# Find the mean and median.

13th Edition
Anderson
Publisher: CENGAGE L
ISBN: 9781305881884

13th Edition
Anderson
Publisher: CENGAGE L
ISBN: 9781305881884

#### Solutions

Chapter 3, Problem 62SE

a.

To determine

## Find the mean and median.

Expert Solution

The mean and median are 2.95 and 3, respectively.

### Explanation of Solution

Calculation:

The given information is that the data represent the number of times a sample of 20 families dined out last week.

Software Procedure:

Step by step procedure to obtain the mean and median using the MINITAB software:

• Choose Stat > Basic Statistics > Display Descriptive Statistics.
• In Variables enter the columns Variable.
• In Statistics select mean and median.
• Click OK.

Output using the MINITAB software is given below:

Thus, mean and median is 2.95 and 3.

b.

To determine

### Find the first and third quartiles.

Expert Solution

The first quartile is 1 and the third quartile is 4.75.

### Explanation of Solution

Calculation:

Software Procedure:

Step by step procedure to obtain the first and third quartiles using the MINITAB software:

• Choose Stat > Basic Statistics > Display Descriptive Statistics.
• In Variables enter the columns Variable.
• In Statistics select first quartile and third quartile.
• Click OK.

Output using the MINITAB software is given below:

Thus, the first and third quartiles are 1 and 4.75, respectively.

c.

To determine

### Find the range and interquartile range.

Expert Solution

The range and interquartile range are 7 and 3.75, respectively.

### Explanation of Solution

Calculation:

Software Procedure:

Step by step procedure to obtain the range and interquartile range using the MINITAB software:

• Choose Stat > Basic Statistics >.Display Descriptive Statistics.
• Click OK.
• In Variables, enter the column of Variable.
• In Statistics select range and interquartile range.
• Click OK.

Output using the MINITAB software is given below:

From the MINITAB output, it is clear that the range of the data is 7 and the interquartile range is 3.75.

d.

To determine

### Find the variance and standard deviation.

Expert Solution

The variance and standard deviation are 4.366 and 2.089, respectively.

### Explanation of Solution

Calculation:

Software Procedure:

Step by step procedure to obtain the variance and standard deviation using the MINITAB software:

• Choose Stat > Basic Statistics >.Display Descriptive Statistics.
• Click OK.
• In Variables, enter the column of Variable.
• In Statistics select variance and standard deviation.
• Click OK.

Output using the MINITAB software is given below:

From the MINITAB output, it is clear that the variance of the data is 4.366 and the standard deviation is 2.089.

e.

To determine

Expert Solution

### Explanation of Solution

The given information is that the skewness measure for the data is 0.34.

Skewness:

• If the value of skewness is equal to zero, then the distribution is normal and symmetric.
• If the skewness value is less than zero, then the distribution is negatively skewed
• If the skewness value is greater than zero, then the distribution is positively skewed.

Here, the skewness is 0.34. This measure is greater than zero. Hence, the shape of the distribution is positively skewed.

f.

To determine

### Check whether the data contain any outliers.

Expert Solution

There are no outliers.

### Explanation of Solution

Calculation:

The formula for lower limit is,

Lower limit=Q11.5IQR

Where, Q1 is the first quartile and Q3 is the third quartile.

Substitute IQR=3.75 and Q1=1

Lower limit=11.5(3.75)=15.625=4.625

Thus, the lower limit is –4.625.

The formula for upper limit is,

Upper limit=Q3+1.5IQR

Substitute IQR=3.75 and Q3=4.75

Upper limit=4.75+1.5(3.75)=4.75+5.625=10.375

Thus, the upper limit is 10.375.

Outlier:

The observation that fall outside of the overall pattern of the data is called an outlier.

The data values less than –4.625 or greater than 10.375 are considered as the outliers.

Here, all data values are lies within the limits. Thus, there are no outliers.

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