Question

The steps to find the inter quartile range(IQR) of the data set 4, 8 5, 3, 9, 8, 5, 6 and 7, representing the quiz scores of students is given. Find which of the following is an error statement.

• A. No error
• B. Arrange the data set in ascending order : 3, 4, 5, 5, 6, 7, 8, 8, 9
• C. Lower half of the data set is 3, 4, 5, 5. and lower quartile = 5.
• D. Calculate the median, median = 6.

Answer 1

The correct option is C Lower half of the data set is 3, 4, 5, 5. and lower quartile = 5.

To find the lower quartile range of the data set, first we have to arrange the data set in ascending order.

Hence, the first option, "Arrange the data set in ascending order : 3, 4, 5, 5, 6, 7, 8, 8, 9" is correct.

The next step is to find the median.

Hence, the next option "Calculate the median, median = 6" is also correct.

The next step is to find the median of lower half data (lower quartile) and upper half data (upper quartile).

The lower half data is 3, 4, 5, 5

Median = $\frac{4+5}{2}$

= 4.5

But, median of lower half data is given as 5.

Hence, the error statement is "Lower half of the data set is 3, 4, 5, 5. and lower quartile = 5"