Question

the following data represent the weights (in grams) of a simple random sample of a candy. 0.92 0.89 0.89 0.92 0.92 0.87 0.92 0.86 0.80 0.90 determine the shape of the distribution of weights of the candies by drawing a frequency histogram and computing the mean and the median. which measure of central tendency best describes the weight of the candy? choose the correct frequency histogram below.

Explanation:

Step1: Sort data

Sorted weights: 0.80, 0.86, 0.87, 0.89, 0.89, 0.90, 0.92, 0.92, 0.92, 0.92

Step2: Determine classes

Classes: [0.79,0.85), [0.85,0.91), [0.91,∞)

Step3: Count frequencies

Class1:1 (0.80), Class2:5 (0.86,0.87,0.89,0.89,0.90), Class3:4 (0.92×4)

Step4: Calculate mean

Mean = (0.80+0.86+0.87+0.89+0.89+0.90+0.92×4)/10 = 8.89/10 = 0.889

Step5: Calculate median

Median = (5th + 6th)/2 = (0.89 + 0.90)/2 = 0.895

Step6: Analyze shape

Mean ≈ median, distribution symmetric.

Answer:

The correct frequency histogram is the one with frequencies 1, 5, 4 for classes [0.79,0.85), [0.85,0.91), [0.91,∞). The mean is the best measure of central tendency.