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Definition

Measures of central tendency in statistics are single values that can be derived from the data set such that it can be used as the representative of the whole data.

The most common measures of central tendency includes:

Mean
mode
Median

Mean

Mean is the average value for the data set. It is obtained by finding the total sum of all the values in the data set then divining it by the total frequency.That is;

Mean = (Sum of all Values)/(Total frequency)

consider the following set of data represents marks scored by a group of students in a math test:

68,65,59,30,42,45,46,59,80,23,54, 45,54,30

The sum of values in the data= 68+65+59+30+42+45+46+59+80+23+54+45+54+30=700

The total frequency of the data set = 14 because there are 14 results in the test

Mean = 700/14 = 50

Mean value could be interpreted to mean the value that could result if data set was modified so that each item will have the same quantity.

Example Problem

10 athletes measured their masses which were recorded and their mean determined as 60.45 Kg. The mass for nine of them were 62.10kg, 58.90kg,56.8kg, 49.70kg, 57.1kg, 64.56kg,58.35kg,55.21kg, 58.67kg but the weight of one athlete was never recorded. Help determine the missing mass.

Solution

Mean = (Sum of all Values)/(Total frequency)

let the missing value be x

then total mass for the ten athletes will be 62.10+58.90+56.80+49.70+57.1+64.56+58.35+55.21+58.67+x

frequency = 10 as there are 10 athletes

but mean = 60.45

hence 60.45 =(521.39 + x)/10

hence 604.5 = 521.39+x

x=604.45 – 521.39 = 83.06 kg

Practice Question

Four numbers have the following number of animals: 134, 233, a, 2a. The mean number of animals owned by the farmers is 250. Find a

The mode

Mode is the value that has the greatest occurrence in the data set.

Consider the following data sets.

14, 33, 16, 15, 12, 16, 10, 17, 16, 13, 15, 11,9,8,14,16

16 is repeated most of the times, hence it is the mode.

Median

Median is the value that will be in the middle of the data when data is arranged in an ascending order.

if the total number of items is even number, median is the average of two values in the middle of the data arranged in the ascending order.

Tag: mode

Measures of central Tendency