Question

Data set 1: 0, 25, 50, 75, 100

Data set 2: 30, 40, 50, 60, 70
Data set 3: 40, 45, 50, 55, 60
Note that all three data sets have a median of 50. Notice how spread out the points are in each data set and compare this to the standard deviations for the data sets. Describe the relationship you see between the amount of spread and the size of the standard deviation and explain why this connection exists.

Answer 1

am going to assume you know how to calculate standard deviation, as it is long and tedious to type up. If you really don't understand how to calculate them, I will explain it. The standard deviation is larger in data set 1 than 2, because the spread is larger. The larger the spread, the larger the deviation of the numbers in the set are from the mean (average) number. The standard deviation in 1 is greatest. 2 is in the middle, and 3 is the lowest standard deviation. Hope this helps, good luck.

Answer 2

Larger the standard deviation larger the spread present in data.

Explanation:

Standard Deviation is the square root of sum of square of the distance of observation from the mean.

`Standard deviation(\sigma) = \sqrt{(1)/(n)\sum_(i=1)^(n){(x_(i)-\bar{x})^(2)}}`

where,
`\bar{x}` is mean of the distribution.

It is used to measure dispersion (spread) of the data. Larger the standard deviation larger the dispersion (spread) present in data.

The Standard deviation of 1st data set is 39.53

The Standard deviation of 2nd data set is 15.81

The Standard deviation of 3rd data set is 7.91

Hence,

(Spread of 1st data set) > (Spread of 2nd data set) > (Spread of 3rd data set)