Worked solution
Use a frequency list for daily car sales
The table records the number of cars sold per day over 50 days.
| Cars sold | 1 | 2 | 3 | 4 | 5 | 6 |
|---|---|---|---|---|---|---|
| Days | 18 | 8 | 8 | 5 | 7 | 4 |
Find unbiased estimates of the mean and variance of the number of cars sold.
CJC · Lecture · Example 3
Method 1: frequency-weighted totals
, and . Thus cars and in squared car-count units.
Method 2: calculator with two lists
Choose STAT → 1:Edit and enter the six car counts in L1, their frequencies in L2. Choose STAT → CALC → 1:1-Var Stats, set List L1 and FreqList L2 using 2nd 2, then Calculate and ENTER. The output is , , , , , , minimum 1 and first quartile 1. Squaring stored gives 2.971836735, hence 2.97. The teacher’s point is that L2 supplies counts: there are 50 observations, not six.
Common mistakes
Leaving FreqList empty treats 1,2,3,4,5,6 as equally frequent. As in Example 2, Sx² estimates variance without bias; Sx itself is not generally an unbiased SD estimate.
Solution notes
Teacher page 12 explicitly highlights the need for L2. Both source methods and every table entry retained. No marks printed.