Question

These box plots show the number of electoral votes won by Democratic and

Republican presidential candidates for the elections from 1984 through 2012


Republican


159


170


525


Democratic


299


3675


0


50


100


150


400


450


500


550


200 250 300 350


Electoral votes


Which statement best compares the spreads of the data sets?

Answer 1

(a) is true

Explanation:

Given

See attachment for box plots

Required

Which of the options is true?

Option A compares the IQR of both plots.

IQR is calculated using:

`IQR = Q_3 - Q_1`

Where

`Q_1 \to` Lower quartile

`Q_2 \to` Upper quartile

From the attached plots, we have:

Republican

`Q_1 = 170.5`

`Q_3 = 356`

So:

`IQR = 356 - 170.5`

`IQR = 185.5`

Democratic

`Q_1 = 181`

`Q_3 = 367.5`

So:

`IQR = 367.5 - 181`

`IQR = 186.5`

We have:

`IQR = 185.5` --- Republican

`IQR = 186.5` --- Democratic

Hence, (a) is true