The following frequency distributions show the heights (in cm) of students in two different schools, P and Q.
School P
150–155 : 3
155–160 : 7
160–165 : 12
165–170 : 10
170–175 : 5
School Q
150–155 : 2
155–160 : 6
160–165 : 8
165–170 : 14
170–175 : 7
Using the class mid-points, answer the following.
a. (i) Calculate the mean height for each school.
b. (ii) Calculate the standard deviation of heights for each school (correct to one decimal place).
c. (iii) Which school has a more uniform height distribution? Support your answer with the calculations obtained.