Chapter ISG, Problem 10.5.2P

a.

To determine

To calculate center and spread of data.

Answer to Problem 10.5.2P

For investment A

Median=3.52

IQR=0.02

For investment B

Median=3.67

IQR=0.65

Explanation of Solution

Given information:

  

  

Formula used:

IQR=Q₃-Q₁ IQR is interquartile range

Q₃ is upper quartile

Q₁ is lower quartile

Calculation:

For investment A

Ordered data set: 3.47, 3.50, 3,51, 3.51, 3.52, 3.52, 3.52, 3.53, 3.54, 3.57

n=10

Middle number: 3.52, 3.52

Median=3.52

Lower quartile, Q₁=3.51

Upper quartile, Q₃=3.53

Substituting value of Q₃and Q₁ in the formula

IQR=3.53-3.51 On solving,

IQR=0.02

For investment B

Ordered data set: 1.67, 2.71, 3.32, 3.42, 3.53, 3.81, 3.89, 3.97, 5.14, 5.81

n=10

Middle number: 3.53, 3.81

  

On solving,

=3.67

Lower quartile, Q₁=3.32

Upper quartile, Q₃=3.97

Substituting value of Q₃and Q₁ in the formula

IQR=3.97-3.32 On solving,

IQR=0.65

b.

To determine

To find center and spread tell about investments.

Answer to Problem 10.5.2P

Median of investment A is less

Interquartile range of investment A is also less

Explanation of Solution

Given information:

  

  

For investment A

Median=3.52

IQR=0.02

For investment B

Median=3.67

IQR=0.65

Median is the middle value of the series, so it is not affected by the extreme value like mean.Median can be easily represented graphically.

Interquartile range is defined as the difference between the 25th and 75th percentile (also called the first and third quartile). Hence the interquartile range describes the middle 50% of observations. If the interquartile range is large it means that the middle 50% of observations are spaced wide apart. The important advantage of interquartile range is that it can be used as a measure of variability if the extreme values are not being recorded exactly (as in case of open-ended class intervals in the frequency distribution). Other advantageous feature is that it is not affected by extreme values.

Median of investment A is less

Interquartile range of investment A is also less

b.

To determine

To find center and spread tell about investments.

Answer to Problem 10.5.2P

Suggestion is that J invest in A to obtain greater profit

Explanation of Solution

Given information:

  

  

For investment A

Median=3.52

IQR=0.02

For investment B

Median=3.67

IQR=0.65

Median is the middle value of the series, so it is not affected by the extreme value like mean.Median can be easily represented graphically.

Interquartile range is defined as the difference between the 25th and 75th percentile (also called the first and third quartile). Hence the interquartile range describes the middle 50% of observations. If the interquartile range is large it means that the middle 50% of observations are spaced wide apart. The important advantage of interquartile range is that it can be used as a measure of variability if the extreme values are not being recorded exactly (as in case of open-ended class intervals in the frequency distribution). Other advantageous feature is that it is not affected by extreme values.

Median of investment A is less

Interquartile range of investment A is also less

Low IQR means less interest obtained by J

So, suggestion is that J invest in A to obtain greater profit