Measures of Central Tendencies

MEASURES OF CENTRAL

TENDENCIES

Ungrouped data

MEAN

Do you have an idea what MEAN(Statistics) is?

Mean

Is the average value of a data.

Population Mean

Is the mean of the whole population

Sample Mean

Is the mean of the part of the population

Example Problems

1) The number of faculty members in 10 different colleges are 16, 25, 40, 24, 15, 20, 50, 15, 35 and 20. Treating the data as a population, find the population mean of faculty members for the 10 colleges.

2) The following are the ages of the 9 children in a squatters area. Find the mean.Ages: 9, 8, 1, 3, 4, 5, 6, 7, 2

MEDIAN

So, what is median? Can you give some ideas about it?

MedianIs the value found at the middle when the data are arranged in an array form from the highest to the lowest or from the lowest to the highest.

x987654321

5

Example

The MEDIAN

1)

x9876543211

2)

4

5

The MEDIAN

MODE

Mode

Is the value which occurs most often or with greatest frequency.

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9

Example

The MODE1) 9

x18181717171616161515

2)

16

17

The MODE

1717

16

16

17 and 16

grouped data

What is a grouped data?

MEAN

In finding the mean in a grouped data, we use this formula:

Example

A frequency distribution of the scores in English of 34 Education students.

x f m fm35 – 39 330 – 34 525 – 29 820 – 24 1015 – 19 410 – 14 2

5 - 9 2

x f m fm35 – 39 3 37 11130 – 34 5 32 16025 – 29 8 27 21620 – 24 10 22 22015 – 19 4 17 6810 – 14 2 12 24

5 - 9 2 7 14

MEDIAN

Where: __– median___– half sumF – cumulative

frequencyf – frequencyi – interval

x f F35 – 39 330 – 34 525 – 29 820 – 24 1015 – 19 410 – 14 2

5 - 9 2

x f F35 – 39 3 3430 – 34 5 3125 – 29 8 2620 – 24 10 1815 – 19 4 810 – 14 2 4

5 - 9 2 2

MODE

Where:___ - mode__ - median__ - mean

Mean = 23.91Median = 24Find the mode using the formula given.