use the display of data items to find the standard deviation.\nthe standard deviation is \n(do not round…

Explanation:

Step1: List data items and frequencies

Scores: 6 (frequency=4), 9 (frequency=8), 11 (frequency=4)

Step2: Calculate mean

$$\bar{x} = \frac{6 \times 4 + 9 \times 8 + 11 \times 4}{4 + 8 + 4} = \frac{24 + 72 + 44}{16} = \frac{140}{16} = 8.75$$

Step3: Calculate squared deviations from mean

For 6: $(6 - 8.75)^2 \times 4 = (-2.75)^2 \times 4 = 7.5625 \times 4 = 30.25$
For 9: $(9 - 8.75)^2 \times 8 = (0.25)^2 \times 8 = 0.0625 \times 8 = 0.5$
For 11: $(11 - 8.75)^2 \times 4 = (2.25)^2 \times 4 = 5.0625 \times 4 = 20.25$

Step4: Compute variance

$$s^2 = \frac{30.25 + 0.5 + 20.25}{16} = \frac{51}{16} = 3.1875$$

Step5: Compute standard deviation

$$s = \sqrt{3.1875} \approx 1.7857$$

Answer:

1.79