Chapter 4 - Exploring Data Section 1 - Describing Distribution with Numbers

Measuring Center Mean Median Mode

Mean

Swiss Hysterectomies Fifteen Swiss doctors were surveyed. Here are the number of hysterectomies performed by each one in a year

Swiss Hysterectomies Make a stemplot of the previous numbers. Find the mean of the data. What do you think would happen to the mean if 85 and 86 were removed? This is because the mean is non-resistant.

Median To find the median of a distribution: 1Arrange the observations from smallest to largest. 2If the number of observations is odd, the median M is the center observation. 3If the number of observations is even, the median M is the mean of the two center observations.

Swiss Hysterectomies Find the median: Ordered: Center observation:

Swiss Hysterectomies The study also surveyed 10 female doctors and found these numbers: Here the number n is even. So, take the mean of the two middle numbers, 18 and 19. The median then is 18.5.

Foreign Languages “Forget French and Spanish. As China’s economy grows, so does our need to master the Chinese language. Talk about playing catch-up: 24,000 American kids are learning Mandarin today; 240 million Chinese kids are learning English.” - From Reader’s Digest, August 2005

Find the mean and median... {20,30,40,50,60,70} {20,43,44,46,47,70} {40,43,44,46,47,50} Now, find the spread of each set.

5 Number Summary The 5 number summary also measures spread. Min, Q1, Median, Q3, Max Q1 is the median of the lower half of the data. Q3 is the median of the upper half of the data. Do not include the Median when you find Q1 and Q3

IQR The innerquartile range measures the distance between Q1 and Q3. IQR = Q3 - Q1 A point can be defined as an outlier if it falls more than 1.5 * IQR above Q3 or below Q1.

Boxplots The five number summary leads nicely to boxplots. You may see modified boxplots or side-by- side boxplots. Sometimes boxplots are graphed “up and down.”

Boxplots A boxplot is made either horizontally or vertically. The main box has its ends at the quartiles and a center line at the median. It has “whiskers” that extend to the smallest and largest observations. Remember to include a scale. Because there is less detail on a boxplot than a stemplot, dotplot or histogram, they are generally used for side-by-side display of data. Note how some displays are right or left skewed.

Age of Stat Students

Modified Boxplot