Descriptive statistics and histograms

Econometrics
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8 May 2019

i. Descriptive statistics and histograms
Answer
Descriptive statistics
Table 1 below presents the descriptive statistics for the variables in the study. As can be seen, the
average sales for the companies was found to be 1700.2 with median sales being 1068.2 and a
standard deviation of 1632.2. The minimum and the maximum sales values were 50.8 and 7935.4
respectively. All these information shows that there is wide spread out in the sales values. The
skewness value for sales data is 1.6763 which clearly points that the distribution of sales data is
heavily skewed to the right (positively skewed).
Table 1: Summary Statistics, using the observations 1 - 80
Variable Mean Median S.D. Min Max Skewness
sales 1700.2 1068.2 1632.2 50.8 7935.4 1.6763
pcm1 0.689 0.679 0.101 0.492 0.889 0.13693
pcm2 0.304 0.304 0.0933 0.137 0.594 0.57360
grow 0.0692 0.0577 0.0804 -0.105 0.369 1.0164
adint 0.0597 0.0538 0.0274 0.0233 0.141 1.0642
conc 0.450 0.395 0.237 0.0900 0.980 0.48092
The average for the price cost margin 1 (pcm1) and 2 (pcm2) was found to be 0.689 and 0.304
respectively. The skewness values for these two variables showed that pcm1 is close to normal
distribution while pcm2 is slightly positively skewed. Rate of growth of industry sales (growth)
and advertising intensity (adint) were also found to be positively skewed as per the skewness
values obtained from the summary statistics. 5-firm concentration ratio (conc) was slightly
positively skewed.

Histograms
In this section, we present the histograms for the variables in the study.
Figure 2: Histogram for pcm1
Figure 1 shows the histogram for the industry sales where we can observe that the distribution of
sales is clearly skewed to the right (longer tail to the right). This confirms the conclusions made
earlier based on the skewness value. Figure 2 presents the histogram for the price cost margin 1
(pcm1) which clearly show that the distribution follows a normal distribution as the shape of the
histogram is close to bell-shaped curve.
Figure 4: Histogram for grow
Figure 1: Histogram for sales
Figure 3: Histogram for pcm2