In a statistics class, the standard deviation of the heights of all students was 4.2 inches. The standard deviation of the heights of males was 3.4 inches and the standard deviation of females was 3.3 inches. Why is the standard deviation of the entire class more than the standard deviation of the males and females considered separately?

Answer

given,

the standard deviation:-

of the students height in the class = 4.2 inches

of the male heights in the class = 3.4 inches

of females height in the class = 3.3 inches

standard deviation is the deviation of the value from the target value.

the given question standard deviation of the students is more than that of the individual standard deviation of the heights of males and females because of the distribution of the entire class has more dispersion.