Problem Set – A4 One Variable Statistics

Work on another sheet of paper.

DOT PLOTS & HISTOGRAMS

1.)
The histogram shows the birth weights of 100 new born babies. Describe the shape, center, and spread of the data.

2.) A group of scientists made the following measurements to see how many of a certain type of bats were present in a given location within 20 minutes of their flight from their cave. They recorded the following data set:

{98, 103, 104, 103, 101, 98, 99, 104, 100, 104, 98, 103, 105, 103, 102, 104, 104, 103, 99, 100}

Choose the best representation for this data set. What number would best describe the “typical” amount of bats at that location at that time of night? Explain your choice.

3.) Thirteen friends discussed the amount of homework they had each week. The data set generated from their responses is below.

1, 3, 4, 4, 6, 6, 9, 9, 10, 11, 12, 14, 17

Decide whether you should make a dot plot or histogram and create it. Give the center, spread, shape, and list any outliers for this data set.

BOX PLOTS

4.) Find the median, upper quartile, lower quartile, and interquartile range for the given set of temperatures.

5.) Construct a box–and–whisker plot for the given data.

56, 32, 54, 34, 23, 67, 23, 45, 12, 32, 34, 24, 36, 47, 19, 43

6.) The box–and–whisker plot shows the GPA of a class. Label the five number summary. Is the number of students with GPA between 1.5 and 3.0 more or less than the number with GPA between 3.0 and 3.5? Explain how you know.


MEAN AND STANDARD DEVIATION

7. The weather was tracked for one week. The temperature was as follows.

What is the standard deviation?

24, 26, 21, 20, 25, 26, 27

8. The weight of patients is recorded in the hospital. The weights are listed

below. What is the standard deviation of the weight?

56 kgs, 64 kgs, 78 kgs, 66 Kgs, 70kgs, 65 kgs, 89 kgs

9.) A college only accepts top 10% of students. The average score is 1148.2 and the standard deviation is 121.6. What is the lowest score you can make and still get accepted?

A/B Practice Problems

1.) A batch of Brightwiselight bulbs is tested to see how close they come to the manufacturer's specification that their resistance is 47 ohms. Data is tabulated in bins of 0.2 ohm as follows:

Resistance (ohms) / Frequency
46.0-46.2 / 3
46.2-46.4 / 5
46.4-46.6 / 6
46.6-46.8 / 9
46.8-47.0 / 5
47.0-47.2 / 6
47.2-47.4 / 5
47.4-47.6 / 2
47.6-47.8 / 3
47.8-48.0 / 1

Make a histogram of this data. From your plot, estimate the median resistance. What can you say about the accuracy and the precision of the manufacturer's claim that all of their light bulbs have a resistance of 47 ohms?

You compare 10 of Brightwise bulbs to 10 Brilliant bulbs. The resistance that you measured for each bulb is below:

Brightwise: 37, 38, 40, 40, 42, 43, 67

Brilliant: 35, 40, 40, 47, 51, 52, 57

Find the standard deviation for each company. What does that say about which company has a more consistent product? Explain your answer.

2.) The data represents the number of dolphin sightings reported on both the south and north side of an island. Using the data, sketch the parallel boxplots. Then, write a paragraph comparing the two distributions. What is the best place to go to see dolphins? Explain your reasoning.

Min / Q1 / Med / Q3 / Max
North Side / 11 / 14 / 19 / 21 / 22
South Side / 13 / 15 / 17 / 19 / 21