Question

3.3.13 Male and female populations of elephants under 80 years old are represented by age in the table below Complete parts (a) through (d) (a) Approximate the population mean and standard deviation of age for males 41.33 (Round to two decimal places as needed.) Age Females Males (Round to two decimal places as needed) 11 10-19 10 16 20-29 15 16 p0-39 40-49 17 20 25 20 50-59 25 23 60-69 15 18 70-79 15 14

b. approximate the population mean and standard deviation

u=

o=

c. which gender has a higher mean age?

d. which gender has the higher dispersion in age?

please help

Answer 1

Mean and standard deviation for the gender Males Males Class mark f*x2 f*x Age f X 0 9 11 4.5 49.5 222.75 10 -19 14.5 16 232 3364 392 20 29 16 24.5 9604 30-39 17 34.5 586.5 20234.25 44.5 40 49 25 1112.5 49506.25 1362.5 50 -59 25 54.5 74256.25 60 -69 967.5 15 64.5 62403.75 1043 77703.5 70-79 14 74.5 139 5745.5 297294.8 Mean f*x Σf 45.5 -41.33 139 Variance n*£fx2-(Efx)2 _139*297294.8-(5745.5)433.3855 139* (139-1) n*(n-1) Standard deviation -Vvariance V433.3855 20.82

Mean and standard deviation for the gender females Class mark Females f*x2 f*x Age f х 31.5 0 9 7 4.5 141.75 10 -19 10 14.5 145 2102.5 20 29 15 24.5 367.5 9003.75 30 -39 20 34.5 23805 690 40 - 49 20 44.5 890 39605 50-59 1253.5 23 54.5 68315.75 1161 60 -69 18 64.5 74884.5 70-79 15 74.5 1117.5 83253.75 301112 128 5656 Mean x _5656-44.19 Σf 128 Variance n*£fx2-(Efx)2 _128*301112-(5656)-403.05118 128*(128-1) п*(п-1) Standard deviation =Vvariance =V403.05118=20.08

a) Approximate mean for the male is u =41.33 Approximate standard deviation for the male is o=20.82 b) Approximate mean for the female is u =44.19 Approximate standard deviation for the female is g=20.08 c) Female gender has the higher mean age d) Since standard deviation for the male is higher than female Hence male gender has higher dispersion in age