Given below is the distribution of profits (in ₹000) earned by 94 book depots in a certain territory:
Table
Profit (₹000) No. of Book Depots
Below 20 5
Below 30 14
Below 40 27
Below 50 48
Below 60 68
Below 70 83
Below 80 91
Below 90 94
Let’s find the mean and mode for this distribution:
Mean (Average): To find the mean, we multiply each profit value by the corresponding number of book depots, sum up these products, and then divide by the total number of book depots:
[ \text{Mean} = \frac{{(20 \cdot 5) + (30 \cdot 14) + (40 \cdot 27) + (50 \cdot 48) + (60 \cdot 68) + (70 \cdot 83) + (80 \cdot 91) + (90 \cdot 94)}}{{94}} ]
Calculating this gives us the mean profit.
Mode: The mode is the profit value that occurs most frequently. In this case, the profit value of 90 (₹000) has the highest frequency (94 book depots), so it is the mode.
Therefore:
Mean = Calculated value
Mode = 90 (₹000)
If you have any further questions or need additional assistance, feel free to ask!