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Puppy Weights


Alignments to Content Standards: 6.SP.A.2 6.SP.B.4

Task

Below are the 25 birth weights, in ounces, of all the Labrador Retriever puppies born at Kingston Kennels in the last six months.

13, 14, 15, 15, 16, 16, 16, 16, 17, 17, 17, 17, 17, 17, 17, 18, 18, 18, 18, 18, 18, 18, 18, 19, 20

  1. Use an appropriate graph to summarize these birth weights.
  2. Describe the distribution of birth weights for puppies born at Kingston Kennels in the last six months. Be sure to describe shape, center and variability.
  3. What is a typical birth weight for puppies born at Kingston Kennels in the last six months? Explain why you chose this value.

IM Commentary

A dotplot, histogram or boxplot are appropriate ways to summarize these data. The description in part (b) should address the shape, center and spread in the distribution, using mean or median for center and mean absolute deviation or interquartile range for spread.

Solution

  1. Possible graphical displays are a dotplot, histogram or boxplot (see below).

    Sol_1_42fd67e5508e64d62f55a7d783f7bc0b Sol_3_192f34b6356dc5d59b3fadc804c4ef03 Sol_2_0cfcdcadf59ff4e706231a1ea2fc0a20
  2. The distribution of birth weights is centered at approximately 17 (median = 17 ounces, mean = 16.92 ounces), and the interquartile range is 2 ounces and the mean absolute deviation (MAD) is 1.149 ounces. The distribution has a longer tail for lower values (that is, it is skewed left).
  3. A typical weight is one that is about 17 ounces. A student might also choose 18 ounces, the mode of this data distribution.

roxypeck says:

almost 5 years

Although weight is actually a continuous variable, it is common to see weight reported rounded to the nearest pound or the nearest ounce, as it is here. When a data set consists of just a few different whole number values, it is not unusual to see the data summarized with a histogram that has a bar that is centered at each of the possible values, as is shown in this solution. I do agree that for a data set of this size, students would be most likely to just construct a dotplot like the one shown--I think the author of the task was just trying to include other possilbe correct answers to illustrate that there are several correct ways to complete the task.

St. Christopher School says:

almost 5 years

I would prefer that the histogram show ranges of weights on the horizontal axis, as that is the way histograms are always depicted in the examples I've seen. I wouldn't expect a student to choose a histogram to display the data if the weights are kept as individual values.