Round statistics calculated from quantitative data to one Rounding Rule for Quantitative Data: more decimal place to the right than is present in the original data. Notice the numbers in the data set ended in the tenths place (one place to the right of the decimal). This means that we should round our statistic to one more place value to the right. Therefore, we would round to two places to the right of the decimal (hundredths place). Mean Average Weight of the Bricks = 4.871428571 4.87 kilograms ≈ Remember; focus on interpreting the meaning of this statistic. What does a mean average of 4.87 kilograms tell us about the data? A mean average of 4.87 kg tells us that the balancing point for the distances for all the numbers in the data set is 4.87 kg. What does this tell us? Look at the numbers in the data set above the mean: 6.2, 5.1, and 7.4 Let us look at how far are each of numbers from the mean? Remember we rounded the mean, so these are just approximate distances. 6.2 4.87 1.33 – ≈ 5.1 4.87 0.23 – ≈ 7.4 4.87 2.53 – ≈ Therefore, for numbers in the data set above the mean, we have a total approximate distance from the mean of 1.33 + 0.23 + 2.53 4.09 ≈ Now look at the numbers in the data set below the mean: 2.9, 3.3, 4.5, and 4.7 Approximately how far are these numbers from the mean? If we subtract in the same order with the value minus the mean we will get negative differences. This issue of negative number differences is a reoccurring problem in statistics that is usually addressed by squaring the values 2.9 4.87 -1.97 – ≈ 3.3 4.87 -1.57 – ≈ 4.5 4.87 -0.37 – ≈
Rounding Rule for Quantitative Data: Round statistics calculated from quantitative data to one more decimal place to the right than is present in the original data. Notice the numbers in the data set ended in the tenths place (one place to the right of the decimal). This means that we should round our statistic to one more place value to the right. Therefore, we would round to two places to the right of the decimal (hundredths place). Mean Average Weight of the Bricks = 4.871428571 ≈ 4.87 kilograms Remember; focus on interpreting the meaning of this statistic. What does a mean average of 4.87 kilograms tell us about the data? A mean average of 4.87 kg tells us that the balancing point for the distances for all the numbers in the data set is 4.87 kg. What does this tell us? Look at the numbers in the data set above the mean: 6.2, 5.1, and 7.4 Let us look at how far are each of numbers from the mean? Remember we rounded the mean, so these are just approximate distances. 6.2 – 4.87 ≈ 1.33 5.1 – 4.87 ≈ 0.23 7.4 – 4.87 ≈ 2.53 Therefore, for numbers in the data set above the mean, we have a total approximate distance from the mean of 1.33 + 0.23 + 2.53 ≈ 4.09 Now look at the numbers in the data set below the mean: 2.9, 3.3, 4.5, and 4.7 Approximately how far are these numbers from the mean? If we subtract in the same order with the value minus the mean we will get negative differences. This issue of negative number differences is a reoccurring problem in statistics that is usually addressed by squaring the values 2.9 – 4.87 ≈ -1.97 3.3 – 4.87 ≈ -1.57 4.5 – 4.87 ≈ -0.37
Ch3_Intro_to_data_analysis_1st_ed_Oct_2017.docx