Lesson on statistical analysis-Blog 4

Hello, Class! My name is Professor Bolz and today I will be teaching you about some terms involving statistical analysis. In an attempt to make my lesson as clear and effective as possible, I will go over terms and examples to further explain the terms.

Mean: the mean is also known as the average. To find the mean of data, we add up all of the data and then divide by how much data there is.

 For example, if Mary got a 90, 83, 47, 77, and 94 on her math exams, what would her mean score be?

90+83+47+77+94=391

Together there are 5 exam scores so we divide 391 by 5. 391÷5=78.2

Her mean score is a 78.2

Mode: the mode is the most commonly seen data. There can be more than one mode, but they have to be equally common.

For example, if Rupert got a 98, 67, 45, 98, and 77 on his exams, the mode would be 98 because it is the most commonly seen data. If Rubert got a 98, 98, 67, 67, and 45, the mode would be 98 and 67 because they are equally common.

IF Rupert got a 98, 98, 98, 67, and 67, the mode would be 98 because although there are 2 67's there are 3 98's which means it is the most common.

Median: The median is the middle number of the data. To find the median we list the data in ascending order and cross off the smallest number, then the largest, then the second smallest, then second largest, until you're left with 1 or 2 numbers. If there is an even amount of data then there will be 2 numbers left over. To find the median from these 2 numbers, you add them together and divide by two. If there is only 1 number, that is the median. The median is also known as Q2.

For example, if we have the data 56, 75, 89, 92, 98 (already in ascending order) We know 89 is the median because it is the middle number.

If we have the data 34, 56, 73, 88 the median is 56+73÷2

Range: range is the difference between the highest and lowest number.

For example, if we have data that is 67, 54, 88, 92 the range would be 92-54 which equals 38.

Upper Quartile: The Upper Quartile aka Q3 is the median of the second half of the data, excluding the median of the whole data.

For example, if we have the data 56, 75, 89, 92, 98, the median is 89. If we exclude 89, the upper half of the data consists of 92 and 98, so we add 92+98=190 and divide that by 2...190÷2=95. So the upper quartile is 95 because it is the average of the two data points.

Lower Interquartile: aka Q1 is the median of the first half of the data, excluding the median of the whole data.

For example, if we have the data 56, 75, 89, 92, 98, as said before the median is 89. Q3 is 95. That means we are left with 56 and 75...so we add 56+75=131 and divided by 2 is 65.5. So, Q1 is 65.5.


Interquartile Range: this is the difference of the upper and lower quartiles. if the upper quartile is 45 and the lower is 38. 45-38=7. 7 is the IQR.

Outliers: a data point that 1.5 times bigger than the IQR either subtracted from the lower quartile or added to the upper quartile.

For example, with the data used above (56, 75, 89, 92, 98) if Q1 is 65.5, and Q3 is 95, our IQR is 29.5. 29.5 x 1.5=44.25

Q1(65.5)-44.25=21.25
Q3(95)+44.25=139.25

Since none of the data above is smaller than 21.25 or bigger than 139.25, there are no outliers!

Thanks for paying attention so well today, class! Tomorrow we will cover graphing statistical analysis, standard deviation, variance, and the difference between quantitative/qualitative data.

Cheers,

Professor Bolz