Question

complete the sentence:
when the data is spread further apart from the mean,......
there is less variability and the data will have a low standard deviation.
the mean will be zero.
there is more variability and the data will have a high standard deviation.
the data is skewed right.

Explanation:

Step1: Recall the concept of standard deviation

Standard deviation measures the spread of data from the mean.

Step2: Analyze each option

• Option 1: If data is spread further apart, variability is more, not less. So this is wrong.
• Option 2: Mean being zero has no relation to data spread from the mean. So this is wrong.
• Option 3: When data is spread further apart from the mean, there is more variability. And standard deviation which measures spread will be high. This is correct.
• Option 4: Data being skewed right is about the shape of the distribution (tail on the right), not about spread from the mean. So this is wrong.

Answer:

there is more variability and the data will have a high standard deviation.