Histogram showing the distribution of dates on 100 collected pennies. The x-axis re...
Check the final answer first, then review the worked steps.
Problem
Histogram showing the distribution of dates on 100 collected pennies. The x-axis represents the date on the penny, and the y-axis represents the number of pennies. The intervals are 1960-1970, 1970-1980, 1980-1990, 1990-2000, 2000-2010, and 2010-2020. The number of pennies in each interval are approximately 2, 4, 8, 26, and 53. The question asks to identify the interval containing the median date.
Answer
\(2000-2010\)
Step-by-step solution
- Understand the Median: The median is the middle value in a dataset. For 100 data points, the median will be the average of the 50th and 51st values when ordered. Since we are dealing with intervals, we need to find the interval where the cumulative count reaches or exceeds 50.
2. Read the Histogram Data: From the histogram, we can estimate the number of pennies in each interval:
- 1960-1970: Approximately 2 pennies
- 1970-1980: Approximately 4 pennies
- 1980-1990: Approximately 8 pennies
- 1990-2000: Approximately 26 pennies
- 2000-2010: Approximately 53 pennies
- 2010-2020: The bar is not fully visible, but the total is 100 pennies. Let's check the cumulative count.
3. Calculate Cumulative Frequencies: We sum the number of pennies from the beginning of the dataset to find out which interval contains the 50th and 51st penny.
- Up to 1970: 2 pennies
- Up to 1980: $2 + 4 = 6$ pennies
- Up to 1990: $6 + 8 = 14$ pennies
- Up to 2000: $14 + 26 = 40$ pennies
- Up to 2010: $40 + 53 = 93$ pennies
- Identify the Median Interval: The 50th and 51st pennies fall within the interval where the cumulative count surpasses 50. As calculated, the cumulative count reaches 40 by the end of the 1990-2000 interval. The next interval, 2000-2010, adds 53 pennies. Therefore, the 50th and 51st pennies are within the 2000-2010 interval.
- Determine the Final Answer: The interval that contains the median date is 2000-2010.