Question

Summarizing Data (#37-45) The weights (in lbs) of the offensive linemen for the Pittsburgh Steelers at the start of the 2019-2020 season are given below. 205 218 243 250 250 295 317 320 335 Use this dataset to compute the following summary statistics.

Range _________

Mean __________

Q1 _____________

Q3 _____________

IQR _____________

Median _____________

Upper Fence ___________

Lower Fence ______________

Sample Variance _________________

Answer 1

Solution:- Given that values = 205,218,243,250,250,295,317,320,335

Range = 150

Mean = 270.33

Q1 = 230.5

Q3 = 250

IQR = 318.5

Median = 250

upper Fence = 98.5

Lower fence = 450.5

sample Variance = 2252

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Explanation:-

1) The range is the difference between the highest and lowest values in the data set.

Ordering the data from least to greatest, we get:

205 218 243 250 250 295 317 320 335   

The lowest value is 205.

The highest value is 335.

The range = 335 - 205 = 130.

2) The mean of a data set is the sum of the terms divided by the total number of terms. Using math notation we have:

Mean = sum of terms/Number of terms

Mean = 2433/9

= 270.33
3)

The first quartile (or lower quartile or 25th percentile) is the median of the bottom half of the numbers. So, to find the first quartile, we need to place the numbers in value order and find the bottom half.

205 218 243 250 250 295 317 320 335   

So, the bottom half is

205 218 243 250   

The median of these numbers is 230.5.

4) The third quartile (or upper quartile or 75th percentile) is the median of the upper half of the numbers. So, to find the third quartile, we need to place the numbers in value order and find the upper half.

205 218 243 250 250 295 317 320 335   

So, the upper half is

295 317 320 335   

The median of these numbers is 318.5.

5) The interquartile range is the difference between the third and first quartiles.

The third quartile is 318.5.

The first quartile is 230.5.

The interquartile range = 318.5 - 230.5 = 88

6) The median is the middle number in a sorted list of numbers. So, to find the median, we need to place the numbers in value order and find the middle number.

Ordering the data from least to greatest, we get:

205 218 243 250 250 295 317 320 335   

So, the median is 250 .

7) Lower fence: 98.5

8) Upper fence: 450.5   

9) Variance