Question

find the mean, median, mode, range, and Quartiles of the following 13,13,10,8,7,6,4,5,14,12,4,2,9,8,8,12

Answer 1

Solution:-

Solution:- Given that samples: 13,13,10,8,7,6,4,5,14,12,4,2,9,8,8,12

Mean : sum of terms/number of terms = 135/16 = 8.4375

Median : 8

Explanation

The median is the middle number in a sorted list of numbers. So, to find the median, we need to place the numbers in value order and find the middle number.

Ordering the data from least to greatest, we get:

2 4 4 5 6 7 8 8 8 9 10 12 12 13 13 14   

As you can see, we do not have just one middle number but we have a pair of middle numbers, so the median is the average of these two numbers:

Median = (8+8)/2 = 8

=> Mode = 8

Range : 12

Explanation

The range is the difference between the highest and lowest values in the data set.

Ordering the data from least to greatest, we get:

2   4   4   5   6   7   8   8   8   9   10   12   12   13   13   14   

The lowest value is 2.

The highest value is 14.

The range = 14 - 2 = 12.

Explanation

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

Ordering the data from least to greatest, we get:

2 4 4 5 6 7 8 8 8 9 10 12 12 13 13 14   

We see that the mode is 8 .

Quartiles:

Q1 = 5.5

Explanation

The first quartile (or lower quartile or 25th percentile) is the median of the bottom half of the numbers. So, to find the first quartile, we need to place the numbers in value order and find the bottom half.

2 4 4 5 6 7 8 8 8 9 10 12 12 13 13 14   

So, the bottom half is

2 4 4 5 6 7 8 8   

The median of these numbers is 5.5.

Q2 = Median = 8

Q3 = 12

Explanation

The third quartile (or upper quartile or 75th percentile) is the median of the upper half of the numbers. So, to find the third quartile, we need to place the numbers in value order and find the upper half.

2 4 4 5 6 7 8 8 8 9 10 12 12 13 13 14   

So, the upper half is

8 9 10 12 12 13 13 14   

The median of these numbers is 12