The following is the record of goals scored by team A in a football session:

No. of goals scored 0 1 2 3 4
No. of matches 1 9 7 5 3

For the team B, mean number of goals scored per match was 2 with a standard deviation 1.25 goals. Find which team may be considered more consistent?

Asked by Abhisek | 11 months ago |  97

1 Answer

Solution :-

\( \displaystyle\sum_{i=1}^{15} f_i x_i=\dfrac{50}{25}=2\)

Thus, the mean of both the teams is same

Variance = \( \dfrac{1}{N^2}[ N\displaystyle\sum f_i x_i^2-(\displaystyle\sum f_i x_i)^2] \)

\( \dfrac{1}{25^2}[(25\times 30)-2500]\)

\( \dfrac{750}{625}=1.2\)

Standard deviation σ = \( \sqrt{Variance}\)

\( \sqrt{1.2}\)  = 1.09

The standard deviation of team B is 1.25 goals. The average number of goals scored by both the teams is same i.e., 2. Therefore, the team with lower standard
deviation will be more consistent. Thus, team A is more consistent than team B.

Answered by Pragya Singh | 11 months ago

Related Questions

Find the mean deviation from the mean and from a median of the following distribution:

Marks 0-10 10-20 20-30 30-40 40-50
No. of students 5 8 15 16 6

 

Class 11 Maths Statistics View Answer

The age distribution of 100 life-insurance policy holders is as follows

Age (on nearest birthday) 17-19.5 20-25.5 26-35.5 36-40.5 41-50.5 51-55.5 56-60.5 61-70.5
No. of persons 5 16 12 26 14 12 6 5

 

Class 11 Maths Statistics View Answer

Compute mean deviation from mean of the following distribution:

Marks 10-20 20-30 30-40 40-50 50-60 60-70 70-80 80-90
No. of students 8 10 15 25 20 18 9 5

 

Class 11 Maths Statistics View Answer

Find the mean deviation from the mean for the following data:

Classes 95-105 105-115 115-125 125-135 135-145 145-155
Frequencies 9 13 16 26 30 12

 

Class 11 Maths Statistics View Answer

Find the mean deviation from the mean for the following data:

Classes 0-100 100-200 200-300 300-400 400-500 500-600 600-700 700-800
Frequencies 4 8 9 10 7 5 4 3

 

Class 11 Maths Statistics View Answer