Answer to Question #107611 in Statistics and Probability for Yusuf

Question

Number if people
108
44
206
85
57

Question 21 Which of the following statements is correct? (1) The median is 85 and equals the mean. (2) The value of Q1 is 57. (3) The position of Q2 is 2. (4) The value of Q3 is 157. (5) The distribution of the number of people living with ASD is symmetric.
Question 22 The interquartile range is __________________? (1) Equals to the range. (2) Always less than the range. (3) 149: (4) 51: (5) 0:

Answer 1

From the data set,

$Mean=\frac{108+44+206+85+57}{5}\\Mean =100$

Therefore the statement 1 is wrong.

From the sorted data,

$44\ 57\ 85\ 108\ 206$

First quartile,

$Q_1=\frac{1}{4}(5+1)\ =1.5^{th}\ term \\ Q_1=50.5$

since the first quartile is in betweeen 44 and 57. therefore statement 2 is wrong

Second quartile,

$Q_2=\frac{1}{2}(5+1)\ =3$

Second quartile is the $3^{rd}$ term, therefore statement 3 is also wrong

$Q_3=\frac{3}{4}(5+1)\ =4.5$

which is ,

$\frac{108+206}{2}=157$

Since the statement 4 is correct.

The answer is (4)

Question 22

The inter quartile range of the above problem,

$=Q_3-Q_1\\ =157-50.5\\ =106.5$

SInce statments (3),(4),(5) are wrong

And the range of the data set,

$Range=206-44\\ =162$

which is not equal to the range, since statement (1) is wrong

For a data set inter quartile range is always less than the range.

Thus, the answer is (2).