ICT Mathematics Project - Essay Example

Averages The mean, median and mode are the measures to determine the central tendency of test data. As the data sets are not grouped the mean is achieved through summing all values (x) of the test data and dividing by the total number of values (n) i.e. 500. Similarly the median for ungrouped data is estimated by finding the middle value of the test data when arranged in ascending order. Mode for ungrouped data is found by spotting out the most occurring value of the data set. In this case, mode for house is 146, while that for car is 0.

Table 1 Mean, Median and Mode of Raw Datasets House Car Mean 354.174 276481.878 Median 359 217174 Mode 146 0 Using mode we can know which value mostly contributes in the mean value estimated. Standard Deviation and Variation Mean, median and mode give limited information about the data. E.g. two data sets having the same mean may be broadly apart in their value from one another. So, the measures of Standard Deviation (s) and Variation (v) were used to estimate how far each value of the dataset is from the mean of the dataset.

The high standard deviation and variance values of the car data indicates the wide spread of data from the mean. The relatively smaller standard deviation and variance value of the house indicates that the data lies relatively close on either sides of the mean as compared to the car. As the data sets are ungrouped, the formula used for estimating standard deviation was: Squaring the value of standard deviation gives us the Variation. Table 2 Variance and Standard Deviation of Raw Datasets House (in 10,000rmb) Car Variance 39872.

45172 69623323280 Standard Deviation 199.6808747 263862.3188 Standard Deviation and Variance is used to understand what a normal value is for a data set. For example, using the mean value of House from Table 1 (i.e. 354) and considering the above table, the value of 199 indicates that all data values that generate SD value as 199 are normal values. Any value outside this range is considered as an outlier i.e. House value is either too low or too high. Range and IQR The mean, median, mode, standard deviation and variance are not able to indicate the spread of the data.

So, Range and IQR are two measures of spread. Through range of house and car, we would know the difference of the lowest and highest values. In case we wish to know the median of the middle 50% of data, we would use the Interquartile Range. This specialized version of range would tell us the difference of the middle values of the first and third halves (25th and 75th percentile) of the data that is arranged in ascending order. Table 3 gives the range and IQR of the datasets. Table 3 Range and IQR of Raw Datasets   House Car Range 689 998897 Q1 180 72017.

5 Q3 515 339674.75 IQR 335 267657.25 The value of Range of car tells us the difference of the lowest and highest value of the entire data set. IQR, on the other hand, provides us with the range of only the middle 50% subset of the dataset. Difference of the two measures from Standard Deviation is that as SD considers all data points, so the effect of any outlier data points is accounted for as well while estimating the mean which is undesirable. With range the spread estimated is intended to include the outlier data points.

With IQR, as only the middle points of data portions are considered, the extreme or outlier data points are ignored, unlike the standard deviation. Scatter Plot of Raw