Difference between Mean and Median: Overview, Questions, Preparation

Mean, and Median have their importance in statistics. When the data is bigger, it is difficult to compare this data, and at this point, mean and median comes into the picture.

Mean

Mean can be defined as the sum of all the observations divided by the number of observations. There are different types of means- Arithmetic mean, Harmonic mean, Geometric mean, Quadratic mean, etc.
Mean = (a₁ + a₂ + a₃ + a₄ + …. + a_n)/n

Median

The number present in the middle of the set is known as the median. Median is used to separate the set into two equal sets: the upper half set and the lower half set. 
Arrange the observations in ascending order and pick the middle number. This is easy when you have an odd number of observations, but for even observations, select the middle pair, add it and divide it by two.

Median = {(n+1)/2} (For odd observations)

Median = [(n/2) th term +  {(n+1)/2} th term]/2

Difference between mean and median

In the chapter, ‘Statistics,’ you will understand the mean, median, and mode in detail, along with the graphical representation of cumulative frequency distribution.

1. The following table gives the productivity yield per hectare of wheat of 100 villages. Change the distribution to a more than type distribution and draw its ogive.

Solution.

> 50          2 + 98 = 100

> 55        8 + 90 = 98

> 60        12 + 78 = 90

> 65        24 + 54 = 78

> 70        38 + 16 = 54

> 75        16

Coordinates are A (50,100), B(55,98), C(60,90), D(65,78), E(70,54), F(75,16)

2. The following distribution gives the daily income of 50 workers. Change the distribution to a less than type cumulative frequency distribution and draw its ogive.

Solution.

Daily income            No. of workers
Coordinates are A(120,12), B(140,26), C(160,34), D(180,40), E(200,50)

3. During the medical check-up of 35 students, their weights are recorded as follows. Draw a less than type ogive for the data. Hence obtain the median weight from the graph and verify the result by using the formula.

Solution.

∑f_i = 35, so n =35
      = n/2 = 17.5

Weight        No. of students
 0-38            0
38-40            3 - 0 = 3
40-42            5 - 3 = 2
42-44            9 - 5 = 4
44-46            14 - 9 = 5
46-48            28 - 14 = 14
48-50            32 - 28 = 4
50-52            35 - 32 = 3

Median class = 46-48, I= 46, c= 14, f= 14, h= 40 -38 = 2, n/2= 17.5

Median = I + {[(n/2) - c]/f} * h
      = 46 + {[(17.5)- 14]/14} * 2
      = 46.5

Q: What is the mean?

Q: What is the median?

Q: What are the different kinds of means?

Q: Where do you use the skewed type of distribution?

Q: Which is sensitive towards outlier data?

Q: Which uses positional and arithmetic average?