Categories
Economics

MEASURES OF CENTRAL TENDENCY

The arithmetic mean, also popularly referred to as the “mean” is the average of a series of figures or values. The arithmetic mean can also be prepared for grouped data. In this case, the class mark (mid-point) of the individual class interical is used for the X – column

Formula used is

Arithmetic Mean

Example

Calculate the mean of the following marks scored by students in an econo

20, 12, 18.

Use a class interval of 0-9, 10-19, 20-29, e.t.c.

Solution

Frequency table for marks scored by students in Economics Examination

Scores (grouping)Class marks (X)TallyFrequency (F)FX
0-94.5III313.5
10-1914.5     IIII   IIII9130.5
20-2924.5   IIII6147
30-3934.5      IIII5172.5
40-4944.5IIII4178
50-5954.5II2109
60-6964.5I164.5

The Median

The median is defined as an average, which is the middle value when figures are arranged in order of magnitude.

When the items are large, it may be necessary to use other methods other than arranging in order of magnitude to calculate the median. This will require that a frequency table be prepared.

Hence, from a frequency distribution, the median is calculated thus;

median

Member for even number of items i.e. N is even.  Where N is the summation of all the frequency and this is the terminal cumulative frequency.

Example 1

Use the information in the table: Calculate the median age of ssII students

Age Distribution of SSII Students

Age (yrs)681011121314
Frequency510387108

Solutions

Cumulative frequency for age Distribution of SSII Students

Age Distribution of SSII Students

Age (yrs)681011121314
No of students(Frequency)510387108
median2

Example 2

The data in table represents the marks scored by Economics students in NECO examination.  Calculate the median score.

Marks scored by Economics students in

Marks %12182430364048
Frequency611081234

Solution

Cumulative frequency of table for Marks scored by Economics students in NECO Examination

Marks %12182430364048
Frequency6110181234
Cumulative Frequency671725374044

From the table, there are 44 members as indicated by the terminal (last) cumulative frequency. Since this 44 is even, the median score will be;

median3

Mode for Grouped Data

mode

Example

The table below shows the distribution of the weight of students in a certain school.

Weight (kg)40-4445-4950-5455-5960-6465-69
Frequency41115938

Obtain the modal of the weight.

Class Boundary          Frequency

39.5 – 44.5                           4

44.5 – 49.5                           11

49.5 – 54.5                            15

54.5 – 59.5                           9

59.5 – 64.5                           3

64.5 – 69.5                           8

From the table, the modal class has frequency of 15.  The class boundaries are 49.5 -54.5. Therefore, the lower boundary of the modal class is 15, while the frequency is before and after it are 11 and 9 respectively.

mode2

Questions

Marks (kg)55-5960-6465-6970-7475-7980-8485-8990-9495–99100-104
Frequency26923251310651
  1. State the modal class
  2. Estimate the mode of the distribution, correct to one decimal place
  3. The frequency table below represents the number of oranges picked by 20 students.

Calculate the median of the table.

X012345 
F256421 

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