Probablity and Statistics

Assignment No.02

What is the significance and importance when Mean, Median, Mode

Jalil Maqsood

1/1/2351

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Arithmetic Mean:

The arithmetic mean of a set of data is found by taking the sum of the data, and then dividing the sum by the total number of values in the set. A mean is commonly referred to as an average.

Median:

Median is the middle value of a list of numbers. The median of a set of data is the middlemost number in the set. The median is also the number that is halfway into the set. To find the median, the data should first be arranged in order from least to greatest.

Mode:

The mode of a set of data is the value in the set that occurs most often.

From the above definitions it is clear to us that mean, median and mode are three different quantities in "Probability and Statistics", and as there definitions differ, so there applications and usage differ from one another. All three are the different tools to study the data we acquired from the sample and population. On their basis we can make determine the parameters of population and statistics of samples. Mean gives us the average of our data, which we think is the finding near to the midpoint of our data as it is the average but mean is greater affected by the extreme values of our data. For example;

Calculate Mean: 4,5,4,9,6,3,7,4

Answer: (4+5+4+9+6+3+7+4)/8 = 5.25

now,

Calculate Mean: 63,5,4,9,6,3,7,50

Answer: (63+5+4+9+6+3+7+50)/8=18.375

It is clear that only shift in the extreme values can cause a huge rise or fall in the mean of the data. This affect of mean greatly enhanced if we are dealing with a greater numbers of samples.

So, Now jumps in the median, now median gives us the middle value of the data. It is also evident that most of our data will be close to the center point or midpoint. so if we identify median then we can find out the trend by which the data is rising or falling. so median is a better measurement in order to find the center of our data. For example if we studying the income of different classes of society then median will give us more satisfying result for middle class

income then the mean which is greater affected by the extreme data entries. similarly principles also apply in engineering.

Mode is the measure which gives us the most occurring data item. It may seem useful if we are taking in consideration a single sample but it usefulness clears to us if we take multiple samples i.e. mixed distributions. For example we want to find out that how many people prefer thalasemic tests before marriage , and we have the asked a multiple samples of population in different regions then mode will be the measure that gives us the answer which is given most.

Mean, Median and Mode are quantities which are closely related to the data acquired from the sample. As we have change in data these quantities also shift from one end toward others. for example if income the elite class is increasing more the poor we can easily identify it by movement of mean in data, it will moving towards the elite class income. Similarly different traits of our data can be identified.

Example 1.34:

1 2 3 4 5 6 7 8 9 10 11 12 13 14 154.6

4.7

4.8

4.9

5

5.1

5.2

5.3

5.4

5.5

5.6 RBC Count in 15 Days

Series 1

c: Since the normal RBC count is from 4.7-6.1(millions) in male and 4.2-5.4(millions) in female. if the patient is male then it is normal but if patient is female then there is an abnormality. High RBC count may be due to one of following causes;

Cigarette smoking Congenital heart disease Cor pulmonale Dehydration (such as from severe diarrhea) Kidney tumor (renal cell carcinoma) Low blood oxygen levels (hypoxia) Pulmonary fibrosis Polycythemia vera

Histogram:

Quarts Frequency Relative Frequency

0 2 .08

1 5 .20

2 9 .36

3 5 .20

4 3 .12

Category 10

1

2

3

4

5

6

7

8

9

10

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