5) consider the following back to back stemplot: which of the following are true statements? i. the…

Explanation:

Step1: Find minimum values

For males, minimum is 159. For females, minimum is 155. So I is false.

Step2: Find number of data - points

Number of male data - points (n_m=15), number of female data - points (n_f = 10).

Step3: Calculate medians

For males ((n_m = 15), odd), median is the (\left(\frac{15 + 1}{2}\right)=8^{th}) ordered value. Arranging male data: 159,167,169,172,172,173,173,173,174,177,178,179,179,180,188. Median of males is 174. For females ((n_f=10), even), median is the average of the (\frac{10}{2}=5^{th}) and (\left(\frac{10}{2}+1\right)=6^{th}) ordered values. Arranging female data: 155,157,162,163,164,165,165,165,168,169. Median of females is (\frac{164 + 165}{2}=164.5). So II is false.

Step4: Calculate IQR

For males:

• First, find (Q_1) and (Q_3). Since (n_m = 15), (Q_1) is the (\left(\frac{15+1}{4}\right)=4^{th}) ordered value, (Q_1 = 172). (Q_3) is the (3\times\left(\frac{15 + 1}{4}\right)=12^{th}) ordered value, (Q_3=179). (IQR_m=Q_3 - Q_1=179 - 172 = 7). For females:
• Since (n_f = 10), (Q_1) is the (\left(\frac{10+1}{4}\right)\approx3^{rd}) ordered value, (Q_1 = 162). (Q_3) is the (3\times\left(\frac{10 + 1}{4}\right)\approx8^{th}) ordered value, (Q_3=168). (IQR_f=Q_3 - Q_1=168 - 162 = 6). So III is false.

Answer:

E. None of the statements are true