Question

below are the prices of snowboards at two competing snowboard stores: middletown snowboards 345,350,356,360,375,405 snowboard central 343,370,386,392,395,402 a) identify the 5 number summaries for both stores middletown snowboards snowboard central b) draw a double box - and - whisker plot of the above data on the scale below: 340 350 360 370 380 390 400 410

Explanation:

Step1: Recall 5 - number summary components

The 5 - number summary consists of the minimum, first quartile ($Q_1$), median ($Q_2$), third quartile ($Q_3$), and maximum.

Step2: For Middletown Snowboards

Arrange data in ascending order: $345,350,356,360,375,405$.

• Minimum: $345$
• Since $n = 6$ (even), median $Q_2=\frac{356 + 360}{2}=358$
• Lower half of data: $345,350,356$. So $Q_1 = 350$
• Upper half of data: $360,375,405$. So $Q_3=375$
• Maximum: $405$

Step3: For Snowboard Central

Arrange data in ascending order: $343,370,386,392,395,402$

• Minimum: $343$
• Since $n = 6$ (even), median $Q_2=\frac{386+392}{2}=389$
• Lower half of data: $343,370,386$. So $Q_1 = 370$
• Upper half of data: $392,395,402$. So $Q_3 = 395$
• Maximum: $402$

Answer:

Middletown Snowboards: Minimum = 345, $Q_1$ = 350, Median = 358, $Q_3$ = 375, Maximum = 405
Snowboard Central: Minimum = 343, $Q_1$ = 370, Median = 389, $Q_3$ = 395, Maximum = 402

(Note: Drawing the double - box and whisker plot is a visual task. For the plot, for Middletown Snowboards, mark the minimum at 345, $Q_1$ at 350, median at 358, $Q_3$ at 375 and maximum at 405. For Snowboard Central, mark the minimum at 343, $Q_1$ at 370, median at 389, $Q_3$ at 395 and maximum at 402 on the given scale and draw the boxes and whiskers accordingly.)