Measures of Central Tendency Section 14.2 Measures of Central Tendency

Objectives Determine measures of central tendency and spread.

Key Terms Median: the middle value in a list of numbers arranged in increasing order. 1st Quartile: the median of the lower half of the data, symbolized by Q1. 3rd Quartile: the median of the upper half of the data, symbolized by Q3. Five-number summary: minimum value, Q1, median, Q3, maximum value.

Key Terms Mode: the data item that occurs most frequently. Mean: the average of the data, symbolized by Χ. Measures of Central Tendency: numbers that will help us understand the center of a set of data. The four measures of central tendency are: mean, median, mode, and quartiles.

Computing the Mean If a data set contains n data values, the mean Χ of the data set is: Χ =

Computing the Mean of a Frequency Distribution. We use a frequency table to compute the mean of a data set as follows: Write all products x*f of the scores times the frequencies in a new column of the table. Represent the sum of the products you calculated in step 1 by Σ(x*f). Denote the sum of the frequencies by Σf. The mean is then .

Computing the Mean Arrange the data in increasing (or decreasing order), the median is the middle value in the list of numbers. However, there are two cases to consider. If there is an odd number of numbers, then the median is the number in the middle position. If there is an even number of numbers, then the median is the average of the two middle numbers.

Example 1: Find mean, median, and mode for the following distributions. TB pg. 801/1

Using the Graphing Calculator TI 83/84 Input data into STAT, EDIT, L1, STAT,  CALC, Press 1 (Var Stats) and ENTER.

Example 2: Find mean, median, and mode. TB pg. 801/7

Example 3: TB pg. 801/9

Example 4: TB pg. 802/15

Example 5: TB pg. 803/17

Example 6: TB pg. 803/19

Example 7: TB pg. 803/21

Example 8: TB pg. 803/23

Example 9: TB pg. 803/25

Example 10: TB pg. 803/27

Example 11: TB pg. 804/33

Example 12: TB pg. 804/35

Example 13: TB pg. 804/39

Example 14: TB pg. 805/41

Example 15: TB pg. 805/45

Section 14.2 Assignment Class work: TB pg. 801/2 – 28 Even, and 24 – 46 Even Remember you must show ALL work and attach problems to work. Assignment is due Wednesday, Dec. 14, 2011.