Find the median and quartiles for the data.

Question
Find the median and quartiles for the data.

Answers (1)

2020-11-07
Calculation:
Median:
- If the data set consists of odd number of entries then the median is the middle value of the data.
- If the data set consists of even number of entries then the median is the mean of the middle vales in the data set.
Arrange the data in ascending order.
120, 120, 130, 140, 150, 150, 150, 160, 180
Here the number of observations is 9 which is an odd number. Therefore the median is the center value of the data that is, 150
Thus, the median cost of compact refrigerators is \(\$150\).
First quartile \(Q_{1}\):
The median of the data values that are to the left of the overall median is termed as first quartile.
Here the number of observation below median is 4 which is an even number.
The middle values represent \(2^{nd}\) observation and \(3^{rd}\) observation.
Here the \(2^{nd}\) observation is 120 and \(3^{rd}\) observation is 130.
\(Q_{1}=\frac{120+130}{2}\)
\(=\frac{250}{2}=125\)
Thus, the first quartile \(Q_{1},\ is\ \$125\).
Third quartile \(Q_{3}\):
The median of the data entries that are to the right of the overall median is termed as third quartile
Here the number of observation above median is 4 which is an even number.
The middle values represent \(7^{th}\ and\ 8^{th}\) observations.
Here the \(7^{th}\) observation is 150 and \(8^{th}\) observation is 160.
\(Q_{3}=\frac{150+160}{2}\)
\(= \frac{310}{2} = 155\)
Thus, the third quartile \(Q_{3},\ is\ \$155\).
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