Data handling - calculating means and standard deviations

• The mean () is calculated using the equation below:

 =

• The standard deviation () is calculated* using the equation below:

= 85.43658304

2. The table blow shows the height of 60 students after dividing each height by 5:

 

• The mean () is calculated using the equation below:

 =

• The standard deviation () is calculated* using the equation below:

= 3.417463322

The table below shows the same data set used in this question using a = - 3, where each value is multiplied by a;

• The mean () is calculated using the equation below:

 =

• The standard deviation () is calculated using the equation below:

= 51.26194983

Question 4

The table below shows the grouped intervals and the cumulative frequency table of the heights.

Table 7

Table 8

Question 5

1. The following table shows a comparison between the original data set and the modified one (5 is added to each value).

Table 9

2. The following table shows a comparison between the original data set and the modified one (12 is subtracted from each value).

Table 10

Question 6

3. The following table shows a comparison between the original data set and the modified one (each value is multiplied by 5).

Table 11

4. The following table shows a comparison between the original data set and the modified one (each value is divided by 5).

Table 12

Table 13

Question 7

The tables below summarize the results obtained and calculated.

Table 14

Table 15

Based on these tables, it can be concluded that the mean and the median change exactly as the data set values change.

Furthermore, the standard deviation and the interquartile range remain unchanged in addition and subtraction but change in the same way when the data set values are multiplied or divided.

This is because the standard deviation is a measure of how widely values are dispersed from the average value (the mean). When all the values are changed equally the mean changes and the dispersion from the mean stays constant.

As for the interquartile range, the 1st and the 3rd quartile are changed equally so that the interquartile range remains constant.

Question 8

(a) The table below shows the new data set which has a mean = 0

• The mean () is calculated using the equation below:

• =

(b) The table below shows the new data set which has a standard deviation=1

• The standard deviation () is calculated using the equation below:

= 1

(c) The table below shows the new data set which has a standard deviation=1

• The mean () is calculated using the equation below:

• =

• The standard deviation () is calculated using the equation below:

= 1

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