Statistics - Economics Assignment
Statistics - Economics Assignment
Task 1
Life span in hours (x)
8
10
11
12
13
Number of batteries
5
15
30
40
10
Finding the mean
Sum of given numbers=100
Number of given numbers=5
Mean of number of breakdowns=20
Note that the mean isn't a value from the original list. This is a common result. You should not assume that your mean will be one of your original numbers.
Frequency diagram
A frequency diagram means of displaying raw data in a graphical form that is easier to interpret. Commonly used frequency diagrams are bar charts, histograms, pie charts, and scatter diagrams.
Task 2
MTBF (Hours)
50 to 100
100 to 200
200 to 300
300 to 500
500 to 600
500 to 700
100 to 1000
No of machines
3
4
10
8
5
4
2
Histogram
In statistics, a histogram is a graphical representation, showing a visual impression of the distribution of data. It is an estimate of the probability distribution of a continuous variable and was first introduced by Karl Pearson. A histogram consists of tabular frequencies, shown as adjacent rectangles, erected over discrete intervals (bins), with an area equal to the frequency of the observations in the interval. The height of a rectangle is also equal to the frequency density of the interval, i.e., the frequency divided by the width of the interval. The total area of the histogram is equal to the number of data (Basu and Dasgupta 1997). A histogram may also be normalized displaying relative frequencies. It then shows the proportion of cases that fall into each of several categories, with the total area equaling 1. The categories are usually specified as consecutive, non-overlapping intervals of a variable. The categories (intervals) must be adjacent, and often are chosen to be of the same size.
Histograms are used to plot density of data, and often for density estimation: estimating the probability density function of the underlying variable. The total area of a histogram used for probability density is always normalized to 1 (Bickel 2003). If the length of the intervals on the x-axis are all 1, then a histogram is identical to a relative frequency plot.
An alternative to the histogram is kernel density estimation, which uses a kernel to smooth samples. This will construct a smooth probability density function, which will in general more accurately reflect the underlying variable.
Task 3
Length of L(mm)
10
15
20
25
30
35
40
No of nails
7
17
52
63
35
35
8
Finding the mean
Sum of given no. of nails=217
Number of given number of nails=7
Mean of given number of nails=31
When observations are grouped into class intervals, the interval that contains the most frequently occurring value is known as the modal class. When considered in the perspective of the histogram the height of each bar times its width (that is, its area) gives the frequency, so that the visual impression is accurate; but the highest bar (the modal class) shows where the data is most concentrated, rather than just which class we happen to have chosen to take in most of the data.
The Median is the 'middle value' in your list (Gannoun, Saracco and Yu 2010). When the totals of the list are odd, the median is the middle entry in the list after sorting the list ...