Mean, Median, Mode and Range

Did You Know… That you probably use Statistics such as Mean, Median, Mode and Range almost every day without even realizing it?!?

Today We Will Learn about… Mean Median Mode Range Quartiles and Interquartile Range

What Do We Already Know? Sure, the words “Mean, Median, Mode and Range” all sound confusing… But what about the words we already know, like Average, Middle, Most Frequent, and Difference? They are all the same ideas!

Mean The mean is the Average of a group of numbers It is helpful to know the mean because then you can see which numbers are above and below it It is very easy to find!

Mean Example Here is an example test scores for Ms. Math’s class. 82 93 86 97 82 To find the Mean, first you must add up all of the numbers. 82+93+86+97+82= 433 Now, since there are 5 test scores, we will next divide the sum by 5. 440÷5= 88 The Mean is 88!

Try For Yourself Q1 Pg 210

Objective Check Mean Median Mode Range Quartiles and Interquartile Range

Median The Median is the middle value on the list. The first step is always to put the numbers in order.

Median Example Odd First, let’s examine these five test scores. 78 93 86 97 79 We need to put them in order. 78 79 86 93 97 The number in the middle is 86 78 79 86 93 97 In this case, the Median is 86!

Median Example Even Here the Median is 87 Now, let’s try it with an even number of test scores. 92 86 94 83 72 88 First, we will put them in order 72 83 86 88 92 94 This time, there are two numbers in the middle, 86 and 88 72 83 86 88 92 94 Now we will need to find the Average of these two numbers, by adding them and dividing by two. 86+88= 174 174÷2= 87 Here the Median is 87

Try For Yourself! Q 5 Page 210

Objective Check Mean Median Mode Range Quartiles and Interquartile Range

Mode The Mode refers to the number that occurs the most frequently. It’s easy to remember… the first two numbers are the same! MOde and MOst Frequently!

Mode Example Here is an list of temperatures for one week. Mon. Tues. Wed. Thurs. Fri. Sat. Sun. 77° 79° 83° 77° 83° 77° 82° Again, We will put them in order. 77° 77° 77° 79° 82° 83° 83° 77° is the most frequent number, so the mode= 77°

Try For Yourself Q2 Pg210

Objective Check Mean Median Mode Range Quartiles and Interquartile Range

Range The range is the difference between the highest and the lowest numbers of the series. All we have to do is put the numbers in order and subtract!

Range Example Let’s look at the temperatures again. 77° 77° 77° 79° 82° 83° 83° The highest number is 83, and the lowest is 77. All you need to do is subtract! 83-77= 6 In this case, the Range is 6

Try Yourself Q1 Pg 215

Objective Check Mean Median Mode Range Quartiles and Interquartile Range

Quartiles and Interquartile Range When data is arranged in order of size we have learnt that the median is the value half- way into the data We can also divide the median, to give us quaerters Measures of Variation Lower quartile is the median of the lower half of the data. For Example: The 11 Workers at a company have the following ages: 27, 39, 40, 22, 19, 25, 41, 58, 53, 49, 51 Order data from least to greatest: 19, 22, 25, 27, 39, 40, 41, 49, 51, 53, 58 Upper quartile is the median of the upper half of the data. Lower Quartile Median Upper Quartile

Example Find the quartiles for the data set below. 7, 9, 10, 11, 11, 12, 12, 13, 14, 16, 16 Lower Quartile Median Upper Quartile More Measures of Variation Range is the difference between the greatest and least values in a data set. Range 16 – 7 = 9 Interquartile Range is the range in the middle of the data. It is the difference between the upper and lower quartiles in a data set. Interquartile Range 14 – 10 = 4

Example 2 In his 21 major league seasons, Cal Ripken hit the following number of home runs: 0, 28, 27, 27, 26, 25, 27, 23, 21, 21, 34, 14, 24, 13, 17, 26, 17, 14, 18, 15, 14 Find the range and interquartile range. Order data from least to greatest. 0, 13, 14, 14, 14, 15, 17, 17, 18, 21, 21, 23, 24, 25, 26, 26, 27, 27, 27, 28, 34 26.5 14.5 Lower Quartile Median Upper Quartile Range 34 – 0 = 34 Interquartile Range 26.5 – 14.5 = 12.0

Try for Yourself Q 4 Pg 215

Objective Check Mean Median Mode Range Quartiles and Interquartile Range

Homework Q 4 pg 210 Q2 pg 215