M6 6.PS.2 Review- Measures of Center

A line plot shows the following data points: 3, 3, 4, 5, 5, 5, 6, 7. What is the mean of this data set?

• 4.5

• 4.75

• 5.5

• 6

Answer explanation

To find the mean, add all the data points: 3 + 3 + 4 + 5 + 5 + 5 + 6 + 7 = 38. Then divide by the number of points (8): 38 / 8 = 4.75. The closest answer is 5, which is the correct choice.

Tags

VA.6.PS.2.a

If the number 8 is added to the data set 3, 4, 5, 5, 6, what happens to the mean?

• It decreases

• It stays the same

• It increases

• It doubles

Answer explanation

Adding 8 to the data set increases the total sum from 23 to 31. The new mean is 31 divided by 6, which is approximately 5.17, higher than the original mean of 4.6. Thus, the mean increases.

Tags

VA.6.PS.2.b

In a data set, the numbers are 2, 3, 3, 4, 4, 4, 5, 5, 100. Which number is an outlier?

• 2

• 3

• 5

• 100

Answer explanation

The number 100 is significantly higher than the other values in the data set, which range from 2 to 5. This large difference makes 100 an outlier, as it does not fit the pattern of the other numbers.

Tags

VA.6.PS.2.c

A line plot shows the data points: 1, 2, 2, 3, 3, 3, 4, 4, 5. What is the balance point (mean) of this data set?

• 2.5

• 3

• 3.5

• 4

Answer explanation

To find the mean, sum the data points: 1 + 2 + 2 + 3 + 3 + 3 + 4 + 4 + 5 = 27. There are 9 data points, so divide the sum by 9: 27 / 9 = 3. The balance point (mean) is 3.

Tags

VA.6.PS.2.a

If the number 10 is removed from the data set 5, 6, 7, 8, 10, what happens to the mean?

• It decreases

• It stays the same

• It increases

• It becomes zero

Answer explanation

Removing 10 from the data set reduces the total sum from 36 to 26, while the number of data points decreases from 5 to 4. The new mean is 26/4 = 6.5, which is less than the original mean of 7.2, so the mean decreases.

Tags

VA.6.PS.2.b

In the data set 10, 12, 12, 13, 14, 15, 15, 16, 100, which measure of center is most affected by the outlier?

• Mean

• Median

• Mode

• Range

Answer explanation

The mean is most affected by the outlier (100) because it takes all values into account, leading to a significant increase. The median and mode remain unchanged, while the range only reflects the spread of values.

Tags

VA.6.PS.2.c

A line plot shows the data points: 2, 2, 3, 3, 3, 4, 4, 5. What is the mean of this data set?

• 3

• 3.25

• 3.5

• 4

Answer explanation

To find the mean, add all the data points: 2 + 2 + 3 + 3 + 3 + 4 + 4 + 5 = 26. Then divide by the number of points (8): 26 / 8 = 3.25. Thus, the mean is 3.25.

Tags

VA.6.PS.2.a

If the number 20 is added to the data set 5, 5, 6, 7, 8, what happens to the median?

• It decreases

• It stays the same

• It increases

• It becomes 20

Answer explanation

The original data set is 5, 5, 6, 7, 8, with a median of 6. Adding 20 shifts the middle of the data to 6 & 7 so the median is 6.5. 6.5 is greater than 6.

Tags

VA.6.PS.2.b

Which is the correct data set for the line plot?

• 1, 2, 3, 4, 5, 6, 7, 8, 9, 

• 1, 2, 2, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 7, 9

• 1, 2, 3, 4, 5, 7, 9

Answer explanation

The correct data set for the dot plot is '1, 2, 2, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 7, 9' as it accurately represents the frequency of each number, which is essential for creating a line plot.

Tags

CCSS.3.MD.B.4

Justin collected data on how many miles he drove for each day for a week. This data is displayed on this line plot. What is the balance point for this set of data?

• 24 Miles

• 25 Miles

• 26 Miles

• 27 Miles

Answer explanation

The balance point, or mean, of Justin's data is calculated by adding the total miles driven over the week and dividing by the number of days. The correct balance point is 25 miles, as it represents the average of the data.

Tags

CCSS.4.MD.B.4