Project II Data Analysis and Inference: Median, Mode and Mean - Essay Example

The sample chosen by random sampling method is a representative of the population, so the sample results can be used to interpret the population results, such as on a level of significance it can be seen that the sample mean is an unbiased estimator of population mean. Moreover, the results drawn are free of any biasness. Different statistical measures including mean, median, mode, standard deviation, variance, range, quartiles etc., are calculated using the given sample data, and details are included in the given text.

Median, Mode and Mean The central tendency measures help in selecting a single unit out of a sample as a representative of sample. The most commonly used measures include mean, median and mode. These measures calculated for the given data are as follows. Table 1: Mean, Mode and Median Measures of central tendency Mean 7.295 Median 7.3 Mode 7.5 These measures show that the middle value, calculated as median is 7.5cm, The most recurring value in the sample as shown by mode is 7.5cm and the average as calculated by mean is 7.295 cm i.e.

, around 7.3cm. Since the mean value and the median are approximately same, hence, both of them can be regarded as the best representative of the given sample. Dispersion Measures: The significance of the mean value to be the representative of the given sample can be assessed by using the dispersion measures. The range being the simplest measure of variation explains how distant the lowest value and the highest value in a data set are located. Variance and standard deviation, on the other hand, show how much each data point varies from the mean value calculated.

For the given data set these are as follows. Table 2: Standard Deviation, Range and Variance Measures of variation Standard Deviation 0.451749 Variance 0.204077 Range 1.8 The standard deviation shows that each unit in the given sample varies by 0.45 from the mean value. The sample variance is 0.20 while the data range is 1.8 showing that the highest and the lowest value in the given sample differ by 1.8. However, the small value of standard deviation shows that the majority of the values lie near the mean value.

The Box and Whisker Plot and The Five Number Summary The box and whisker plot is a tentative graphic is employed to explain the sample distribution at a glance. Before drawing a box plot, a five number summary that includes the following is prepared. Table 3: Five number summary Five statistical summary   First Quartile 7 Second Quartile 7.3 Third Quartile 7.5 Interquartile Range 0.5 Lower Limit 6.25 Upper Limit 8.25 BOX PLOT Q1 Q2 Q3 5 5.5 6 6.5 7 7.5 8 8.5 Q1 represents the first quartile, 7 in this case, showing that a quarter of the whole data set lies above this value.

Q2 represents the median which divides the whole data set into two halves, so that half of the values lie above the median value and half lie below this value. Q3 represents the third quartile, 7.5 in this case, shows that 75% of the values lie above it while remaining 25% lie below the third quartile. The horizontal bars show the upper and lower limit, in this case, it is 8.25 and 6.25 respectively. Outliers are the values within the data set that do not lie in between the lower and the upper limits; in this case only one value 8.

3 is the outlier, represented in the box plot as a circle. Moreover, the distribution of the given data set is left skewed as shown in the box plot and the middle values of the data set fall within