Question

a brand of frozen green beans lists a weight of 32 ounces on its bag. because of variability in the manufacturing process, the bags often contain slightly more, or less, than 32 ounces of green beans. an inspector takes a random sample of 25 bags of green beans and records their weights. the weights and their relative frequencies are summarized in the histogram. which interval contains the median bag weight? 31.9 - 32.0 ounces 32.1 - 32.2 ounces 32.2 - 32.3 ounces 32.0 - 32.1 ounces

Explanation:

Step1: Find the position of the median

Since $n = 25$ (odd - numbered sample size), the median is at the $\frac{n + 1}{2}=\frac{25+1}{2}=13$th position when the data is ordered.

Step2: Calculate cumulative frequencies

We need to find cumulative frequencies for each interval. Starting from the left - hand side of the histogram. Let's assume the frequencies corresponding to the intervals (from left to right) are $f_1,f_2,f_3,f_4,f_5$. The cumulative frequency $CF_i=\sum_{j = 1}^{i}f_j$.
We know that the sum of all frequencies is $n = 25$. By looking at the relative - frequency histogram, we can estimate the cumulative frequencies. The first few intervals have small relative frequencies. The interval $32.0 - 32.1$ ounces starts to accumulate enough data such that the 13th value will fall within it.

Answer:

$32.0 - 32.1$ ounces