For the data given below, Find the LCM of Mode, Mean and Median.

7, 2, 10, 4, 3, 12, 8, 4, 6, 4

Given:

7, 2, 10, 4, 3, 12, 8, 4, 6, 4

Formula used:

Mode - The mode is the value that appears most frequently in a data set.

Mean = sum of data/number of data

Median = When data set is even = {(n/2)th + (n/2 + 1)th}/2

Calculation:

7, 2, 10, 4, 3, 12, 8, 4, 6, 4

Firstly data arrange in ascending order

⇒ 2, 3, 4, 4, 4, 6, 7, 8, 10, 12

The mode is the value that appears most frequently in a data set.

⇒ Mode = 4

Mean = sum of data/number of data

⇒ (2 + 3 + 4 + 4 + 4 + 6 + 7 + 8 + 10 + 12)/10

⇒ 60/10

⇒ 6

Median = When data set is even = {(n/2)th + (n/2 + 1)th}/2

⇒ {(10/2)th + (10/2 + 1)th}/2

⇒ (5th + 6th)/2

here 5th term is 4 and 6th term is 6

⇒ (4 + 6) /2

⇒ 10/2

⇒ 5

LCM of Median, Mean and Mode

⇒ LCM of 5, 6, 4

⇒ 3 × 4 × 5

⇒ 60

∴ The LCM of Median, Mean and Mode is 60.

 Confusion PointsHere the value of 5th term and 6th term is divided by 2 during Median calculation.