GIRLS
BOYS
GIRLS
Summary of statistically calculated information
There are two types of summary measures used in the above tables. The first, average or mean measures the ‘location’ of the numbers and tells at what general level the data are. The fourth, range measures ‘scatter’ and indicates how widely spread the data are. The two measures reflect the important attributes of the data. For each type of measure there is a choice of measure to use. For location, the choice is among mean, mode and median. For scatter the choice is between the range and interquartile range.
Measures of location
Measures of location are intended to show, in general terms, the size of set data.
Arithmetic mean
The most common and useful is the well known arithmetic mean. It is defined as,
Mean = Sum of readings___
Number of readings
Median
This is the middle value of a set of numbers. There is no mathematical formula for calculating it. It is obtained by listing the numbers in ascending order and then the median is that number at the halfway point.
Mode
The third measure of location is the mode. This is the most frequently occurring value. Again there is no mathematical formula for the mode. The frequency with which value occurs is noted and the value with the highest frequency is the mode.
Measures of scatter
Measures of scatter do exactly as their name implies. They are a measure of the extent to which the readings are grouped closely together or are scattered over a wide interval. They are called measures of dispersion.
Range
The best known and certainly simplest measure of scatter is the range which is the total interval covered by numbers.
Range = Largest reading – Smallest reading
Interquartile range
The range is defined entirely on the two extreme values and this might be misleading. To overcome this problem the interquartile range is the range of numbers after eliminating the highest and the lowest 25%. This measure is no longer sensitive to extremes.
Interquartile range =Range of the middle 50% of readings.
Comparison of measures of scatter
I have some evidence to describe the performance in science by boys and girls and their difference in their IQ.
The average performance in science of boys and girls are same since both are having the mean as grade 4. Performance of boys seems better than girls in terms mode considering grade 5 attainment. 40% of boys achieved grade 5 and only 17% of girls achieved grade5.
On the other hand 63% of girls achieved grade 4 and 23% of boys achieved grade 4. The typical grade attained by the boys is grade 5 and girls is 4 (median).
The average IQ of the boys is higher than that of the girls. The average (mean) in this instance distorted by high and low value outliers. There are some low values of IQ (187, 15 and 25). There could be also a distortion by means of clusters. The More girls (53%) have IQ than boys (43%) between 100 and 110. Typical IQ of girls (103) is higher than that of boys (94) [median].
Block Diagram
The block diagram shows the science results of the boys. It shows that no student graded a one but only one boy graded grade 2. Grade 3 is obtained by 9 boys and grade 4 by 7 boys. The highest grade which the boys obtained is 5 because12 students obtained it. Only one boy got the highest grade 6.
This block diagram shows the science results of the girls. None of the girls obtained grade 1or grade 2. 5 girls obtained grade 3. The highest grade which the girls obtained in science is 4 because19 girls obtained it. 5 girls obtained grade 5. Only one girl got the highest grade 6.
The comparison block diagram shows boys science results in blue and the girls science results in purple. It shows that there are 2 students from each side are able to score the highest grade. The majority of boys whose achievement is grade 5. 9 boys achieved grade 3 and 7 boys achieved grade 4. Only one achieved grade 2. The majority of girls achieved grade 4. 5 girls achieved grade 3 and 5 girls achieved grade 5. None of the girls achieved grade 1 or 2.
The comparison block diagrams shows that girls are better than boys in science because girls did not achieve grade 1 or2. In addition to that 19 girls achieved grade 4.
Scatter Graph
The scatter diagram shows the relationship between two variables. The relationship could be investigated considering correlation and regression. Correlation is a method for measuring the strength of a relationship and regression is a method for determining a formula expressing the relationship. Correlation shows whether a connection exists and regression finds what the connection. I know that although discrete variables cannot really give a continuous curve. I am interested in the trend pattern of the points. I wish to investigate whether there is a tendency for students who do well in the science examination have high IQ. Also to establish the tendency is high for boys or girls. By plotting points on a diagram I can get some idea of trend or pattern. Even though scatter diagrams cannot give precise information, they can give a feel for the relationship and are often a first step. There are many statistical techniques which allow more specific analysis than this and at this stage these techniques are beyond my knowledge. Even then a scatter diagram is still a good start to investigation.
The scatter diagram of the boys for their IQ shows a positive correlation. The line of best fit passes through three points. The points are very narrow and separated into 3 horizontal lines. One point is completely out.
The girls’ IQ scatter diagram shows also a positive correlation and the line of best fit passes through 4 to 6 points. Two points are completely out and most of the points are
also separated horizontal lines, like in the boys scatter diagram.
From both graphs I can see that as the I Q increases as the Grade attained also increases. For the boys the IQ for the attainment of grade 5 is 117. For the girls the IQ for the attainment of grade 5 is 110. The lines of best are drawn arbitrarily without any principles. The comparison of IQ between boys and girls need further statistical analysis to reach a valid conclusion.
Bar chart and Histogram
I have drawn the bar chart for Science grade attained among boys and girls, because these are discrete data. Histogram is more appropriate in the case of IQ because these are continuous data. From both these diagrams mean, mode and median can be calculated
Frequency polygon
From the frequency polygon I can find that the more number of boys the have value of IQ (115) than girls.
Stem and Leaf Diagram
I have drawn a stem and leaf diagram because IQ data are continuous and are grouped into class interval.
Stem and leaf diagram for IQ
Boys
Girls
Cumulative frequency table
Cumulative frequency graph
Cumulative frequency graph is more appropriate for IQ value rather than science grades.
Because former are continuous data and latter are discrete data.
Science
IQ
Interquartile range shows better value of dispersion because it eliminates the extreme values there by distorting the statistical inference. The data of the boys are widely dispersed. Range is not appropriate in this instance.
I have drawn Box and Whisker diagrams for science and IQ.
Summary
The achievement of science grades are better among boys than girls because they have higher value of IQ. The conclusion is based on small samples and further analysis should be made considering larger samples. The samples should also test to show that it represents the true population by sampling techniques.