Mathematics
Mathematics
Problem
A factory records the daily output of widgets in the following frequency distribution. The mean daily output is 45 widgets.| Daily output (widgets) | 10–20 | 20–30 | 30–40 | 40–50 | 50–60 | 60–70 | 70–80 |
|---|---|---|---|---|---|---|---|
| Number of days | 4 | 7 | 12 | 15 | 8 | k | 4 |
Intuitive explanation
This problem combines two key skills: using the mean to find a missing frequency, then locating the middle value in a grouped distribution. Start by setting up the mean formula with class midpoints—the mean equals the sum of (midpoint × frequency) divided by total frequency. Once you've solved for , you'll use cumulative frequencies to pinpoint which class contains the median, then interpolate within that class to find the exact value.
Intuitive explanation
This problem combines two key skills: using the mean to find a missing frequency, then locating the middle value in a grouped distribution. Start by setting up the mean formula with class midpoints—the mean equals the sum of (midpoint × frequency) divided by total frequency. Once you've solved for , you'll use cumulative frequencies to pinpoint which class contains the median, then interpolate within that class to find the exact value.