Question

Use the information given to answer the question. Vanessa and Moe record their quiz scores in music class for a semester. The dot plot shows Vanessa’s quiz scores, and the list shows Moe’s quiz scores.

Answer 1

Answer:

Vanessa records a total of 11 quiz scores

Moe records a total of 10 quiz scores

According to the data, Vanessa's mean score is 80

According to the data, Vanessa's median score is 85

The range of Moe's quiz score is 45

The interquartile range of Moe's quiz score is 16.25

Step-by-step explanation:

Vanessa's score is given in the dot plot

Moe's scores are; 75, 80, 90, 90, 95, 55, 100, 95, 85, 85

1) The number of quiz scores Vanessa records is given by the number of dots on the dot plot, n = 11 dots ≡ 11 quiz scores

2) The number of quiz scores Moe records is given by the number of data points, n = 10 data points ≡ 10 quiz scores

3) Vanessa's mean score = ∑x$_i$/n

∑x$_i$/n = (60 + 2× 65 + 75 + 4 × 85 + 2 × 90 +95)/11 = 80

Vanessa's mean score = 80

4) Vanessa's median score is the (11 + 1)/2 th score = Her 6th score = 85

Vanessa's median score = 85

5) The range of Moe's score = Her largest score - Her least score = 100 - 55 = 45

The range of Moe's score = 45

6) Sorting Moe's scores gives;

75, 80, 90, 90, 95, 55, 100, 95, 85, 85

55, 75, 80, 85, 85, 90, 90, 95, 95, 100

The first quartile, Q₁ = 11/4th score = 2.75th score = 75 + 0.75 × 5 = 78.75

The 3rd quartile, Q₃ = The 3/4×11 score = 8.25th score = 95 + 0.25 ×0 = 95

The interquartile range, I = Q₃ - Q₁ = 95 - 78.75 = 16.25

The interquartile range of Moe's quiz score = 16.25.