Question
The table below shows the frequency distribution of the weights (in grams) of pre-1964 quarters. Weight (g) & Frequency 6.000-6.049 & 1 6.050-6.099 & 4 6.100-6.149 & 8 6.150-6.199 & 10 6.200-6.249 & 12 6.250-6.299 & 4 6.300-6.349 & 3 6.350-6.399 & 1 Use the frequency distribution to construct a histogram. Does the histogram appear to depict data that have a normal distribution? Why or why not?
Solution
4.1
(363 Votos)
Manoel
Veterano · Tutor por 11 anos
Resposta
### The histogram does not depict a perfect normal distribution because it lacks symmetry and has a sharp drop-off after the peak.
Explicação
## Step 1: Understanding the Frequency Distribution### The table provides a frequency distribution of weights for pre-1964 quarters. Each weight range has an associated frequency, indicating how many quarters fall within that range.## Step 2: Constructing the Histogram### To construct a histogram, plot the weight ranges on the x-axis and the corresponding frequencies on the y-axis. Each bar represents a weight range, with the height of the bar corresponding to the frequency of that range.## Step 3: Analyzing the Shape of the Histogram### A normal distribution typically appears as a symmetric bell-shaped curve. In this case, observe the frequencies: they increase from the first interval to the fifth, then decrease. This suggests a peak around the middle intervals (6.150 - 6.249), which is characteristic of a normal distribution.## Step 4: Determining Normality### Although the histogram shows a peak in the middle, it is not perfectly symmetrical. The frequencies do not decrease symmetrically after the peak; instead, there is a sharp drop. This asymmetry indicates that while the data may have some characteristics of a normal distribution, it does not perfectly fit the criteria for a normal distribution.