Respuesta :

garybgajiton

Answer:

4

Step-by-step explanation:

17, 18, 18, 19, 20, 21, 21, 23, 25

find the median first:

17, 18, 18, 19, 20, 21, 21, 23, 25

median: 20  

let's find the median of the lower half also known as Q1 (we won't include the 20)

lower quartile Q1            median     upper quartile Q3              

17, 18, 18, 19                       20             21, 21, 23, 25

(18+18 = 36, 36 ÷ 2 = 18)                 (21+23 = 44, 44÷2 = 22)

Q1: 18

Q3: 22

22 - 18 (Q3 - Q1)

22 - 18 = 4

Interquartile Range (IQR) = 4

The interquartile range of the given set of data is 4

Interquartile range is the difference between the first quartile (Q₁) and the third quartile (Q₃). That is,

Interquartile range = Q₃ - Q₁

The first quartile (Q₁) is the middle value in the first half of the given data.

The given data is 17, 18, 18, 19, 20, 21, 21, 23, 25

The first half of the data is: 17, 18, 18, 19;

Since we have even number of values, the middle value will be the average of the 2nd and 3rd terms

∴  [tex]Q_{1} = \frac{18+18}{2}[/tex]

[tex]Q_{1} = \frac{36}{2}[/tex]

Q₁ = 18

The first quartile (Q₁) = 18

For the third quartile, Q₃

The third quartile (Q₃) is the middle value in the second half of the given data

The second half is: 21, 21, 23, 25

The middle value will be the average of the 7th and 8th terms

∴  [tex]Q_{3} = \frac{21+23}{2}[/tex]

[tex]Q_{3} = \frac{44}{2}[/tex]

Q₃ = 22

The third quartile (Q₃) = 22

Recall,

Interquartile range = Q₃ - Q₁

∴ Interquartile range = 22 - 18

Interquartile range = 4

Hence, the interquartile range of the given data is 4.

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