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?
The mean and the standard deviation of goals scored by team A are calculated as follows
No. of goals scored | No. of matches | \(fx_i\) | \(x_1^2\) | \(fx_1^2\) |
0 | 1 | 0 | 0 | 0 |
1 | 9 | 9 | 1 | 9 |
2 | 7 | 14 | 4 | 28 |
3 | 5 | 15 | 9 | 45 |
4 | 3 | 12 | 16 | 48 |
- | 25 | 50 | - | 130 |
\(Mean=\frac{\sum_{i=1}^{5}f_ix_i}{\sum_{i=1}^{5}f_i}=\frac{50}{25}=2\)
Thus, the mean of both the teams is same.
\(σ=\frac{1}{N}√N\sum{f_i}{x_i}^2-(\sum_{f_i}{x_i})^2\)
\(=\frac{1}{25}√25 ×130-(50)^2\)
\(\frac{1}{25}√750\)
\(=\frac{1}{25}×27.38\)
=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.
(i) List the deeds that led Ray Johnson to describe Akhenaten as “wacky”.
(ii) What were the results of the CT scan?
(iii) List the advances in technology that have improved forensic analysis.
(iv) Explain the statement, “King Tut is one of the first mummies to be scanned — in death, as in life...”
Give reasons for the following.
(i) King Tut’s body has been subjected to repeated scrutiny.
(ii) Howard Carter’s investigation was resented.
(iii) Carter had to chisel away the solidified resins to raise the king’s remains.
(iv) Tut’s body was buried along with gilded treasures.
(v) The boy king changed his name from Tutankhaten to Tutankhamun.
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.
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.
The types of the frequency distribution are as follows: