Descriptive Statistics of ALDI According to States - Assignment Example

Executive Summary For any business organisation, it is very necessary to be updated about the latest market trends and competitor position. Decisions then shall be taken upon the basis of the statistical analysis that emerges from the data. For this purpose, ALDI collected the data for 4 supermarkets, and analyzed. The various analysis that were done were the analysis of descriptive statistics according to the various supermarkets, the statistics according to the state and statistics according to the location. Descriptive Statistics for various supermarkets The various descriptive statistics for the different supermarkets is as shown in table 1. Supermarkets Supermarket 1 Supermarket 2 Supermarket 3 Supermarket 4 No. Of Cases 30 30 30 30 Maximum Price 91.65 88.15 91.95 62.65 Minimum Price 77.77 77.00 77.66 59.61 Average Price 83.30 82.11 84.47 60.43 Median Price 82.37 81.52 84.50 60.25 S.D. of Price 3.731027038 2.315454351 3.391110573 0.615465808 Kurtosis of Price -0.098788851 1.188374162 -0.169290128 4.372788571 Skewness of Price 0.826175082 0.404893195 0.292120114 1.510641078 First Quartile 80.95 81.18 82.34 60.05 Third Quartile 83.875 83.455 86.3875 60.845 Range 13.88 11.15 14.29 3.04 Table1. Descriptive Statistics according to the various supermarkets Analysis As can be seen from the table, all the types of supermarkets have 30 stores in total. The maximum price is highest at Independent supermarkets. It can be seen that prices at ADLI are significantly lower as compared to other stores. If we compare the mean prices at the various stores, we see that all stores except ADLI have average prices higher than 82, whereas ADLI stores have an average price of just 60.43. It shall be noted that mean prices are affected by presence of extreme values. The median explains the middle value of the distribution. The median price for supermarket 1 is 82.37, which implies that half of the stores have prices above 82.37 and half have prices below 82.37. The standard deviation of price is the lowest in supermarket 4. The reason for this may be low mean, and a consistent pricing policy amongst all stores. Another parameter that may be useful in analyzing the variance is the Kurtosis defines the peakedness of a distribution (Levin & Rubin, 2007, pp. 70-71). A higher kurtosis indicates that more variance in the distribution is because of uncommon extreme deviations, rather than common small deviations. We can see that the distribution of supermarket 4 (ADLI) has higher kurtosis value. This implies that majority of the standard deviation in the distribution is because of the presence of an extreme value. To confirm this, we can draw the histogram of the frequency of price for supermarket 4. This diagram is shown in Figure 1. We can see that there is an extreme value lying between 62 and 63, which might be the cause of majority of the standard deviation. Supermarket 3 is having the lowest kurtosis implying that most of the variation in independent price distribution can be explained by small deviations from the means. The next descriptive statistic that can be observed is the kurtosis and skewness of the price distribution. Skewness is an assessment of the asymmetry of the distribution of the given construct. A negatively skewed distribution implies that that the variable is skewed towards left, and the number of observations that are higher is greater than the number of lower observations. If we see the skewness values for all the 4 supermarket categories, it can be implied that all are skewed towards the right. This implies that they have more number of smaller values than higher values. This can again be confirmed by having a look at the frequency histogram of the price. For example, let us take the histogram for supermarket 1. The graph for the same is in Figure 2. It can be clearly seen that the distribution of the variable price is skewed towards right, and the tail is longer at the higher end of the distribution. Comments It can be seen that Supermarket 4 has the lowest average prices across all the supermarkets. The Standard Deviation of the prices of supermarket 2 and supermarket 4 is majorly because of presence of presence of extreme values. The distribution of prices across all supermarkets is positively skewed towards right implying that there are more number of lower values than the number of higher values. Descriptive statistics for the prices across 3 States Table 2 contains the value of descriptive statistics across all the states. State State 1 State 2 State 3 No. Of Cases 40 40 40 Maximum Price 86.51 91.95 90.41 Minimum Price 59.69 59.61 60.75 Average Price 77.01 77.64 78.08 Median Price 81.82 81.23 81.42 S.D. of Price 9.928598566 10.84615243 10.4869891 Kurtosis of Price -0.703283684 -0.75813818 -0.803124229 Skewness of Price -1.073358649 -0.863855952 -0.866144751 First Quartile 73 73.715 73.9075 Third Quartile 83.475 84.5425 84.4925 Range 26.82 32.34 29.66 Table2. Descriptive Statistics across all the States Analysis As can be seen from the table, each state has 40 stores that have been included in the sample. The highest maximum price is found in State 2, with a maximum price of 91.95. State 3 on the other hand is having the maximum average price of 78.08. State 1 is having relatively lesser priced supermarkets. All the states have approximately same median price, implying that the middle point of distribution of the price is approximately same for all the states. The Standard deviation is lowest for State 1 implying it to be least variant price state. All the States have a negative skewness. This implies that they are skewed towards left, with longer tail towards the lower side of the distribution. Figure 3 contains the frequency histogram of price for state 1. The normal curve estimation line confirms the negative skewness of the distribution. The first quartile value represents the value below which 25% of the data point will lie. The third quartile represents the value below which 75% of the data points will lie. The first quartile value is minimum for state 1 implying that it is having the least number of lower prices. This fact is also confirmed by the highest negative skewness amongst all three states and lower average value. The Range is a measure of dispersion and is used to calculate the distance between the extreme points of the distribution. State 2 is having the maximum range which means that the difference between the maximum and minimum value is highest for state 3 supermarkets. Another level of analysis that can be done for the situation is the state-wise descriptive statistics for various supermarkets. Figure 4 contains the graphical model of the average prices of the staple food basket across various states and supermarkets. It can be seen from the graph, that supermarket 1 is having the highest average price in State 3. On the same lines, independent supermarkets have their highest average prices in State 2. Similarly, the highest average price in State 1 is that of independent stores. Comments It is seen that state 3 has the highest average prices amongst all states. The standard deviation and the range for state 1 is minimum implying that the supermarket prices have minimum variation in state 1. A look at the skewness and the frequency histogram showed the negative skewness of price in all the three states. Then, analysis of various statistics of the supermarkets according to the states was done. The results showed some interesting facts such as supermarket 1 having minimum variance in state 1, and maximum average price in state 3. Descriptive Statistics At Different Location The supermarkets have been classified into two places where they might have been possibly located. Location 1 represents supermarkets stored in metropolitan area of capital city of the State, whereas location 2 represents other places. Table 3 contains the descriptive statistics for the various locations. Location Location 1 Location 2 No. Of Cases 60 60 Maximum Price 90.30 91.95 Minimum Price 59.61 59.70 Average Price 77.62 77.54 Median Price 81.68 81.20 S.D. of Price 10.31992954 10.46453572 Kurtosis of Price -0.766855415 -0.754867119 Skewness of Price -0.946253813 -0.866412848 First Quartile 73.4125 73.4575 Third Quartile 83.915 83.9725 Range 30.69 32.25 Table 3: Descriptive Statistics According to the locations Analysis As can be seen from the table, both location 1, as well as location 2 is having 60 supermarkets each. However, Location 1 is more negatively skewed as compared to location 2. This implies that the price distribution of location 1 is more skewed towards left in comparison to location 2. Figure 5 shows the probability distribution function for the two locations. In order to get the comparison of the various supermarkets according to location, a cross tabulated result of the descriptive statistics is helpful. Figure 6 shows the graph for the average price of the basket at various stores according to the location. It can be seen from the graph that supermarket 1 and supermarket 2 is having a higher average price at location 2. On the other hand, independent stores and ALDI have higher average price on location 1. Descriptive Statistics of ALDI according to states Table 4 contains the descriptive statistics of ALDI prices across various states. State State 1 State 2 State 3 No. Of Cases 10 10 10 Maximum Price 61.00 60.20 62.65 Minimum Price 59.69 59.61 60.75 Average Price 60.36 59.94 61.01 Median Price 60.25 60.03 60.84 S.D. of Price 0.449974073 0.186678571 0.577993656 Kurtosis of Price -1.018839197 -0.683284742 9.86698928 Skewness of Price 0.388224209 -0.562633216 3.133484427 First Quartile 60.05 59.8125 60.8025 Third Quartile 60.7375 60.05 60.85 Range 1.31 0.59 1.90 Table 4: Descriptive Statistics of ALDI according to states As can be seen from the table, ALDI stores have the highest average prices in state 3. State 3 is also has the highest standard deviation and range. This implies the maximum variability in the price of ALDI stores in state 3. If we see the kurtosis value of state 3, it is a high 9.87. This means that majority of the standard deviations is primarily because of the presence of some uncommon extreme values. A look at the frequency histogram of the price in state 3 will confirm that. Figure 7 contains the graph. The distribution has all its values except one in the price range of 60.50-61.00. This also explains the high positive skewness of the distribution. In fact, if we see the kurtosis of the other states, they are also relatively high in the negative direction as compared to the kurtosis for the states with other supermarkets. One of the possible reasons for this is the significantly lower prices of ADLI store baskets as compared to other stores. Conclusion Based on the statistical analysis, the key findings that can be drawn are: 1. ADLI is having the least average price of baskets in the supermarket industry. The company shall evaluate if its’ low-cost strategy is working. Further data about the company’s sales shall be needed for this analysis. 2. The kurtosis value for ADLI is maximum in the industry, which implies that majority of the variance in the distribution, is explainable by uncommon extreme values. 3. The price distribution of ADLI is highly positively skewed towards right because of the presence of low prices in the distribution. 4. Amongst all supermarkets, ADLI is having the minimum variance in its data distribution. 5. State 3 is the most expensive state. 6. All the three states are negatively skewed indicating more higher data points as compared to lower data points. 7. Average price does not vary with the location. However, the supermarkets in location 1 are more negatively skewed as compared to those in location 2. Reference List Levin, R.I. & Rubin, D.S. 2007. Statistics For Management, 7th ed. New Delhi: Pearson Education Inc. Read More