Properties of a Median

Q. Consider the following conclusions regarding the median of a given data set.

Conclusion I: Equal number of data point(s) lie before and after the median(s).

Conclusion II: The data point(s) belong(s) to the left of median(s) is/are less than the median, whereas the data point(s) belong(s) to the right of the median is/are greater than the median.

1. Only conclusion I is correct.
2. Both conclusions are correct.

Q.

The data set shows the fuel efficiencies, in miles per gallon, of the vehicles featured in a car-buying guide.

$293140281923353843462830$
(a) What is the five-number summary of the data set?
(b) What is the range of the data set? Show your work.
Highest number $46$ minus lowest number $19$ equals $27$ range.
(c) What is the interquartile range (IQR) of the data set? Show your work.

Q. The number of chicken sandwiches sold in the school canteen over the past week was recorded as shown below.



What is the median for the above data?

1. 102
2. 108
3. 101.5
4. 110

Q.

Consider the following observations regarding the median of a data set:

Observation I: The median is defined only for numerical data.

Observation II: For an odd number of data points, the median is the central value after rearranging, whereas for an even number of data points, the median is the mean of two central values after rearranging.

Observation III: Unlike mode, the median may or may not be the same as an existing data point.

1. Only observation I and II are correct.
2. All the observations are correct.

Q. Which of the following data sets cannot have a median?

1. Data sets 1 and 2
2. Only data set 3
3. Only data set 2
4. None of the above

Q. The amount of time George takes to run 1 mile in eight consecutive days is as shown below.

Ava says that the median will be from the data set.
Elijah says that the median will not be from the data set.
Who is correct?

1. Ava
2. Elijah
3. Both Ava and Elijah
4. Neither Ava nor Elijah

Q. The number of eggs Friedrich's chickens lay is as shown below.


Anthony says that the median will be from the data set.
Benny says that the median will not be from the data set.
Who is correct?

1. Anthony
2. Benny
3. Neither Anthony nor Benny
4. Both Anthony and Benny