Question

1. a coach is taking his high school x-country team to ottawa for ofsaa. he researched the minimum daily temperatures for the days of the competition. they are listed below. find the mean median and mode for each year.

	oct 25	oct 26	oct 27	oct 28
2004	6°c	8°c	6°c	4°c
2001	11°c	6°c	4°c	2°c

Explanation:

For 2006:

Mean:

Step1: Sum the temperatures

The temperatures are \(5^\circ\text{C}\), \(4^\circ\text{C}\), \(3^\circ\text{C}\), \(4^\circ\text{C}\). The sum is \(5 + 4+3 + 4=16\).

Step2: Divide by number of days (4)

Mean \(=\frac{16}{4} = 4^\circ\text{C}\).

Median:

Step1: Order the data

Ordered data: \(3^\circ\text{C}\), \(4^\circ\text{C}\), \(4^\circ\text{C}\), \(5^\circ\text{C}\).

Step2: Find the middle value (average of 2nd and 3rd)

Median \(=\frac{4 + 4}{2}=4^\circ\text{C}\).

Mode:

The value that appears most frequently. \(4^\circ\text{C}\) appears twice, others once. Mode \(= 4^\circ\text{C}\).

For 2004:

Mean:

Step1: Sum the temperatures

Temperatures: \(6^\circ\text{C}\), \(8^\circ\text{C}\), \(6^\circ\text{C}\), \(4^\circ\text{C}\). Sum \(=6 + 8+6 + 4 = 24\).

Step2: Divide by 4

Mean \(=\frac{24}{4}=6^\circ\text{C}\).

Median:

Step1: Order the data

Ordered data: \(4^\circ\text{C}\), \(6^\circ\text{C}\), \(6^\circ\text{C}\), \(8^\circ\text{C}\).

Step2: Average of 2nd and 3rd

Median \(=\frac{6 + 6}{2}=6^\circ\text{C}\).

Mode:

\(6^\circ\text{C}\) appears twice, others once. Mode \(= 6^\circ\text{C}\).

For 2001:

Mean:

Step1: Sum the temperatures

Temperatures: \(11^\circ\text{C}\), \(6^\circ\text{C}\), \(4^\circ\text{C}\), \(2^\circ\text{C}\). Sum \(=11 + 6+4 + 2=23\).

Step2: Divide by 4

Mean \(=\frac{23}{4} = 5.75^\circ\text{C}\).

Median:

Step1: Order the data

Ordered data: \(2^\circ\text{C}\), \(4^\circ\text{C}\), \(6^\circ\text{C}\), \(11^\circ\text{C}\).

Step2: Average of 2nd and 3rd

Median \(=\frac{4 + 6}{2}=5^\circ\text{C}\).

Mode:

All values appear once, so there is no mode (or all values are modes with frequency 1).

Final Answers:

• 2006: Mean \(= 4^\circ\text{C}\), Median \(= 4^\circ\text{C}\), Mode \(= 4^\circ\text{C}\)
• 2004: Mean \(= 6^\circ\text{C}\), Median \(= 6^\circ\text{C}\), Mode \(= 6^\circ\text{C}\)
• 2001: Mean \(= 5.75^\circ\text{C}\), Median \(= 5^\circ\text{C}\), Mode \(=\text{No unique mode (all values occur once)}\)

Answer:

For 2006:

Mean:

Step1: Sum the temperatures

The temperatures are \(5^\circ\text{C}\), \(4^\circ\text{C}\), \(3^\circ\text{C}\), \(4^\circ\text{C}\). The sum is \(5 + 4+3 + 4=16\).

Step2: Divide by number of days (4)

Mean \(=\frac{16}{4} = 4^\circ\text{C}\).

Median:

Step1: Order the data

Ordered data: \(3^\circ\text{C}\), \(4^\circ\text{C}\), \(4^\circ\text{C}\), \(5^\circ\text{C}\).

Step2: Find the middle value (average of 2nd and 3rd)

Median \(=\frac{4 + 4}{2}=4^\circ\text{C}\).

Mode:

The value that appears most frequently. \(4^\circ\text{C}\) appears twice, others once. Mode \(= 4^\circ\text{C}\).

For 2004:

Mean:

Step1: Sum the temperatures

Temperatures: \(6^\circ\text{C}\), \(8^\circ\text{C}\), \(6^\circ\text{C}\), \(4^\circ\text{C}\). Sum \(=6 + 8+6 + 4 = 24\).

Step2: Divide by 4

Mean \(=\frac{24}{4}=6^\circ\text{C}\).

Median:

Step1: Order the data

Ordered data: \(4^\circ\text{C}\), \(6^\circ\text{C}\), \(6^\circ\text{C}\), \(8^\circ\text{C}\).

Step2: Average of 2nd and 3rd

Median \(=\frac{6 + 6}{2}=6^\circ\text{C}\).

Mode:

\(6^\circ\text{C}\) appears twice, others once. Mode \(= 6^\circ\text{C}\).

For 2001:

Mean:

Step1: Sum the temperatures

Temperatures: \(11^\circ\text{C}\), \(6^\circ\text{C}\), \(4^\circ\text{C}\), \(2^\circ\text{C}\). Sum \(=11 + 6+4 + 2=23\).

Step2: Divide by 4

Mean \(=\frac{23}{4} = 5.75^\circ\text{C}\).

Median:

Step1: Order the data

Ordered data: \(2^\circ\text{C}\), \(4^\circ\text{C}\), \(6^\circ\text{C}\), \(11^\circ\text{C}\).

Step2: Average of 2nd and 3rd

Median \(=\frac{4 + 6}{2}=5^\circ\text{C}\).

Mode:

All values appear once, so there is no mode (or all values are modes with frequency 1).

Final Answers:

• 2006: Mean \(= 4^\circ\text{C}\), Median \(= 4^\circ\text{C}\), Mode \(= 4^\circ\text{C}\)
• 2004: Mean \(= 6^\circ\text{C}\), Median \(= 6^\circ\text{C}\), Mode \(= 6^\circ\text{C}\)
• 2001: Mean \(= 5.75^\circ\text{C}\), Median \(= 5^\circ\text{C}\), Mode \(=\text{No unique mode (all values occur once)}\)