What is the range of the middle 50% of data a. 2 b. 3 c. 6.5 d. 8

Mathematics

1 answer:

Andreyy893 years ago

8 0

The correct option is: b. 3

Explanation

Middle 50% data means the "Interquartile Range" which is measured as the difference between the third quartile $(Q_{3})$ and the first quartile $(Q_{1})$ in a data set.

In the given box plot, we can see that: $Q_{1}= 4$ and $Q_{3}= 7$

So, the Interquartile range, $IQR= Q_{3}-Q_{1} = 7-4= 3$

Thus, the range of the middle 50% of data will be 3.

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Step-by-step explanation:

To calculate the mean and the variance of the number of successful surgeries (X), we first have to enumerate the possible outcomes:

1) Both surgeries are successful (X=2).

$P(e_1)=0.90*0.67=0.603$

2) Left knee unsuccessful and right knee successful (X=1).

$P(e_2)=(1-0.9)*0.67=0.1*0.67=0.067$

3) Right knee unsuccessful and left knee successful (X=1).

$P(e_3)=0.90*(1-0.67)=0.9*0.33=0.297$

4) Both surgeries are unsuccessful (X=0).

$P(e_4)=(1-0.90)*(1-0.67)=0.1*0.33=0.033$

Then, the mean can be calculated as the expected value:

$M=\sum p_iX_i=0.603*2+0.067*1+0.297*1+0.033*0\\\\M=1.206+0.067+0.297+0\\\\M=1.57$

The variance can be calculated as:

$V=\sum p_i(X_i-\bar{X})^2\\\\V=0.603(2-1.57)^2+(0.067+0.297)*(1-1.57)^2+0.033*(0-1.57)^2\\\\V=0.603*0.1849+0.364*0.3249+0.033*2.4649\\\\V=0.1115+0.1183+0.0813\\\\V=0.3111$