Question

Unit sales for new product ABC have varied in the first seven months of this year as follows: Month Jan Feb Mar Apr May Jun Jul Unit Sales 148 329 491 167 228 285 441 What is the interquartile range (IQR) of the data? Please specify your answer as an integer. Note: Use the following formula to find quartile locations: Lq=(n+1)⋅(q4) where q is the quartile index (e.g., q=1 for the first quartile) and n is the number of data points.

Answer 1

IQR = 274

Explanation:

Given the unit sales for the months as:

148, 329, 491, 167, 228, 285, 441

Let's rearrange in ascending the values in ascending order (from lowest to highest), we have:

148, 167, 228, 285, 329, 441, 491

Here the total number of data, n is 7

Let's find the quartile locations using the formula:

`Lq = (n + 1) * ((q)/(4))`

where q is quartile index.

For first quartile, Q1:

`Lq = (7 + 1) * ((1)/(4))`

`Lq = 8 * ((1)/(4)) = 2`

Thus, the 2nd observation in the data is 167.

Q1 = 167

For third quartile, Q3:

`Lq = (7 + 1) * ((3)/(4))`

`Lq = 8 * ((3)/(4)) = 6`

Thus, the 6th observation in the data is 441.

Q3 = 441

The interquartile range, IQR will be:

Q3 - Q1

= 441 - 167

= 274

IQR = 274