Question

52 randomly selected students were asked how many siblings were in their family. Let X represent the number of pairs of siblings in the student's family. The results are as follows:

# of Siblings	0	1	2	3	4	5	6
Frequency	10	11	7	4	5	10	5

Round all your answers to 4 decimal places where possible.

The mean is:

The median is:

The sample standard deviation is:

The first quartile is:

The third quartile is:

What percent of the respondents have at least 4 siblings? %

72% of all respondents have fewer than how many siblings?

Answer 1

Answer:

Given Data,

52 randomly selected students were asked how many siblings were in their family.

Let X represent the number of pairs of siblings in the student's family.

The results are as follows:

# of Siblings(x)	Frequency(f)	fx	(fx)2
0	10	0	0
1	11	11	121
2	7	14	196
4	5	20	400
5	10	50	2500
6	5	30	900
	f=48	fx=125	(fx)2=4117

(a). To find Mean:

Therefore, mean is 2.6042

(b). To find Median:

Median= (Value of observation+Value of observation)/2

Median=(Value of observation+Value of observation)/2

Median=(Value of 24th observation+Value of 25th observation)/2

Median=(2+2)/2

Median=4/2

Therefore, Median=2

(c).To find sample standard deviation:

Sample Standard Deviation   

Therefore, Sample Standard Deviation S=8.9816

(d).First Quartile:

Q₁=    value of the observation

Q₁=    value of the observation

Q₁=    value of the observation

Q₁=    value of the observation

Q₁=1

Therefore Q₁=1.

(e).Third Quartile:

Q₃=37th value of observation

Q₃=4

Therefore Q₃=4

(f).

The percent of the respondents have at least 4 siblings=

%
Therefore, the percent of the respondents have at least 4 siblings=41.67%.

(g).

72% of all respondents have fewer than how many siblings,

i.e,72% of 48 is=34.56=35

35th Value of observation is 5

Therefore, 72% of all respondents have fewer than the 5 siblings.