there's a line chart going from 5 to 10, above five there's 2 dots, above six and seven there's 0 dots, above eight there's 3 dots, above nine there is 0 dots above 10 there's 5 dots

Question

Hortencia made the dot plot to help her plan for her quinceañera. Find the mean and median number of seats per table to show that the mean and median are different in this skewed dataset. Round your answer to the nearest whole number, if necessary.

(1 point)
The mean number of seats is (_____)
, and the median number of seats is (____)

Answer 1

To find the mean and median from the dot plot data provided, we first need to list out all the data points represented by the dots:

• Above 5: 2 dots (2 tables with 5 seats each) → 5, 5
• Above 6: 0 dots (0 tables with 6 seats)
• Above 7: 0 dots (0 tables with 7 seats)
• Above 8: 3 dots (3 tables with 8 seats each) → 8, 8, 8
• Above 9: 0 dots (0 tables with 9 seats)
• Above 10: 5 dots (5 tables with 10 seats each) → 10, 10, 10, 10, 10

Now we can list the data points:

• Data points: 5, 5, 8, 8, 8, 10, 10, 10, 10, 10

Mean Calculation:

1. Sum of all data points:

   • \(5 + 5 + 8 + 8 + 8 + 10 + 10 + 10 + 10 + 10 = 5 \times 2 + 8 \times 3 + 10 \times 5\)
   • \(= 10 + 24 + 50 = 84\)

2. Number of data points:

   • There are 10 total data points.

3. Mean: \[ \text{Mean} = \frac{\text{Total Sum}}{\text{Number of Data Points}} = \frac{84}{10} = 8.4 \] Rounded to the nearest whole number: 8

Median Calculation:

1. To find the median, first, we need to arrange the numbers in ascending order:

   • Data points in order: 5, 5, 8, 8, 8, 10, 10, 10, 10, 10

2. The median of an even number of data points is the average of the two middle numbers.

   • The two middle numbers for 10 data points (5th and 6th values) are both 8 and 10. \[ \text{Median} = \frac{8 + 10}{2} = \frac{18}{2} = 9 \]

After calculating these, we find:

• The mean number of seats is (8)
• The median number of seats is (9)

Thus, the answers are: The mean number of seats is 8, and the median number of seats is 9.