📝 Chapter 7: Statistics

Find the mean of: 12, 18, 22, 25, 30, 35.

Sample standard deviation of 4, 8, 12, 16, 20 (decimal to 4 places). The mean is 12.

A school surveys students by selecting 5 students from each grade (9, 10, 11, 12). This is:

A poll asks: "Don't you agree that the school cafeteria food is poor?" This question shows:

Find the median of: 14, 7, 9, 22, 11, 18, 5.

A box-and-whisker plot shows: min=10, Q1=20, median=30, Q3=40, max=70. The IQR is:

For Q6 data, the value 70 is:

A class has the following test scores: 65, 70, 72, 75, 78, 80, 82, 85, 90, 95.
a) Compute the mean and median.
b) Compute the standard deviation.
c) Compute Q1, Q3, IQR.
d) Identify any outliers using the 1.5 IQR rule.

A market research firm wants to estimate the proportion of Canadians who watch a particular streaming service. Discuss two appropriate sampling methods and one inappropriate one. For each, explain potential sources of bias.

A survey reports the mean salary of a company's employees is $90 000 and the median is $50 000. Explain what this tells you about the salary distribution. Sketch a possible histogram. Why might a press release favour one over the other depending on the message?

Construct a frequency table for the following test scores: 55, 62, 68, 71, 73, 75, 78, 80, 85, 88, 91, 94. Use class intervals 50–60, 60–70, 70–80, 80–90, 90–100. Estimate the mean from the grouped data.

A student claims, "The mean is always the best measure of central tendency." Is this correct? Use a small example involving an outlier to show when the median is more appropriate. Define "resistance" in your answer.

Explain in your own words what "standard deviation" means and why \( \sigma \) is preferred over the range as a measure of spread. Give an example with two small data sets that have the same range but different standard deviations.

Describe a step-by-step procedure for designing an unbiased survey. Cover at least: defining the population, selecting a sampling method, designing neutral questions, ensuring high response rate, and interpreting results responsibly.

Compare a histogram and a box-and-whisker plot. What information does each display? When is each more useful?

A car dealership wants to estimate average customer-satisfaction. They mail surveys to 1000 customers; 200 respond. The average rating is 4.5 / 5. Identify two sources of bias and explain how each could affect the result. Suggest improvements.

A teacher records the heights (in cm) of 8 students: 158, 162, 165, 168, 170, 172, 175, 180. a) Compute mean, median, and standard deviation. b) Estimate what percentage of students fall within 1 \( \sigma \) of the mean (assuming approximate normality).

A monthly survey of grocery prices uses a fixed basket of 50 items. The mean price last month was $4.20 with \( \sigma = \$0.80 \). This month the mean is $4.45. Has the average price increased meaningfully? Justify using a simple comparison (z-score-like reasoning).

A radio call-in poll on a sports talk-show found that 75% of callers thought the local team should fire its coach. The hosts reported this as evidence the coach should be fired. Critique this statement using your understanding of sampling bias. What conclusion is appropriate from this data?