+44+60,+32+29+35+40 = 39.7 years
Range = Higest Observation – Lowest Observation = 60 – 25 = 35
Median
When a given data is arranged in ascending (or descending) order, then the middlemost observation is called the median of the data.
Example : Marks scored by seven students in a class are: 21, 32, 18 ,93, 21, 36, 50.
Observations in ascending order: 18, 21, 21, 32, 36, 50, 93.
Middle most value = 32
∴ Median is 32.
Mode
The mode of a set of observations is the observation that occurs most often.
Example: Given set of numbers: 1, 1, 2, 4, 3, 2, 1, 2, 2, 4
Ascending Order = 1, 1, 1, 2, 2, 2, 2, 3, 4, 4
∴ Mode of this data is 2 because it occurs more frequently.
Note: A data can have more than 1 mode.
Probability
Probability is the measure or the chance of occurrence of a particular event. Experiments which do not have a fixed result are known as random experiments.
Number of outcomes or Sample Space The set of all the possible outcomes to occur in any experiment is known as sample space.
Examples: Experiment : Tossing a coin, Sample Space (S) = {H,T}
Experiment : Rolling a die, Sample Space (S) = {1,2,3,4,5,6}
Favourable outcome – It is one of the possible result(s) of an experiment.
Double Bar Graphs
Double bar graphs are an effective tool to compare the values of two quantities for the same observation. For example, consider the marks obtained by five students of a class in two tests. Using a double bar graph, we can analyse which week students had better marks.
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