Question

The low temperatures (in degrees Fahrenheit) for seven days in February, in Minneapolis, are

-3, 2, 12, -5, -5, -11, and 6. Which one of the following statements is true for this set of data?

A. The mean is smaller than the median.

B. The interquartile range (or IQR) will be negative.

C. The standard deviation will be negative since there are negative values in the data set.

D. The first quartile (or Q1) is 2.

E. If the temperature of 12 is removed from the data set, both the mean and the

median will change.

Answer 1

For the given data set the mean is calclated as:

Mean = ( -11 + -5 + -5 + -3 + 2 + 6 + 12)/7
= -4/7
Mean = -0.5714
and the median is the middle value when rrange in ascending order, as we can see that the median is at 4th value hence medin is -3.

So, Mean is greater than median and options A is false.

for the given data set Q1, the first quartile is the median of the first half of the data set and Q 3 is median of the data set, as we can see that the first half values are negative and 2nd half values are positive so, IQR which is calculated as Q3-Q1 cannot be negative.

So, option B is also false.

The standard deviation is calculated as:

where squaring of all values is done during calculation so, it can never be negative.

So, option C is also false.

Option D which says Q1 is 2 is false the first half values in the data set are negative.

If we remove the value 12 from the data set the mean will certainly change and to check whether the median will change or not we see after removing the data set becomes like -11, -5, -5, -3, 2, 6, now the median lies between 3rd and 4th values which calculated as (-5+(-3))/2 = -4, so, median also changed.

Hence Option E is True for the given dataset.