Question

7. The marks obtained by 12 students are given below:
30, 55, 50, 40, 50, 60, 55, 62, 55, 45, 61, 65
Calculate mean, median and mode for the above data.​

Answer 1

Answer of mean median mode

Answer 2

Answer:

Given set of Observation : {30, 55, 50, 40, 50, 60, 55, 62, 55, 45, 61, 65}

Mean  : 52.33

Mode : 55

Median : 55

Explanation:

Given set of Observation : {30, 55, 50, 40, 50, 60, 55, 62, 55, 45, 61, 65}

Ordered set is : { 30,40,45,50,50,55,55,55,60,61,62,65  }

Mean of a set of observation:

Mean is the Average value of all the observations in a set of observations. It is calculated as (Sum of all observation/No. of observation).

      Mean of the given set = Sum of all observation / No.of observation          = (30+40+45+50+50+55+55+55+60+61+62+65)/12 = 628/12 = 52.33

Mode: The value which occurs most number of times i.e. most frequently is called the mode of the observation set.

we can determine the mode among some numbers by only observing   which number is appearing most frequently in the data set. This can be zero and one and more than one.

     To find the mode of 30,40,45,50,50,55,55,55,60,61,62,65

55 appears 3 times in the set. hence, the Mode of the set is 55.

Median :

Step 1: Arrange the data items in ascending order.

        Ordered Set:  { 30,40,45,50,50,55,55,55,60,61,62,65  }

Step 2: Count the number of observations.

         Number of observations n = 12 (even)

Step 3:  Median can be found by =

      [$\frac{n}{2}$ th observation + ( $\frac{n}{2}$+ 1) th observation ]/ 2

   = (6th observation + 7th observation) / 2

   = (55 + 55)/2 = 55