Question

a box of led light bulbs was tested to see how long the light bulbs last. the standard deviation of the light bulb lifetime data was five years. which of the following is the best interpretation of this value?
fifty percent of the light bulb lifetime data is below five years.
the difference between the longest and shortest light bulb lifetime was five years.
the lifetime of the light bulbs typically varies by about five years from the mean.
the middle half of the light bulb lifetime data has a range that is five years wide.

Explanation:

Standard deviation measures the amount of variation or dispersion of a set of values. It represents how much the data points typically deviate from the mean.

• Option 1: Fifty percent of data being below a value is related to the median (not standard deviation).
• Option 2: The difference between the longest and shortest is the range (not standard deviation).
• Option 3: This correctly describes the meaning of standard deviation as a measure of typical deviation from the mean.
• Option 4: The range of the middle half of data is related to the inter - quartile range (not standard deviation).

Answer:

The lifetime of the light bulbs typically varies by about five years from the mean.