Statistics
Statistics
4th Edition
ISBN: 9780393929720
Author: David Freedman, Robert Pisani, Roger Purves
Publisher: Norton, W. W. & Company, Inc.
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Chapter 4.5, Problem 4ED

a.

To determine

Identify whether the SD is around 1, 2, or 10 for the given list.

a.

Expert Solution
Check Mark

Answer to Problem 4ED

The SD is around 1.

Explanation of Solution

Calculation:

The average of the given list is 50.

The difference between the given observations and the average is,

Deviations={(4950),(5150),(4950),(5150),(4950),(5150),(4950),(5150),(4950),(5150)}=(1,1,1,1,1,1,1,1,1,1)

Here, all deviations from the average is ±1.

Therefore, the SD is around 1.

b.

To determine

Identify whether the SD is around 1, 2, or 10 for the given list.

b.

Expert Solution
Check Mark

Answer to Problem 4ED

The SD is around 2.

Explanation of Solution

Calculation:

The average of the given list is 50.

The difference between the given observations and the average is,

Deviations={(4850),(5250),(4850),(5250),(4850),(5250),(4850),(5250),(4850),(5250)}=(2,2,2,2,2,2,2,2,2,2)

Here, all deviations from the average is ±2.

Therefore, the SD is around 2.

c.

To determine

Identify whether the SD is around 1, 2, or 10 for the given list.

c.

Expert Solution
Check Mark

Answer to Problem 4ED

The SD is around 2.

Explanation of Solution

Calculation:

The average of the given list is 50.

Condition:

  • If the spread of the numbers around the average is larger, then the value of SD is larger.
  • If the spread of the numbers around the average is smaller, then the value of SD is smaller.

The difference between the given observations and the average is,

Deviations={(4850),(5150),(4950),(5250),(4750),(5250),(4650),(5150),(5350),(5150)}=(2,1,1,2,3,2,4,1,3,1)

Here, the given data set has less spread. Hence, the SD is around 2.

d.

To determine

Identify whether the SD is around 1, 2, or 10 for the given list.

d.

Expert Solution
Check Mark

Answer to Problem 4ED

The SD is around 2.

Explanation of Solution

Calculation:

The average of the given list is 50.

The difference between the given observations and the average is,

Deviations={(5450),(4950),(4650),(4950),(5150),(5350),(5050),(5050),(4950),(4950)}=(4,1,4,1,1,3,0,0,1,1)

Here, the given data set has less spread. Hence, the SD is around 2.

e.

To determine

Identify whether the SD is around 1, 2, or 10 for the given list.

e.

Expert Solution
Check Mark

Answer to Problem 4ED

The SD is around 10.

Explanation of Solution

Calculation:

The average of the given list is 50.

The difference between the given observations and the average is,

Deviations={(6050),(3650),(3150),(5050),(4850),(5050),(5450),(5650),(6250),(5350)}=(10,14,19,0,2,0,4,6,12,3)

Here, the spread of the numbers around the average is larger. This provide the largest SD.

Therefore, the SD is around 10.

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