The document provides examples of statistical analysis techniques including finding the five-number summary, creating a histogram, and constructing a box-and-whisker plot for a dataset containing 12 numbers. It shows the step-by-step work for each, such as ordering the data and calculating ranges. The five-number summary includes the minimum of 12, first quartile of 45, median of 89, third quartile of 443, and maximum of 1066. The box-and-whisker plot marks these values on a number line.

1. Statistics Practice Problems

2. Five-Number Summary Find the five-number summary for this set of data 47, 56, 89, 43, 21, 90, 74, 1066, 109, 756, 947, 12, 130

3. Five-Number Summary (Cont.) Find the five-number summary for this set of data 47, 56, 89, 43, 21, 90, 74, 1066, 109, 756, 947, 12, 130 To solve, first put in order by value: 12, 21, 43, 47, 56, 74, 89, 90, 109, 130, 756, 947, 1066 Minimum: 12 First Quartile: 45 Median: 89 Third Quartile: 443 Maximum: 1066

4. Histogram Create a histogram for this set of data 47, 56, 89, 43, 21, 90, 74, 1066, 109, 756, 947, 12, 130

5. Histogram (Cont.) Create a histogram for this set of data 47, 56, 89, 43, 21, 90, 74, 1066, 109, 756, 947, 12, 130 To solve, first create a frequency table: For this problem, let’s use 8 bars in the histogram First, find the range of the data Maximum: 1066 – Minimum: 12 = Range: 1054 Then, divide by the desired number of bars Range: 1054 ÷ 8 = 131.75 (about 135) Finally, create the frequency table (see next slide)

6. Histogram (Cont. II) Create a histogram for this set of data 47, 56, 89, 43, 21, 90, 74, 1066, 109, 756, 947, 12, 130 Completed Frequency Table:

7. Histogram (Cont. III) Create a histogram for this set of data 47, 56, 89, 43, 21, 90, 74, 1066, 109, 756, 947, 12, 130 Next, create the histogram 10 9 8 7 6 5 4 3 2 1 1 0-135 136-271 272-407 680-815 544-679 816-951 952-1087 408-543

8. Box and Whisker Plot Create a box and whisker plot for this set of data 47, 56, 89, 43, 21, 90, 74, 1066, 109, 756, 947, 12, 130

9. Box and Whisker Plot (Cont.) Create a box and whisker plot for this set of data 47, 56, 89, 43, 21, 90, 74, 1066, 109, 756, 947, 12, 130 To solve, first find any outliers: First, find the inter-quartile range of the data Third Quartile: 443 – First Quartile: 45 = Inter-quartile Range: 398 Then, multiply by 1.5 Inter-quartile Range: 398 × 1.5 = 597 Next, add this number to the third quartile and subtract it from the first quartile Third Quartile: 443 + 597 = 1040 First Quartile: 45 – 597 = -552 Finally, find any outliers -552 ≤ (accepted numbers in set of data) ≤ 1040 < 1066

10. Box and Whisker Plot (Cont. II) Create a box and whisker plot for this set of data 47, 56, 89, 43, 21, 90, 74, 1066, 109, 756, 947, 12, 130 Create the plot Draw a number line Mark the median and quartiles Draw lines out to the minimum and maximum (excluding any outliers) 45 443 89 12 947 100 0 200 300 400 500 600 700 800 900 1000 1100