Question

Physical education rescarchers interested in the develoment of the overarm throw measured the horizontal velocity of a thrown ball at the time of release. The results for first-grade children (in feet/sec) (courtesy of L. Halverson and M. Roberton) are: Males: 54.2, 39.6, 52.3, 48.4, 35.9, 30.4, 25.2, 45.4, 48.9, 48.9, 45.8, 44.0, 52.5, 48.3, 59.9, 51.7, 38.6, 39.1, 19.9, 38.3 Females: 30.3, 43.0, 25.7, 26.7, 27.3, 31.9, 53.7, 32.9, 19.4, 23.7, 23.3, 23.3, 37.8, 39.5, 33.5, 30.4, 28.5 (a) Use R to create a histogram for the males and a histogram for the females (any kind of histogram that you want). Adjust the x axis scale so the two groups are more easily compared. (b) Compare the shape of the throws from the male and female students observed in this sample. (c) Compute and compare the mean and median throw velocities observed in the male and famale students across gender. (d) Compute and compare the standard deviation in throw velocities observed in the male and famale students (e) Use R to help you create a boxplots of the two sets so they are easily comparable. (f) Which, if any values were identified as outliers? Would this value have been identified as an outlier if it were thrown by the opposite gender? (g) What would be the shape of the histogram had we combined the boys and girls' throw velocities into one large data set (with 37 values)?

Answer 1

male=c(54.2,39.6,52.3,48.4,35.9,30.4,25.2,45.4,48.9,48.9,45.8,44,52.5,48.3,59.9,51.7,38.6,39.1,49.9,38.3)
female=c(30.3,43.0,25.7,26.7,27.3,31.9,53.7,32.9,19.4,23.7,23.3,23.3,37.8,39.5,33.5,30.4,28.5)
length(male)
length(female)
summary(male)
summary(female)
hist(male,xlab = "velocity",col = "green",border = "red", xlim = c(15,60), ylim = c(0,7))
hist(female,xlab = "velocity",col = "green",border = "red", xlim = c(15,60), ylim = c(0,7))

sqrt(var(male))
sqrt(var(female))

median and mean of male is greater than median and male of female

sd of male and sd of female are approximently same

boxplot(female)
boxplot(male)

boxplot(female)
identify(rep(1, length(female)), female, labels = seq_along(female))

data=c(male,female)
hist(data,xlab = "velocity",col = "green",border = "red", xlim = c(15,60), ylim = c(0,7))