Which of these best describes the meaning of x̄̄ and how its value is found?

An instructor reports two scores for a short quiz: $72$ and $78$. One is the mean and the other is the median. The score distribution is left-skewed because many students scored near the top. Which value is the mean? Choose the best answer.

Listed below are the heights (in inches) of a group of individuals. Find the mean and median for this set of data.

Do the results support or contradict the belief that the average height of the adults in the group is $66$ inches?

$65$, $68$, $66$, $70$, $64$, $69$, $67$, $72$

Which of the following data sets has no mode?

The daily high temperatures (in ${}^{\circ }\text{C}$) for a week in a city are:

$22$, $24$, $21$, $23$, $25$, $24$, $22$.

Find the mean, median, and mode of the temperatures. Which measure best represents a typical day's high temperature? Justify your answer.

Use the data below to calculate the mean, median, and mode of daily screen time. Then, determine whether each measure appropriately represents the central tendency of the data. If any measure is not applicable or does not accurately reflect the data's center, explain why.

Daily screen time (in hours) recorded for a sample of $14$ high school students:

$4.5$, $5$, $6$, $5.5$, $6$, $5$, $7$, $6.5$, $4$, $5.5$, $6$, $5$, $7.5$, $6$

Which term describes the standardized value that shows the distance of a score from the mean in units of standard deviation?

Use the following list of the battery life durations (in hours) for 25 different laptops to find the 60^th percentile.

| 2.1 | 2.3 | 2.5 | 2.7 | 3.0 |

| 3.2 | 3.4 | 3.6 | 3.8 | 4.0 |

| 4.2 | 4.5 | 4.7 | 4.9 | 5.1 |

| 5.3 | 5.5 | 5.7 | 5.9 | 6.2 |

| 6.4 | 6.6 | 6.8 | 7.0 | 7.5 |

A scientist measures the blood pressure of $50$ randomly selected adults from a city to estimate the overall city's blood pressure statistics. Which standard deviation notation is appropriate for this scenario?

Why is it incorrect to use (Sigma x)^2 instead of Sigma x squared in the numerator of the standard deviation formula?

The number of hours of sunlight received by different regions of a city during the summer months is provided below:

$6,8,5,7,9,9,10,7,6,8,10,7$

Find the variance.

Use the given list of the battery life durations (in hours) for 25 different laptops to find the value of the quartile indicated below.

| 2.1 | 2.3 | 2.5 | 2.7 | 3.0 |

| 3.2 | 3.4 | 3.6 | 3.8 | 4.0 |

| 4.2 | 4.5 | 4.7 | 4.9 | 5.1 |

| 5.3 | 5.5 | 5.7 | 5.9 | 6.2 |

| 6.4 | 6.6 | 6.8 | 7.0 | 7.5 |

Q1

Using the class midpoints and corresponding frequencies, estimate the sample mean and standard deviation of the provided data.

In a sample of monthly electric bills, the mean is $\mathrm{\backslash (}95$ and the standard deviation is $\mathrm{\backslash )}12$. The bills follow a bell-shaped distribution. Is a bill of $\$125$ unusual? Provide your reasoning.

The goals scored by the $50$ winning teams in a football tournament final are represented in the ogive below. What score represents the $60$^th percentile? What interpretation could be drawn from this?

Before entering a new dataset, which steps should you take to clear the existing data in L1 on a TI-84 calculator?

Find the five-number summary for the following data set: $12$, $15$, $11$, $14$, $13$, $17$, $16$, $12$, $18$, $15$, $14$, $13$, $19$, $16$, $15$, $17$, $13$, $12$, $18$, $14$

A climatologist measures daily rainfall amounts (mm) for $11$ days: $0.5,0.8,1.0,1.2,1.3,1.5,1.6,1.8,2.0,2.1,2.4$. Use the boxplot/ quartile method to evaluate whether the distribution of these rainfall amounts is symmetric. Which conclusion is correct?