Question:

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

No. of goals scored01234
No. of matches19753

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?

Updated On: Oct 24, 2023
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Solution and Explanation

The mean and the standard deviation of goals scored by team A are calculated as follows

No. of goals scoredNo. of matchesfxifx_ix12x_1^2fx12fx_1^2
01000
19919
2714428
3515945
43121648
-2550-130

Mean=i=15fixii=15fi=5025=2Mean=\frac{\sum_{i=1}^{5}f_ix_i}{\sum_{i=1}^{5}f_i}=\frac{50}{25}=2

Thus, the mean of both the teams is same.

σ=1NNfixi2(fixi)2σ=\frac{1}{N}√N\sum{f_i}{x_i}^2-(\sum_{f_i}{x_i})^2

=12525×130(50)2=\frac{1}{25}√25 ×130-(50)^2

125750\frac{1}{25}√750

=125×27.38=\frac{1}{25}×27.38

=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.

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Concepts Used:

Frequency Distribution

A frequency distribution is a graphical or tabular representation, that exhibits the number of observations within a given interval. The interval size entirely depends on the data being analyzed and the goals of the analyst. The intervals must be collectively exclusive and exhaustive.

Visual Representation of a Frequency Distribution:

Both bar charts and histograms provide a visual display using columns, with the y-axis representing the frequency count, and the x-axis representing the variables to be measured. In the height of children, for instance, the y-axis is the number of children, and the x-axis is the height. The columns represent the number of children noticed with heights measured in each interval.

Types of Frequency Distribution:

The types of the frequency distribution are as follows:

  1. Grouped frequency distribution
  2. Ungrouped frequency distribution
  3. Cumulative frequency distribution
  4. Relative frequency distribution
  5. Relative cumulative frequency distribution