Measures of Central Tendency

Measures of central tendency

There are majorly three measures of central tendency:

• Mean
• Median
• Mode

Mean: Mean is the average of the given set of data. x̄=∑ x/n

Where n is the number of observations

Median: The median is the value that divides the given number of observations into exactly two parts. First, the data set has to be arranged in an order, either ascending or descending. There are again two conditions here:

• If the number of observations is odd, then;

Median = [(n+1)/2]th observation or term

• If the number of observations is even, then the median will be the mean of (n/2)th term and (n/2+1)th term.

Mode: The mode represents the frequently occurring value in the dataset.

Example: Find the mean, median and mode of the following data set.

2,3,6,7,4,5,3,8,3,9

Solution: Mean is the average of the given data;

x̄ = (2+3+6+7+4+5+3+8+3+9)/10 = 50/10 = 5

Now, to find the median, we need to arrange the data in ascending order.

2,3,3,3,4,5,6,7,8,9

Since, here the number of observations is even, therefore, the median will be the mean of the two middle terms.

Median = (4+5)/2 = 9/2 = 4.5

Mode = 3, since 3 is repeated here a maximum number of times.

Practice Questions

Q.1: Give one example of a condition in which:

(i) the mean is a proper measure of central tendency.

(ii) the mean is not a proper measure of central tendency but the median is a proper measure of central tendency.

Q.2: Find the mean, median mode of 14, 25, 14, 28, 18, 17, 18, 14, 23, 22, 14, 18.

Q.3: The relative humidity (in %) of a certain city for a month of 30 days was as follows:

98.1 98.6 99.2 90.3 86.5 95.3 92.9 96.3 94.2 95.1 89.2 92.3 97.1 93.5 92.7 95.1 97.2 93.3 95.2 97.3 96.2 92.1 84.9 90.2 95.7 98.3 97.3 96.1 92.1 89

(i) Write a grouped frequency distribution table with classes 90 – 95, 80 – 85, etc.

(ii) Which month or season do you think this data is about?

(iii) What is the range of this data?

(iv) Represent the data set using a bar-graph and histogram