109k views
1 vote
Find the median, first quartile, third quartile, and interquartile range of the data.

68, 74, 67, 72, 63, 70, 78, 64, 76

1 Answer

5 votes

Given:

The data set is:

68, 74, 67, 72, 63, 70, 78, 64, 76

To find:

The median, first quartile, third quartile, and interquartile range of the data.

Solution:

We have,

68, 74, 67, 72, 63, 70, 78, 64, 76

Arrange the given data in ascending order.

63, 64, 67, 68, 70, 72, 74, 76, 78

Now divide the data in two equal parts.

(63, 64, 67, 68), 70, (72, 74, 76, 78)

So, the median of the given data set is 70.

Divide each parenthesis in two equal parts.

(63, 64), (67, 68), 70, (72, 74), (76, 78)

Now, the first quartile is:


Q_1=(64+67)/(2)


Q_1=(131)/(2)


Q_1=65.5

The third quartile is:


Q_3=(74+76)/(2)


Q_3=(150)/(2)


Q_3=75

The interquartile range (IQR) is the difference between third quartile and first quartile.


IQR=75-65.5


IQR=9.5

Therefore, median is 70, first quartile is 65.5, third quartile is 75 and the interquartile range is 9.5.

User Hongyi Li
by
8.4k points
Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories