Question

In: Statistics and Probability

Male and female populations of tortoises under 80 years old are represented by age in the...

Male and female populations of tortoises under 80 years old are represented by age in the table below. Complete parts​ (a) through​ (d).0-9 M 13 F 8 ​10-19 M 12 F 5 ​20-29 M 17 F 17 ​30-39 M 15 F 18 ​40-49 M 22 F 23 ​50-59 M 24 F 24 ​60-69 M 19 F 18 ​70-79 M 13 F 13 ​(a) Approximate the population mean and standard deviation of age for males. ​(a) Approximate the population mean and standard deviation of age for males. ​(a) Approximate the population mean and standard deviation of age for males. Approximate the population mean and standard deviation of age for females. ​(c) Which gender has the higher mean​ age? ​(d) Which gender has the higher dispersion in​ age?

Solutions

Expert Solution

a) the population mean and standard deviation of age for males.

Age Midpoint Males()
0-9 4.5 13 58.5 263.25
10-19 14.5 12 174 2523
20-29 24.5 17 416.5 10204.25
30-39 34.5 15 517.5 17853.75
40-49 44.5 22 979 43565.5
50-59 54.5 24 1308 71286
60-69 64.5 19 1225.5 79044.75
70-79 74.5 13 968.5 72153.25
Sum =135 =5647.5 =296893.8

Mean :

  

=5647.5/135

=41.83

  

Standard deviation :

  

  

=21.194

  

#Mean=41.83

#Standard deviation=21.194

b) Approximate the population mean and standard deviation of age for females. ​

Age Midpoint females()
0-9 4.5 8 36 162
19-Oct 14.5 5 72.5 1051.25
20-29 24.5 17 416.5 10204.25
30-39 34.5 18 621 21424.5
40-49 44.5 23 1023.5 45545.75
50-59 54.5 24 1308 71286
60-69 64.5 18 1161 74884.5
70-79 74.5 13 968.5 72153.25
Sum - 126 5607 296711.5

Mean :

  

=5607/126

=44.5

  

Standard deviation :

  

  

=19.355

  

#Mean=44.5

#Standard deviation=19.355

. ​(c) Which gender has the higher mean​ age?

Ans:

Mean of Male< Mean of Female

Female has higher mean age

​(d) Which gender has the higher dispersion in​ age?

Ans: Standard deviation Male>Standard deviation Female

Male has higher dispersion in​ age

orchestra answered 1 year ago
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