Question

1. spreads in the news find an article in a newspaper, a magazine, or the internet that discusses a measure of spread.

a) does the article discuss the w’s for the data?
b) what are the units of the variable?
c) does the article use the range, iqr, or standard deviation?
d) is the choice of measure of spread appropriate for the situation? explain.

1. thinking about shape would you expect distributions of these variables to be uniform, unimodal, or bimodal? symmetric or skewed? explain why.

a) the number of speeding tickets each student in the senior class of a college has ever had.
b) players’ scores (number of strokes) at the u.s. open golf tournament in a given year.
c) weights of female babies born in a particular hospital over the course of a year.
d) the length of the average hair on the heads of students in a large class.

1. more shapes would you expect distributions of these variables to be uniform, unimodal, or bimodal? symmetric or skewed? explain why.

a) ages of people at a little league game.
b) number of siblings of people in your class.
c) pulse rates of college-age males.
d) number of times each face of a die shows in 100 tosses.
t 7. cereals the histogram shows the carbohydrate content of 77 breakfast cereals (in grams)
histogram image
t 9. vineyards the histogr... 36 vineyards in the fin...
histogram image
a) approximately what perce... 60 acres?
b) write a brief description of... spread, unusual features?
t 10. run times one of the authors... it took him to run 4 miles on var... period. here is a histogram of the...
histogram image

Explanation:

To solve these problems, we analyze each part based on the concepts of data distribution (uniform, unimodal, bimodal, symmetric, skewed) and measures of spread (range, IQR, standard deviation). Here are the key steps for a few sub - questions:

Question 5a: Number of speeding tickets per senior student

Step 1: Analyze the distribution type

Most students will have 0 speeding tickets (a common value), and a few will have 1, 2, etc. So, the distribution will be unimodal (peaked at 0) and right - skewed (since there are a few students with a relatively large number of tickets, pulling the tail to the right).

Step 2: Justify the skewness

The majority of students have 0 tickets, so the peak is at 0. The presence of some students with 1, 2, or more tickets creates a long tail on the right - hand side of the distribution.

Question 5b: Golf scores at the U.S. Open

Step 1: Analyze the distribution type

Most golfers will have scores around a typical value (e.g., par - related scores), so the distribution is unimodal. It is likely to be symmetric or slightly left - skewed.

Step 2: Justify the symmetry/skewness

Golf scores are centered around a mean or median score. While there may be a few very low scores (good players) and a few very high scores (bad players), in general, the distribution of scores for a large tournament like the U.S. Open is relatively symmetric around the average score.

Question 5c: Weights of female babies

Step 1: Analyze the distribution type

The weights of female babies follow a normal - like (unimodal and symmetric) distribution. This is because most babies will have weights around the average birth weight, with equal numbers of babies above and below the average (in a symmetric manner).

Step 2: Justify the symmetry

Birth weights of babies are influenced by natural biological processes that lead to a central tendency (average weight) and a symmetric spread around this average. Most babies are born within a relatively narrow range around the mean weight, and the number of babies with weights above the mean is roughly equal to the number with weights below the mean.

Question 5d: Length of average hair on students' heads

Step 1: Analyze the distribution type

The distribution will be bimodal (peaked at typical lengths for males and females) and skewed (depending on the gender distribution and hair length norms). For example, females may have longer hair on average, and males shorter, creating two peaks.

Step 2: Justify the bimodality

There are two distinct groups (males and females) in a class, and each group has a typical hair length. Males tend to have shorter hair, and females tend to have longer hair (on average), so there are two peaks in the distribution of hair lengths.

Question 4 (General for measures of spread)

Step 1: Find an article

Look for an article (e.g., a news report on income distribution, test scores, or product prices).

Step 2: Analyze the W’s

Check if the article mentions the Who (population), What (variable), When (time), Where (location), Why (purpose), and How (data collection method) for the data.

Step 3: Identify units

Determine the units of the variable (e.g., dollars for income, points for test scores).

Step 4: Identify the measure of spread

See if the article uses range (difference between max and min), IQR (inter - quartile range, difference between Q3 and Q1), or standard deviation (average deviation from the mean).

Step 5: Evaluate appropriateness

If the data is skewed, IQR is appropriate. If the data is symmetric, standard deviatio…

Step 1: Distribution Type

Most students have 0 tickets (peak at 0), so unimodal.

Step 2: Skewness

Few students have 1+, so right - skewed.

Step 1: Distribution Type

Most babies have weights around the average, so unimodal.

Step 2: Symmetry

Equal numbers above/below average, so symmetric.

Step 1: Distribution Type

Each die face has equal probability, so uniform.

Step 2: Justification

100 tosses: each face ~17 times, so uniform.

Answer:

Unimodal, right - skewed. Most have 0 tickets, few have more, creating a right tail.

For question 5c: