Question

jen works at a library. one afternoon, she counted the number of books on each shelf. books per shelf based on the histogram, which number could be the median number of books on a shelf? 17 24 31 43 58

Explanation:

Step1: Calculate total number of shelves

The number of shelves in each interval: 0 - 9 has 0, 10 - 19 has 5, 20 - 29 has 3, 30 - 39 has 5, 40 - 49 has 3, 50 - 59 has 6. Total number of shelves $n=0 + 5+3 + 5+3+6=22$.

Step2: Determine position of median

Since $n = 22$ (an even - numbered data set), the median is the average of the values at positions $\frac{n}{2}=11$ and $\frac{n}{2}+1 = 12$ when the data is ordered.

Step3: Find the cumulative frequencies

Cumulative frequencies: For 10 - 19: 5; For 20 - 29: $5 + 3=8$; For 30 - 39: $8 + 5 = 13$. The 11th and 12th values fall within the 30 - 39 interval.

Answer:

31