Question

Below are histograms andnormalfor eachofthe variables Calories and Carbohydrates. Discuss distributions. Focus on the comparison between the two variables, in particular on the skewedness and the closeness to the Normal curve. Include some numerical summaries as well in your discussion. calories mean-154.81, median-150,Q1-55, q3-330.. carbs mean 12.0330, median 12.0050,q1-1.90,q3-32.10 Histogram 30 Mean 1203 sad Dev.-4.946 N- 158 20 10 1000 30 00 Carbohydrates Histogram #0 Norma Histogram Mean-154M d Dew-4403 N-153 30 20 16 50 150 劄 200 Calories

Answer 1

From the above two histograms, it can be seen that the variables calories and carbohydrates tend to follow a normal distribution as frequencies tend to decrease around a central value (mean). Let's compare both the variables on how skewed the distributions are:

For calories, as the mean=154.81> Median=150, it is a positively skewed distribution. The case is same for carbohydrates as mean=12.0330>Median=12.0050. The skewedness seems to be less in carbohydrates as the (Mean-Median)/SD ratio is very small in this case as compared to in the case of calories.

Hence, if we look at the curves and the skewedness, we can say that the carbohydrates follow a normal distribution more closely than calories.