Question

Find the range median first and third interquartile range for each data set

6.3,6.7,6.2,4.9,6.7,6.6,6.1,6.3,6.4,5.8
And
15,16,18,9,18,17,19,19,4,36

Answer 1

Part 1

Range = 1.8

Median = 6.3

First Quartile = 6.3

Third Quartile = 6.8

Interquartile Range = 0.5

Part 2

Range = 32

Median = 17.5

First Quartile = 15

Third Quartile = 19

Interquartile Range = 4

Explanation:

Part 1 data set

To find the above quantities we need to arrange the data in ascending form which will become

4.9, 5.8, 6.1, 6.2, 6.3, 6.3, 6.4, 6.6, 6.7, 6.7

Range

In order to find the range of the data set, we subtract the smaller value from the bigger value

Range = 6.7 - 4.9

Range = 1.8

Median

In order to find the Median we need to get the middle number of the range.

So we get their average because we have two.

Median = 6.3 + 6.3 /2

Median = 6.3

1st Quartile

In order to get the first quartile, we take the median of the lower value of the data set.

4.9, 5.8, 6.1, 6.2, 6.3

The median of the first quartile is 6.1.

3rd Quartile

In order to get the 3rd quartile, we take the median of the upper value of the data set.

6.3, 6.4, 6.6, 6.7, 6.7

The median of the 3rd quartile is 6.6

Interquartile Range

In order to get the interquartile range, we need to subtract the median of the third quartile to the median of the first quartile.

So

Interquartile Range = 6.6 - 6.1

Interquartile Range = 0.5

Part 2

To find the above quantities we need to arrange the data in ascending form which will become

4, 9, 15, 16, 17, 18, 18, 19, 19, 36

Range

In order to find the range of the data set, we subtract the smaller value from the bigger value

Range = 36 - 4

Range = 32

Median

In order to find the Median we need to get the middle number of the range.

So we get their average because we have two.

Median = 17 + 18 /2

Median = 17.5

1st Quartile

In order to get the first quartile, we take the median of the lower value of the data set.

4, 9, 15, 16, 17,

The median of the first quartile is 15.

3rd Quartile

In order to get the 3rd quartile, we take the median of the upper value of the data set.

18, 18, 19, 19, 36

The median of the third quartile is 19.

Interquartile Range

In order to get the interquartile range, we need to subtract the median of the third quartile to the median of the first quartile.

So

Interquartile Range = 19 - 15

Interquartile Range = 4

Answer 2

Range = 1.8

Median = 6.3

First Quartile = 6.3

Thrid Quartile = 6.8

Interquartile Range = 0.5

Explanation:

First we need to arrange the data set from lowest to highest.

4.9, 5.8, 6.1, 6.2, 6.3, 6.3, 6.4, 6.6, 6.7, 6.7

To find the range of the data set, we simply take the highest value and subtract it to the lowest value.

Range = 6.7 - 4.9

Range = 1.8

To find the Median we need to get the middle number of the range. In this case there are two numbers in the middle of the set.

So we get both of them and get their average.

Median = 6.3 + 6.3 /2

Median = 6.3

To get the first quartile, we simply get the median of the lower of the data set.

4.9, 5.8, 6.1, 6.2, 6.3

The median of the first quartile is 6.1.

To get the third quartile, we get the median of the upper half of the data set.

6.3, 6.4, 6.6, 6.7, 6.7

The median of the third quartile is 6.6

To get the interquartile range, we need to subtract the median of the third quartile to the median of the first quartile.

Interquartile Range = 6.6 - 6.1

Interquartile Range = 0.5

Answer:

Range = 32

Median = 17.5

First Quartile = 15

Thrid Quartile = 19

Interquartile Range = 4

Explanation:

First we need to arrange the data set from lowest to highest.

4, 9, 15, 16, 17, 18, 18, 19, 19, 36

To find the range of the data set, we simply take the highest value and subtract it to the lowest value.

Range = 36 - 4

Range = 32

To find the Median we need to get the middle number of the range. In this case there are two numbers in the middle of the set.

So we get both of them and get their average.

Median = 17 + 18 /2

Median = 17.5

To get the first quartile, we simply get the median of the lower of the data set.

4, 9, 15, 16, 17,

The median of the first quartile is 15.

To get the third quartile, we get the median of the upper half of the data set.

18, 18, 19, 19, 36

The median of the third quartile is 19.

To get the interquartile range, we need to subtract the median of the third quartile to the median of the first quartile.

Interquartile Range = 19 - 15

Interquartile Range = 4