Question

find the mean, the median, and all modes for the data in the list. if an answer does not exist, enter dne.)
mean
median
mode(s)
points scored by lynn
points scored in a basketball game frequency
2 8
6 7
11 8
14 6
18 3
20 4
22 3

Explanation:

Step1: Calculate total points

$\text{Total points} = (2 \times 8) + (6 \times 7) + (11 \times 8) + (14 \times 6) + (18 \times 3) + (20 \times 4) + (22 \times 3)$
$= 16 + 42 + 88 + 84 + 54 + 80 + 66 = 430$

Step2: Calculate total number of games

$\text{Total games} = 8 + 7 + 8 + 6 + 3 + 4 + 3 = 39$

Step3: Compute the mean

$\text{Mean} = \frac{\text{Total points}}{\text{Total games}} = \frac{430}{39} \approx 11.03$

Step4: Find median position

Median is the $\frac{39+1}{2} = 20^\text{th}$ value when data is ordered.

Step5: Cumulate frequencies to find median

• Cumulative freq for 2: 8
• Cumulative freq for 6: $8+7=15$
• Cumulative freq for 11: $15+8=23$

The 20th value falls in the 11 points group, so median = 11.

Step6: Identify mode(s)

Mode is the value(s) with highest frequency. Points 2 and 11 both have the highest frequency (8).

Answer:

mean: $\frac{430}{39} \approx 11.03$
median: 11
mode(s): 2, 11