Q: A data set has $$Q_1 = 25$, Q_3$ = 45$$, and $$IQR = 20. $$What is the upper limit for detecting outliers using the IQR method?

$$Upper\ limit = Q_3$ + 1.5 \times IQR = 45 + 1.5 \times 20 = 75$$

Q: A company purchases 100 units at $$5 each and 200 units at 7 $$each. What is the weighted mean price per unit?

$$\frac{(100 \times 5) + (200 \times 7)}{100 + 200} = 6.33$$

Question 1

Which of the following statements best describes the interquartile range (IQR)?

Accepted Answer

It is the range for the middle 50% of the data, calculated as $$IQR = Q_3$ - Q_1$.

Question 2

Given the following sample data: 10, 12, 14, 16, 18. Calculate the sample variance using the formula $$s^2$$ = \frac{\sum (x_i - \bar{x}$$)^2$$}{n-1}$$.

Accepted Answer

$$s^2 = 8$

Question 3

Which of the following is a disadvantage of using the interquartile range (IQR) as a measure of variability?

Accepted Answer

It only considers the middle 50% of the data.

Question 4

A sample has a mean of 20 and a standard deviation of 4. What is the coefficient of variation (cv) for this sample?

Accepted Answer

$$cv = 20\%$$

Question 5

Which of the following best describes a distribution that is skewed to the right?

Accepted Answer

The right tail is longer and the mass of the distribution is concentrated on the left.

Question 6

If a student scores 1.5 standard deviations above the mean on a test, what is their z-score?

Accepted Answer

$$z = 1.5$$

Question 7

According to the empirical rule, approximately what percentage of data falls within two standard deviations of the mean in a bell-shaped distribution?

Accepted Answer

95\%

Question 8

A data set has $$Q_1 = 25$, Q_3$ = 45$$, and $$IQR = 20. $$What is the upper limit for detecting outliers using the IQR method?

Accepted Answer

$$Upper\ limit = Q_3$ + 1.5 	imes IQR = 45 + 1.5 	imes 20 = 75$$

Question 9

Which of the following is NOT part of the five-number summary?

Accepted Answer

The mean

Question 10

A box plot shows the median closer to the lower quartile ($$Q_1) $$and a longer whisker on the right. What does this indicate about the distribution?

Accepted Answer

The distribution is skewed to the right.

Question 11

Given the following paired data for X and Y: X = [2, 4, 6], Y = [3, 7, 11], calculate the sample covariance using $$s_{xy} = \frac{\sum (x_i - \bar{x})(y_i - \bar{y})}{n-1}.$$

Accepted Answer

$$s_{xy} = 8$$

Question 12

Which value of the correlation coefficient $$r_{xy}$$ indicates a perfect negative linear relationship?

Accepted Answer

$$r_{xy} = -1$$

Question 13

A company purchases 100 units at $$5 each and 200 units at 7 $$each. What is the weighted mean price per unit?

Accepted Answer

$$\frac{(100 	imes 5) + (200 	imes 7)}{100 + 200} = 6.33$$

Question 14

For grouped data, the sample mean is calculated as $$\bar{x} = \frac{\sum f_i M_i}{n}. $$What does $$M_i$$ represent?

Accepted Answer

The midpoint of the $$ith $$group/class

Question 15

If a value in a bell-shaped distribution has a z-score of 3.5, how should it be classified?

Accepted Answer

It is considered an outlier.

Question 16

Which of the following statements about the variance is TRUE?

Accepted Answer

The variance is measured in squared units of the variable.

Question 17

A student scored 80 on a test where the mean is 70 and the standard deviation is 5. What is the student's z-score?

Accepted Answer

$$z = \frac{80 - 70}{5} = 2$$

Question 18

Which of the following is a correct interpretation of a coefficient of variation (cv) of 12%?

Accepted Answer

The standard deviation is 12% of the mean.

Question 19

Which scenario best illustrates the use of the weighted mean?

Accepted Answer

Calculating the average grade in a class where assignments have different weights.

Question 20

If the correlation coefficient between two variables is close to zero, what does this indicate?

Accepted Answer

There is no linear relationship between the variables.

Summarising Data: Numerical Methods in Statistics

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