Question

mr. smith, a history teacher, gave a 10-question quiz. he recorded the number of questions each student answered correctly.

history quiz scores

dot plot image

0 1 2 3 4 5 6 7 8 9 10
number of correct answers

select all the statements that describe the distribution of the data.

the distribution is symmetric.

the data has a peak at 10 correct answers.

the data is spread out from 6 to 10 correct answers.

Explanation:

To determine the correct statements, we analyze the dot plot:

1. "The distribution is symmetric."

A symmetric distribution has a mirror - like shape around a central point. Looking at the dot plot, the number of dots on either side of the center (around 8) appears balanced. So this statement is correct.

2. "The data has a peak at 10 correct answers."

The peak of a distribution is the value with the most data points (dots). Here, the number of dots at 8 is the highest (let's count: at 6: 2 dots, 7: 3 dots, 8: 4 dots, 9: 3 dots, 10: 2 dots? Wait, no, re - examining the plot: the top dot is at 8? Wait, the original plot: the first row (top) has 1 dot (at 8), then 3 dots (7,8,9), then 3 dots (6,7,8), then 5 dots (6,7,8,9,10), then 5 dots (6,7,8,9,10)? Wait, no, maybe my initial count was wrong. Wait, the x - axis is 0 - 10, and the dots are: at 6: 2 (from the fourth and fifth rows), at 7: 3 (second, third, fourth, fifth? No, let's look at the layers. The top layer (first) has 1 dot (at 8), second layer: 3 dots (7,8,9), third layer: 3 dots (6,7,8), fourth layer: 5 dots (6,7,8,9,10), fifth layer: 5 dots (6,7,8,9,10)? No, maybe the peak is at 8? Wait, the original selected option is wrong. Wait, the user's initial selection might be incorrect. Let's re - analyze:

The peak is the value with the maximum frequency. Let's count the number of dots for each value:

• 6: Let's see the fourth and fifth rows (the lower two rows) each have a dot at 6, so 2 dots? Wait, no, the plot: the first row (top) has 1 dot (at 8), second row: 3 dots (7,8,9), third row: 3 dots (6,7,8), fourth row: 5 dots (6,7,8,9,10), fifth row: 5 dots (6,7,8,9,10)? No, maybe the rows are:

Row 1 (top): 1 dot (8)
Row 2: 3 dots (7,8,9)
Row 3: 3 dots (6,7,8)
Row 4: 5 dots (6,7,8,9,10)
Row 5: 5 dots (6,7,8,9,10)

Wait, no, the number of dots at each x - value:

• x = 6: number of dots from row 3,4,5: 1 (row3) + 1 (row4) + 1 (row5) = 3? Wait, maybe I'm misinterpreting the plot. Alternatively, the peak is at 8? Because the middle of the symmetric distribution is at 8. So the statement "The data has a peak at 10 correct answers" is wrong, because 10 does not have the most dots.

3. "The data is spread out from 6 to 10 correct answers."

Looking at the dot plot, all the dots are between 6 and 10 on the x - axis (there are no dots for 0 - 5). So the data is spread from 6 to 10. This statement is correct.

So the correct statements are:

• The distribution is symmetric.
• The data is spread out from 6 to 10 correct answers.

The statement "The data has a peak at 10 correct answers" is incorrect.

Answer:

To determine the correct statements, we analyze the dot plot:

1. "The distribution is symmetric."

A symmetric distribution has a mirror - like shape around a central point. Looking at the dot plot, the number of dots on either side of the center (around 8) appears balanced. So this statement is correct.

2. "The data has a peak at 10 correct answers."

The peak of a distribution is the value with the most data points (dots). Here, the number of dots at 8 is the highest (let's count: at 6: 2 dots, 7: 3 dots, 8: 4 dots, 9: 3 dots, 10: 2 dots? Wait, no, re - examining the plot: the top dot is at 8? Wait, the original plot: the first row (top) has 1 dot (at 8), then 3 dots (7,8,9), then 3 dots (6,7,8), then 5 dots (6,7,8,9,10), then 5 dots (6,7,8,9,10)? Wait, no, maybe my initial count was wrong. Wait, the x - axis is 0 - 10, and the dots are: at 6: 2 (from the fourth and fifth rows), at 7: 3 (second, third, fourth, fifth? No, let's look at the layers. The top layer (first) has 1 dot (at 8), second layer: 3 dots (7,8,9), third layer: 3 dots (6,7,8), fourth layer: 5 dots (6,7,8,9,10), fifth layer: 5 dots (6,7,8,9,10)? No, maybe the peak is at 8? Wait, the original selected option is wrong. Wait, the user's initial selection might be incorrect. Let's re - analyze:

The peak is the value with the maximum frequency. Let's count the number of dots for each value:

• 6: Let's see the fourth and fifth rows (the lower two rows) each have a dot at 6, so 2 dots? Wait, no, the plot: the first row (top) has 1 dot (at 8), second row: 3 dots (7,8,9), third row: 3 dots (6,7,8), fourth row: 5 dots (6,7,8,9,10), fifth row: 5 dots (6,7,8,9,10)? No, maybe the rows are:

Row 1 (top): 1 dot (8)
Row 2: 3 dots (7,8,9)
Row 3: 3 dots (6,7,8)
Row 4: 5 dots (6,7,8,9,10)
Row 5: 5 dots (6,7,8,9,10)

Wait, no, the number of dots at each x - value:

• x = 6: number of dots from row 3,4,5: 1 (row3) + 1 (row4) + 1 (row5) = 3? Wait, maybe I'm misinterpreting the plot. Alternatively, the peak is at 8? Because the middle of the symmetric distribution is at 8. So the statement "The data has a peak at 10 correct answers" is wrong, because 10 does not have the most dots.

3. "The data is spread out from 6 to 10 correct answers."

Looking at the dot plot, all the dots are between 6 and 10 on the x - axis (there are no dots for 0 - 5). So the data is spread from 6 to 10. This statement is correct.

So the correct statements are:

• The distribution is symmetric.
• The data is spread out from 6 to 10 correct answers.

The statement "The data has a peak at 10 correct answers" is incorrect.