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A standard deviation (or σ) is a measure of how dispersed the data is in relation to the mean. Low, or small, standard deviation indicates data are clustered tightly around the mean, and high, or large, standard deviation indicates data are more spread out. Problem: In a random survey of 3,015 boys age 11, the average height was 146 cm, and the standard deviation (SD) was 8 cm. A histogram suggested the heights were approximately normally distributed. Fill in the blanks. A) One boy was 170 cm tall. He was above average by __________ SDs. B) Another boy was 148 cm tall. He was above average by __________ SDs. C) A third boy was 1.5 SDs below the average height. He was __________ cm tall. D) If a boy was within SDs of average height, the shortest he could have been is __________ cm and the tallest is __________ cm.
