HOMEWORK #D3

Homework #D3- Histograms

Titleof paper: Histograms

HOMEWORK#D3 – HISTOGRAMS

  1. A dot plot is a graphical representation of observations using dots that are stacked in a column. They are used to give a visual representation of counts in a set of data. Each dot represents one count in the data set. The highest stack will represent the most frequent item in the distribution.

  2. Bedford’s law is a theory that checks on the distribution, occurrence or probability of leading digits in a data set. The percentage occurrence of the leading digit is worked out and compared to the expected percentage. It can be applied in circumstances where fraud is suspected to check on the probability of leading digits in the data. In this case, a leading digit, or two digits can be checked for their occurrence in a distribution and the result recorded as a probability or percentage. This is then compared to the expected probabilities before a conclusion is made on whether the percentage of the digit is a result of fraudulent activities.

  3. A histogram is a graphical presentation of the frequency of occurrence of a value or a range of values of a variable in a distribution, against a given class size. It is used for ascertaining and checking the distribution of frequencies of values of a variable in a given distribution. It is therefore basically a frequency distribution graph.

  4. The number of categories or bins used in a histogram will affect the characteristic shape of the frequency distribution graph. The more the categories, the better the shape of the graph. Fewer categories will give a graph which is more of a bar chart without a shape that can be interpreted easily.

  5. Meaning of data skewed right is that when the data is plotted, the curve slants to the left indicating that more of data is below the mean of the distribution. In most cases, the mode is below the median and the median is below the mean. Age distribution in a given society is likely to be skewed to the right in that the percentage of youths the society is always high yet their age is below the average age of the society. The sketch below illustrates this.

  1. If the data is bell shaped or has a normal distribution, it means that the curve is symmetrical about the mean, median and mode. The mean, mode and median are equal in value and the curve spreads out evenly on both sides of the line of symmetry. Quantities that are typically normally distributed include height and weight in the general human population.

  2. If data is skewed right, then the mean of the data is greater than the mode and there is more data to the left of the curve. If the data is skewed left, then the mean of the data is less than the mode and there is more data to the right of the curve. If the data is not skewed at all, then it is symmetrical and the mean is equal to the mode. The value of skew is zero [ CITATION Owe08 l 1033 ].

Computationalexercise

  1. A sketch of the histogram for the data is given below.

Fromthe sketch, it is clear that more than half of the states have anarea below 100,000 square miles and most of the states have an areabelow 50,000 square miles.

  1. A sketch of the histogram for the data is given below.

Fromthe sketch above, it is evident that most of the States recordedbetween 10 and 15 accidents which occurred by motor vehicles.

References

Owen, F., &amp Jones, R. (2008). Statistics. London: Polytech Publishers.

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