Question 1

A boxplot is shown with a range from approximately 170 to 200, with two outliers near 210 and 220. What does the presence of these outliers suggest about the data distribution?

Accepted Answer

The data contains values that are significantly higher than most of the sample, indicating possible right skew or extreme values.

Question 2

Given a histogram with most values clustered between 170 and 200, and a few values between 210 and 220, which measure of central tendency is most affected by the outliers?

Accepted Answer

Mean

Question 3

If the sample mean is calculated from the data shown in the histogram, which formula should be used?

Accepted Answer

$$\frac{\sum x_i}{n} $$

Question 4

A sample of heights is collected and visualized in a boxplot. If the interquartile range (IQR) is large, what does this indicate about the sample?

Accepted Answer

The sample has high variability between the middle 50% of values.

Question 5

Which of the following best describes the effect of outliers on the sample mean?

Accepted Answer

Outliers can significantly increase or decrease the sample mean, depending on their value.

Question 6

If a sample has a mean of 185 and a median of 180, what can you infer about the distribution?

Accepted Answer

The distribution is likely right-skewed.

Question 7

Which formula represents the calculation of the sample variance?

Accepted Answer

$$\frac{\sum (x_i - \bar{x})^2$}{n-1} $$

Question 8

A histogram shows a peak at 170 and a tail extending to 220. What type of skewness does this distribution exhibit?

Accepted Answer

Right skew (positive skew)

Question 9

If you want to compare the spread of two samples, which statistic would be most appropriate?

Accepted Answer

Sample standard deviation

Question 10

A boxplot shows the lower quartile at 170, the median at 185, and the upper quartile at 200. What is the interquartile range (IQR)?

Accepted Answer

Question 11

A sample of 10 values has a mean of 190. If one value (220) is replaced with 170, what happens to the mean?

Accepted Answer

The mean decreases.

Question 12

Which formula would you use to calculate the sample standard deviation?

Accepted Answer

$$\sqrt{\frac{\sum (x_i - \bar{x})^2$}{n-1}}$$

Question 13

If a sample has values 170, 180, 190, 200, and 210, what is the sample mean?

Accepted Answer

$$\frac{170+180+190+200+210}{5} = 190$$

Question 14

Which of the following is NOT a property of the sample mean?

Accepted Answer

It is a measure of central tendency.

Question 15

If the sample mean is 190 and the sample standard deviation is 15, what is the z-score for a value of 220?

Accepted Answer

$$\frac{220-190}{15} = 2$$

Question 16

A sample has values 170, 180, 190, 200, 210. What is the sample median?

Accepted Answer

190

Question 17

Which of the following best describes the relationship between the sample mean and sample median in a right-skewed distribution?

Accepted Answer

Sample mean \u003e sample median

Question 18

If a boxplot shows a long whisker on the right side, what does this indicate?

Accepted Answer

The data is right-skewed.

Question 19

Which statistic is most robust to outliers?

Accepted Answer

Sample median

Sample Means and Data Visualization in Statistics

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