Statistics Question
Cereal (a) What shape does the histogram have? Bimodal double peak disruption. (b) Which measure of center would be more appropriate for this distribution: the mean or the median? The mean. (c) Based on the shape of the histogram, which value is larger: the mean or the median? Which shelf seems to contain the most sugary cereals? Why? The “why” should have something to do with the “box” parts of the boxplot – the median and quartiles. You can do something like compare the medians to each other, but a better argument would involve comparing the median of one of the shelves to the third quartiles of the other two shelves, along with comparing the first quartile of one shelf to the medians of the other two shelves. Once you have the boxplots, the appropriate comparisons should be apparent. (Note: The “better argument” is necessary for full credit.) Statistics Variable cups N N* Mean SE Mean calories 0.25 1 0 110.00 * 0.33 3 0 86.7 16.7 0.50 7 0 98.57 9.37 StDev Minimum Q1 Median Q3 Maximum * 110.00 * 110.00 * 110.00 28.9 70.0 70.0 70.0 120.0 120.0 24.78 50.00 90.00 100.00 110.00 130.00 0.67 12 0.75 16 0.80 1 0.88 2 1.00 28 1.13 1 1.25 1 1.33 1 1.50 1 0 111.67 6.49 22.50 0 113.75 2.56 10.25 0 100.00 * * 0 100.00 0.000000 0.000000 0 106.07 4.19 22.17 0 110.00 * * 0 110.00 * * 0 110.00 * * 0 110.00 * * 90.00 90.00 100.00 110.00 100.00 * 100.00 * 50.00 100.00 110.00 * 110.00 * 110.00 * 110.00 * 110.00 120.00 110.00 120.00 100.00 * 100.00 * 110.00 110.00 110.00 * 110.00 * 110.00 * 110.00 * 160.00 140.00 100.00 100.00 150.00 110.00 110.00 110.00 110.00 (a) If you compare the three most common serving sizes – 0.67 cup, 0.75 cup, and 1 cup – which one has the highest mean calorie count? (b) To find the mean calorie count per cup for the three serving sizes, multiply the mean for 0.67 cup by 3/2, and multiply the mean for 0.75 cup by 4/3. Which serving size has the highest mean calorie count per cup? Include (and label) the multiplied values in your document, along with the answer to the question Fast Food (a) Which type of food generally appears to contain the most sodium? (b) Which type of food generally appears to contain the least sodium? (c) Which type of food has the most spread in its distribution of sodium? (d) Which type of food has the least spread in its distribution of sodium? (a) Which type of food appears to have the most spread in its distribution of total fat? (b) Which type of food appears to have the least spread in its distribution of total fat? (c) There is an outlier among the chicken nuggets. What restaurant does the outlier come from? (You will probably need to scroll through the data set, but the outlier is not too hard to find.)
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