Question

Which normal distribution has the greatest standard deviation?

Answer 1

Answer with explanation:

Both the normal distribution curves have sample mean equal to 16.

Normal distribution curve 1 is more wider than Curve 2, resulting in greater standard deviation.

So, Curve 1 has the  greatest standard deviation.

Answer 2

Answer:

Graph 1 has the highest standard deviation.

Explanation:

Standard deviation is a basic parameter in statistics. Standard deviation is basically a measure of the amount of variation or dispersion of a set of values from its mean. The shape of graph of normal distribution is like a bell shape.

Further explanation:

Standard deviation has 2 major forms as σ (population standard deviation) or & s (sample standard deviation).  

A low standard deviation indicates that the values tend to be close to the mean & the dispersion is low.  

In contrast a high standard deviation indicates that the values are spread out over a wider range.  

• Consider the graph 1

When examining the shape of the graph it is clear that most of the data has been centered on the mean value. Amount of values which are highly deviating from the mean are low. This feature has given bell shape to the graph. The deviation to left & right sides from the mean is high making the shape of the curve bell shape, broad. This is a graph representing the normal distribution.

The mean of the data set is aprrox 16. The lowest value of the data set is -10. So from the mean there is a 16 - (-10) deviation for the left side which is 26. The highest value is 40. So there is a 40 – 16 deviation which is 24.

• Consider the graph 2  

When examining the shape of the graph it is somewhat similar to the graph 1. Most of the data has been centered on the mean value. This feature has given bell shape to the graph.  Amount of values which are highly deviating from the mean are very low compared to graph 1. Therefore finally the shape of the curve gets a narrow, bell shape. This graph also represents the normal distribution.

The mean is 32. The lowest value of the data set is approx 16. So, the mean there is a 32 – 16 deviation for the left side which is 16. The highest value is 44. So there is a 44 – 32 deviation for right side which is 12.

According to the above explanation it is clear that in the 1st graph there is a higher deviation from the mean. Therefore graph 1 has the greatest standard deviation.

Learn more:

1. Standard deviation of normal distribution: brainly.com/question/12541993 , Answered by MsEHolt

Keywords

Standard deviation, mean, dispersion, normal distribution, bell shape