Question

Following are the observation of throwing a dice 15 times

5, 3, 4, 1, 6, 2, 2, 4, 3, 2, 1, 5, 1, 6, 2

Find the mean, mode and median of this data.​

Answer 1

⇒ Given:

The observations when a die was thrown 15 times:

5, 3, 4, 1, 6, 2, 2, 4, 3, 2, 1, 5, 1, 6, 2

⇒ To Find:

The mean, median and mode of the data.

⇒ Solution:

At first, let's rearrange the data in ascending order:

1, 1, 1, 2, 2, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6

Now,

Mean

Mean of the data simply refers to the average. The formula to be used is:

$\bf{\implies\:Mean=\dfrac{Sum\:of\:all\:values}{No.\:of\:values}}$

Applying the same formula:

$\sf{Mean=\dfrac{1+1+1+2+2+2+2+3+3+4+4+5+5+6+6}{15}}$

$\sf{Mean=\dfrac{47}{15}}$

$\bf{Mean=3.13}$

Mode

Mode refers the value of the data that has the highest frequency.

Here,

No. 1 = 3 times

No. 2 = 4 times

No. 3 = 2 times

No. 4 = 2 times

No. 5 = 2 times

No. 6 = 2 times

We can notice that no. 2 has highest frequency that occurs 4 times.

$\bf{Mode=2}$

Median

Median of a data refers to the value the occupies the middle most position when arranged in ascending/descending order.

Here, we have got odd number of values, i.e., 15. The nearest even number preceding it is 14.

$\sf{\dfrac{14}{2}=7}$

Hence, we need to cancel 7 numbers from both the left and right end:

1, 1, 1, 2, 2, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6

The middle most value is 3.

$\bf{Median=3}$

⇒ Final answers:

→ Mean = 3.13

→ Mode = 2

→ Median = 3