6.5 Measures of central tendency Discrete and continuous data

Simple Discrete Data Mode: most frequent Median: middle value Mean: sum of all values divided by the number of values Consider the numbers: 8 8 3 2 6 5 1 6 8 Find the mode, median and mean Use GDC as well

Sigma Notation 𝚺 Means “sum of” 𝒓=𝟏 𝒏 𝒓 means “the sum of all values of r from r = 1 up to r = n” 𝒓=𝟏 𝒏 𝒓 = 1 +2 +3+ . . . + n Calculate: 𝒓=𝟏 𝟒 𝒓 𝟐

Discrete Data in a Frequency Table Mode is the value with the highest frequency Median is the middle value Mean is found by multiplying each value by its corresponding frequency, summing the products and dividing by the sum of the frequencies. Find the mode, median and mean for the table. X Frequency X*frequency 1 4 2 9 3 23 25 5 16 6 Total 80

Grouped Discrete or Continuous Data Modal group/class with largest frequency Median estimate middle value Estimated value To find the mean Use midpoints multiplied by frequency Add and divide by cumulative frequency To find the median Steps Identify which group it’s in Decide which entry in that group is the median, a Find the total frequency of that group, b Find the width of that group, c Then use the formula: median = lower limit of group + (a ÷b) x c

Find the mode, median and estimated mean. GDC does NOT give the correct median for grouped data because we use mid-interval numbers **Must enter each value in group to be accurate. Time Midpoint Frequency x*f 0≤𝑡<50 20 50≤𝑡<60 61 60≤𝑡<70 83 70≤𝑡<80 90 80≤𝑡<90 106 90≤𝑡<100 62 100≤𝑡<110 49 110≤𝑡<120 29 Total 500

Assignment P.304 #1-7